Abstract

We theoretically and numerically study the influence of both instantaneous and Raman-delayed Kerr nonlinearities as well as a long-wavelength pump in the terahertz (THz) emissions produced by two-color femtosecond filaments in air. Although the Raman-delayed nonlinearity induced by air molecules weakens THz generation, four-wave mixing is found to impact the THz spectra accumulated upon propagation via self-, cross-phase modulations and self-steepening. Besides, using the local current theory, we show that the scaling of laser-to-THz conversion efficiency with the fundamental laser wavelength strongly depends on the relative phase between the two colors, the pulse duration and shape, rendering a universal scaling law impossible. Scaling laws in powers of the pump wavelength may only provide a rough estimate of the increase in the THz yield. We confront these results with comprehensive numerical simulations of strongly focused pulses and of filaments propagating over meter-range distances.

© 2017 Optical Society of America

1. Introduction

Laser filaments produced by ultrashort light pulses proceed from the dynamic balance between Kerr self-focusing and plasma generation [1, 2]. The interplay of these nonlinear effects contributes to broaden the pulse spectrum, promote self-compression [3] and self-guide intense optical wave packets over remote distances for, e.g., sensing applications [4]. Filamentation of pulses with different frequencies has been proposed as an innovative way to downconvert optical radiation into the THz range [5] and create broadband THz sources remotely [6]. In this context, THz generation can proceed from the excitation of plasma currents via longitudinal ponderomotive motions of free electrons [7]. This mechanism is known as “transition-Cherenkov” radiation and leads to forward off-axis conical emission [8]. In addition, photoionization is also able to produce THz radiation through transverse photocurrents that instead emit closer to axis [9,10]. This “photocurrent” mechanism relies on pump fields exhibiting temporal asymmetry, through which the photo-induced transverse current features a net, non-zero low-frequency component cumulated over the stepwise increase of the electron plasma density through tunneling ionization [11–14]. For single-color pulses, the photocurrent mechanism may only prevail for few-cycle laser pulses [15,16]. In contrast, for two-color pulses (e.g., a fundamental and its second harmonic), this process is now accepted as a major player to THz emission, and it promotes THz bandwidths as broad as 100 THz. However, because THz radiation is also emitted by optical rectification through four-wave mixing [17], Kerr self-focusing can contribute to the overall THz yield [18]. Kerr-driven THz sources are expected to emit on-axis, mostly during the early self-focusing stage preceding ionization of air molecules [13], and their characteristic spectrum exhibits a parabolic distribution being maximum at non-zero frequency [17]. At clamping intensities > 50 TW/cm2 from which Kerr self-focusing is stopped by plasma defocusing, THz emission is dominated by photocurrents and the pulse spectrum peaks at smaller THz frequencies [19].

Several important issues still need to be addressed in this physics, such as the role of the Raman-delayed part of the Kerr nonlinearity, which arises due to the excitation of rotational and vibrational transitions of the molecular constituents of air [20]. Another point is the impact of longer pump wavelengths (λ), in particular in the near-infrared domain ∼ 1.6 μm that may be preferred for, e.g., ocular safety reasons. Antecedent studies [19, 21] reported impressive growths of THz energy yields scaling as λα with α ≃ 4 – 5. More recent ones [15,22], however, showed that, although single-color laser pulses produce THz energy yields increasing like λ4, no similar conclusion could be inferred for two-color pulses.

The present paper aims at clarifying the role of the pump wavelength and of the Kerr nonlinearities (instantaneous and delayed) in filament-driven THz pulse generation. We display numerical evidence that four-wave mixing impacts the THz generation process over long propagation distances, even in intensity regimes where the photocurrent mechanism is the dominating THz emitter. We also demonstrate that the Raman-delayed Kerr nonlinearity does not contribute as a THz source. By means of the local current (LC) model [23], we moreover explain the variations in the THz field strength with respect to the fundamental wavelength of the optical radiation. In this respect we emphasize the role of the electron current component associated with the high-frequency laser pulse, whose fundamental at longer wavelength affects more significantly the THz spectrum. Importantly, the scaling of the THz field strength with the fundamental pump wavelength is shown to vary with the relative phase between the fundamental and second harmonic, the pulse envelope and duration, so that no universal λ-dependent scaling is achievable with a two-color pulse. Despite this, the conversion efficiencies reported from the LC model show that the THz yield is roughly scaling as λα with α > 4 for small relative phases between the two colors and α > 2 on the average. For focused pulses [21], these results are confirmed by direct simulations employing a unidirectional pulse propagator [24,25]. Smaller gain factors are achieved by meter-range two-color filaments due to the generation of weaker plasma densities.

The paper is organized as follows: Section 2 proposes a one-dimensional (1D) approach combining known laser-driven THz sources. It recalls that, in the range of intensities reached by two-color filaments in air, photoionization and to a lesser extent the Kerr nonlinearity are the principal players in THz generation. Section 3 discusses analytical estimates of the laser-to-THz conversion efficiency when considering a Raman-delayed nonlinearity and when increasing the fundamental laser wavelength. Section 4 verifies our analytical statements through three-dimensional (3D) comprehensive numerical simulations for both focused and filamentary pulses.

2. Transverse versus longitudinal THz fields - A 1D Approach

Before proceeding with full 3D simulations, we find it instructive to examine the dynamics of THz fields produced in-situ, i.e., inside the plasma channel created by two-color filaments in air. For simplicity, we use a reduced model discriminating THz transverse (x) from longitudinal (z) currents for a laser pulse polarized along the x-axis. Since we focus on interaction regimes driven by femtosecond optical pulses with moderately high intensities < 1015 W/cm2, we can discard ion motions, so that the current density reduces to J⃗ ≃ −eNev⃗e, where Ne and v⃗e are the free electron density and velocity. Following Sprangle et al. [26], the electron current obeys the following equation set in the non-relativistic interaction regime:

(t+νc)J=e2meNeE+Π,
Π=emeJ×B+(J)(JeNe)+JeNe(J),
where νc is the electron collision rate equal to 10 ps−1, B⃗ is the magnetic field associated with the electric field E⃗ that includes both the laser field ELe⃗x and secondary (THz) fields such as E˜=E˜xex+E˜zez. Assuming singly-ionized gases for I0 ≤ 1015 W/cm2, the growth of electron density is governed over femtosecond time scales by
tNe=W(E)(NaNe),
where Na is the initial gas density and W(E) is a field-dependent ionization rate, for instance the quasi-static tunnel (QST) rate [27]
W[E(t)]=4(Ui/UH)52νa|E(t)/Ea|exp(2(Ui/UH)323|E(t)/Ea|),
with Ui being the ionization energy of the gas, νa = 4.13 × 1016 Hz, Ea = 5.14 × 1011 V/m and UH = 13.6 eV is the ionization potential of hydrogen. For air composed of 80% of N2 and 20% of O2, we shall start by considering ionization of oxygen molecules only, as their ionization potential (12.1 eV) is lower than that of nitrogen (15.6 eV). Photoionization of nitrogen molecules will be addressed later when considering, e.g., a field-dependent version of the cycle-averaged ionization rate derived by Perelomov, Popov and Terent’ev (PPT) [28].

Equations (1) and (2), combined with Maxwell-Ampère equation ∇⃗ × B⃗ = c−2tE⃗ + μ0J⃗, readily provide the propagation equation for E⃗:

(t2+c2××+ωpe2)E+νc(tE+c2t××E(t)dt)=Πε0,
where ωpe=e2Ne/ε0me is the electron plasma frequency (ε0 = 1/μ0c2). We here neglect loss currents due to photoionization, which are small for our pump pulse configurations and in gas-based plasmas.

For technical convenience, Eq. (5) is reduced to a one-dimensional, z-propagating model. Discarding temporarily the linear (chromatic) and nonlinear polarizations of air molecules, we omit the diffraction operators (x = y = 0), yielding

νc(t2c2z2)Ex(t)dt+(t2c2z2+ωpe2)Ex=Πxε0,
(t2+νct+ωpe2)E˜z=Πzε0.

As recently derived in [29], further approximations can be applied such as assuming a laser field propagating with the sole variable (zct). For the intensity range < 1015 W/cm−2, we can furthermore neglect the longitudinal current component compared to its transverse counterpart that obeys (t + νc)Jx = e2NeEx/me and use By=ztEx(t)dtEx/c for By travelling like the laser pulse. By splitting Jx = JL + x on the expansion Ex = EL + x, Eq. (6) reads as

[t2c2z2+t(t+νc)1ωpe2]E˜x=1ε0tJL.
The equation for the longitudinal field z is easily expressed as
(t2+νct+ωpe2)E˜z=emeε0cJLEL.
Equations (8) and (9) both involve the current density computed on the laser field, JL=ε0(t+νc)1ωpe2EL. The transverse field x mainly proceeds from this current density [15, 23]. With two colors, the product in t JL [Eq. (8)] between the steplike increase of Ne(t) and the fast oscillations of EL (t) acts as an efficient converter to low frequencies. By comparison, Eq. (9) describes longitudinal plasma oscillations that develop over longer time scales after the laser field has interacted with the gas, as previously established in [7,26].

Including the optical polarization of a noble gas is straightforward by replacing into the Maxwell-Ampère equation the electric field E⃗ by the displacement vector D⃗ = 0E⃗ + P⃗L + P⃗NL, where P⃗L and P⃗NL refer to linear and nonlinear polarization, respectively. In scalar description, this amounts to adding into the right-hand side of Eq. (6) the term ε01t2(PL+PNL). The Fourier transform of PL involves the first-order frequency-dependent susceptibility χ(1)(ω) entering the optical linear index n(ω) = [1 + χ(1)(ω)]1/2. PNL involves the third-order susceptibility χ(3) responsible for four-wave mixing and Kerr self-focusing (in multidimensional media). For molecular gases, the Kerr response admits a fraction xk (0 ≤ xk ≤ 1) of delayed contribution due to Raman scattering by rotational molecular transitions. Assuming that the laser is not resonant with the transition frequencies [20], stimulated Raman scattering usually affects the total time-dependent refraction index of the medium. Its corresponding polarization component describes a delayed-Kerr nonlinearity. Written with the real electric field Ex [2], the overall nonlinear polarization can be expressed as

PNL(t)=(1xk)0χ(3)Ex3(t)+xk320χ(3)(h*Ex2)(t)Ex(t),
where
h(t)=Θ(t)τ12+τ22τ1τ22sin(t/τ1)et/τ2.
Here, symbol * means convolution product in time, Θ(t) is the usual Heaviside step function, τ1 and τ2 represent the rotational Raman time and dipole dephasing time, respectively. In air those quantities take the values τ1 ≈ 62 fs and τ2 ≈ 77 fs for the fraction xk = 0.5 [20,30]. We shall assume that these values still hold for pump wavelengths up to 2 μm. Note that the changes in the molecular orientation due to the excitation of rotational states are here neglected. Picosecond-scaled fluctuations in the optical nonlinearities due to the ensemble-averaged transient alignment (〈cos2 θ〉 − 1/3 [31,32]), potentially induced by the laser electric field forming an angle θ with the axis of air molecules, are assumed to be small for our pump pulse lengths ≤ 60 fs.

To start with, we integrate the (1+1)-dimensional Eqs. (6) and (7) using the initial condition that gives the following temporal profile of the laser field at z = 0 (we impose vacuum for z < 0):

EL(t,z=0)=2I0cε0[1re2ln2(tτp)2cos(ω0t)+re8ln2(tτp)2cos(2ω0t+φ)],
where I0 is the pump intensity, r is the relative intensity ratio of the second harmonic, φ is the relative phase between the fundamental pulse with carrier frequency ω0 and its second harmonic. When integrating Eqs. (6) and (7) the field components are advanced in time. The secondary fields x and z are then extracted by inverse Fourier transform of the overall electric field filtered below a cut-off frequency. More detail on the numerical methods used to solve this set of equations together with unidirectional propagators can be found in [33].

For I0 = 100 TW/cm2 and r = 0.15, Figs. 1(a) and 1(b) show the transverse and longitudinal secondary fields filtered in a 80-THz frequency window for a two-color pulse propagating in the air at ambient pressure. The full width at half maximum (FWHM) duration of the pump pulse centered at 800-nm wavelength is τp = 40 fs with half-duration for the 2ω0 component. Simulations are performed using the quasi-static tunneling ionization, accounting or not for the Kerr nonlinearity, which we here consider instantaneous (xk = 0) with a nonlinear index ∼ 10−19 cm2/W. For simplicity we first ignore linear dispersion whose action will be examined in Figs. 2(e) and 2(f). At such intensities O2 molecules undergo most of the ionization events for a neutral density Na = 5.4 × 1018 cm−3. With two-color pulses, the transverse field at the distance z = 1 cm is found to be orders of magnitude larger than the longitudinal one [Fig. 1(a)]. Around the main peak created by photoionization, residual oscillations occur from filtering the field below the 80-THz cut-off frequency. Plasma wakefield effects characterize the longitudinal field [Fig. 1(b)], with a long plasma wave formed behind the pulse head and oscillating at plasma frequency, as shown in the spectrum (see inset). Note that the plasma frequency varies due to small changes in Ne caused by Kerr-induced self-steepening. At larger propagation distances, the transverse THz field increases, whereas the longitudinal field decreases even more (not shown). The Kerr response, although of minor role in the conversion process, increases the peak of the transverse THz field to some extent. Hence, at air-based filament intensities ∼ 100 TW/cm2, only the transverse secondary fields generated through photocurrents and four-wave mixing appear to be relevant in a two-color pulse configuration (see also [29]).

 

Fig. 1 (a) Transverse and (b) longitudinal fields computed at z = 1 cm from Eqs. (6) and (7) (1D model), and filtered in a 80-THz window for a 800+400-nm pulse with I0 = 100 TW/cm2, φ = π/2 and r = 15%. The red dashed curve displays the THz field computed with the plasma response only (P); the solid curve corresponds to both Kerr (instantaneous) and plasma responses (K+P). Inset in (b) details the THz spectrum of the longitudinal field.

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Fig. 2 1D simulations [Eq. (6)]: (a) Transverse THz field for two-color 800+400-nm pulses (r = 15%) at z = 1 cm by plasma alone (P, red dashed curves), the Kerr response alone (K, blue dash-dotted curves) and both nonlinearities (K+P, black solid curves) at 25 TW/cm2 with φ = 0. (b) Corresponding spectra. (c) Transverse THz field at z = 1 cm by two-color pulses with 100 TW/cm2 intensity and φ = π/2. These fields are filtered in the frequency window ν < 80 THz. (d) Corresponding spectra. (e,f) Evolution of the relative phase φ versus z in the forward component of the electric field for (e) I0 = 25 TW/cm2 and (f) I0 = 100 TW/cm2, including or not linear dispersion (D, see legend). The phase jump near z = 1 and 7 mm is due to sharp distortions of the pulse profile induced by plasma generation.

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Figures 2(a)–2(d) detail the influence of the Kerr (blue dash-dotted curves), plasma (red dashed curves) and combined Kerr-plasma effects (black solid curves) when solving Eq. (6) for a fundamental pulse at 800 nm coupled with its second harmonic interacting with ambient air over short propagation distance (z = 1 cm). The left-hand side column depicts the transverse THz field distributions computed from an inverse Fourier transform of the whole field within the frequency window ν < 80 THz. The right-hand side column shows corresponding spectra. At low intensities (25 TW/cm2), which are characteristic of the self-focusing regime, the THz field exhibits a temporal profile shaped by the four-wave mixing contribution when the initial relative phase between the two colors is chosen to be zero [17]. However, the THz field maximum reaches much higher values in the presence of photoionization [Fig. 2(a)]. The reason is that the phase difference between the fundamental and second harmonic is rapidly dragged away from its initial value by the action of the Kerr term, so that the phase angle at z = 1 cm becomes closer to π/6. Such a relative phase value improves the conditions leading to an efficient THz emission by photocurrents as justified, e.g., in Figs. 4(c)–4(d) of Section 3. The opposite scenario is possible as well, i.e., the Kerr term can also shift the relative phase from π/2 and render the photocurrent mechanism less efficient: Starting with 100 TW/cm2 and φ = π/2, the THz yield in the spectral range ν < 30 THz is reduced by the action of the Kerr term compared to the plasma source alone, as the phase angle is dragged away from the optimum value π/2 [see Fig. 2(f)]. Thus, while keeping a relatively small amplitude as pure THz emitter [see Figs. 2(b)–2(d)], the Kerr response mainly acts by changing the pulse spectrum and the relative phase φ significantly.

 

Fig. 3 Eq. (8) including PNL and discarding the z-derivatives: (a) THz spectra as functions of the fraction xk of Raman nonlinearity with no ionization. (b) Corresponding local fields produced by four-wave mixing and filtered in a 80-THz-wide window. (c,d) THz spectra computed by plugging the temporal profiles of two-color pulses obtained from the 3D unidirectional propagator Eq. (33) into the source terms t J and/or t2PNL, isolated or summed up with (R) or without the Raman contribution (see legend) for the 800-nm pump pulses simulated in (c) Fig. 6 at the distance z = 2.5 cm and (d) Fig. 7(a) at the distance z = 20 cm.

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Fig. 4 The LC phase space: Velocity of free electrons created from t = −∞ as function of their position. Dots locate the minima (red dots) and maxima (black dots) of the laser field. (a) Single color. (b) Two colors with zero relative phase. (c) Two colors with a relative phase of π/4. (d) Two colors with a relative phase of π/2. Squares indicate the location of the strongest extrema for which δNn exceeds the others by more than one order of magnitude.

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So far, linear dispersion has been discarded over propagation ranges ≤ 1 cm along which its action is usually expected to be small in gases [2]. However, over comparable ranges and depending on the pump wavelength, it may already significantly impact the relative phase φ that conditions the efficiency of the THz emitters. To illustrate this point, Figs. 2(e) and 2(f) display the evolution of the phase angle φ numerically extracted from the forward component of the electric field along the z axis. The forward electric field is computed from the 1D version of the unidirectional pulse propagation model [see Eq. (33)] for our two pulse configurations that now undergo air dispersion as modeled in [34]. At low intensity [25 TW/cm2 - Fig. 2(e)], for which the plasma response is small, linear dispersion drags the relative phase out of its initial value upon short distances ∼ 1.5 cm by a phase shift comparable to that driven by the Kerr nonlinearity. A similar conclusion applies to the plasma regime [100 TW/cm2 - Fig. 2(f)]. Despite the smallness of its coefficients in air [34], linear dispersion induces a phase mismatch between the 800-nm and 400-nm pulse components, which, combined with the nonlinearities, is able to drive a phase shift close to π/2 over 1.5 cm that cannot be neglected. This constraint is relaxed to some extent for longer pump wavelengths.

In summary, the above results show a net influence in the THz yield when accounting for the Kerr nonlinearity along cm-propagation ranges. The Kerr response directly alters the pump spectrum as well as variations in the phase angle between the ω and 2ω pulse components. Together with linear dispersion, this impacts the THz conversion efficiency, which is mainly driven by the photocurrent mechanism at clamping intensity.

3. Impact of delayed Kerr nonlinearities and longer pump wavelength

Below we address the influence of the Raman-delayed Kerr nonlinearity on the laser-to-THz conversion efficiency and we quantify the increase in THz generation when the fundamental wavelength belongs to the mid-infrared range. Since from Fig. 1 we expect no significant action from the longitudinal field Ez, we only focus on the transverse field Ex, whose subscript x is henceforth omitted.

3.1. Influence of the Raman-delayed nonlinearity

For notational convenience, we rewrite the initial laser field (12) as

E(t)=ω0(t)aω0cos(ω0t)+2ω0(t)a2ω0cos(2ω0t+φ),
where 0 ≤ ω0,2ω0 (t) ≤ 1, aω0,2ω0 and φ are the pulse envelopes with duration τω0,2ω0, relative amplitude at ω0 or 2ω0 and the relative phase between the two colors, respectively. We assume long enough FWHM durations, i.e., ω0τω0,2ω0 ≫ 1.

Using the input two-color pulse (13), we can evaluate the low-frequency part of the overall Kerr response Eq. (10), when both envelope functions ω0,2ω0 (t) take the value unity for the sake of simplicity. Cook and Hochstrasser’s result [17] is easily recovered for the instantaneous part of the Kerr polarization yielding the direct-current (dc) contribution

Pinstdc=(1xk)340χ(3)aω02a2ω0cosφ.
THz emission due to an instantaneous Kerr response is maximum for the phase offset φ = 0 [π].

Adding the Raman contribution now leads us to evaluate the integral

PRaman=xk320χ(3)E(t)0+τ12+τ22τ1τ22eτ/τ2sin(ττ1)E2(tτ)dτ.

After several trigonometric simplifications, we can extract from Eq. (15) a low-frequency (dc) contribution reading as

PRamandc=xk320χ(3)aω02a2ω0[T1cosφ+T2sinφ],
where
T1=τ12+τ224(τ22+τ12(14τ22ω02)α(τ1,τ2,ω0)+2τ1ω0(τ22τ12(1+τ22ω02))β(τ1,τ2,ω0)),
T2=τ12+τ224(4τ12τ2ω0α(τ1,τ2,ω0)+2τ1τ21(τ22+τ12(1+τ22ω02))β(τ1,τ2,ω0)),
with
α(τ1,τ2,ω0)=(τ12+τ22)2+(2τ1τ2ω0)2(2τ122τ22+4τ12τ22ω02),
β(τ1,τ2,ω0)=(τ12+τ22)2+(τ1τ2ω0)2(2τ122τ22+τ12τ22ω02).
The values of T1 and T2 provide an optimal phase for THz generation when φ = tan−1(T2/T1). For pump wavelengths λ0 comprised between 0.8 and 3 μm, we find that |T1| ≤ 0.021 and |T2| ∼ 0.02|T1|. It is thus reasonable to neglect T2, so that the low-frequency part of the total Kerr response involving the Raman-delayed component simplifies into
PNLdc340χ(3)aω02a2ω0[1xk(12T1)]cosφ.
By analogy with Cook and Hochstrasser’s analysis [17], this formula indicates that the optimal phase difference for THz generation by the Kerr response remains φ = 0 [π]. Maximum THz generation is provided when there is no Raman nonlinearity (xk = 0). PRaman decreases the THz yield by a correction (T1) of the percent order, which is confirmed by Figs. 3(a) and 3(b) for different values of the fraction xk. THz spectra and fields are computed at z = 0 from Eq. (8) including the nonlinear polarization. They indeed decrease in amplitude when xk is augmented. This property reflects the fact that the nonlinear integrand in Eq. (15) acts over relatively long relaxation times τ1τ2 ∼ 60 – 80 fs, along which the high-frequency laser oscillations cancel each other over the integration in time. The resulting integral is slowly varying and PRaman thus barely contributes to the THz spectrum.

This result confirms the behavior expected from envelope-like unidirectional models [2] for which the Raman nonlinearity is assumed insensitive to the pump harmonics and oscillates like the optical field. It justifies that we can employ Eq. (10) within a field description and still applies to alternative formulations of the rotational Raman scattering [31]. Besides the net decrease by the fraction xk, the impact of the overall Kerr source is also expected to decrease from the loss of self- and cross-phase modulations that affect the pump spectrum through the Kerr response. This aspect is detailed in Figs. 3(c) and 3(d), where we have compared the THz spectra obtained from inserting into the source terms t J and/or t2PNL some temporal profiles further computed in Section 4 in a focused geometry [Fig. 3(c)] and in the filamentation regime [Fig. 3(d)] at the distance of maximum THz generation. Although this procedure loses the memory of the THz yield accumulated along previous distances, including that prior to ionization, it clearly indicates that in plasma regime the Kerr source remains minor compared to that associated to photocurrents. The action of the Raman nonlinearity mostly manifests by changing the pulse spectrum, which conditions the photocurrents.

3.2. Increase in the pump wavelength

References [19,21] reported an impressive increase in the THz conversion efficiency when doubling the fundamental wavelength for equal FWHM durations. For single-color pulses of same energy, we can easily expect that doubling λ0 for THz generation triggered in tunneling regime keeps the final electron density Ne unchanged, but it doubles the free electron velocity [23]

νf(t)=emeetτctE(t)etτcdt
through its evident dependency on 1/ω0. Thereby the electron current density is doubled. With two colors involving a dominant fundamental pulse at ω0, the same scaling holds. However, Ne noticeably increases, e.g., by a factor ∼ 2 at 100 TW/cm2, for two superimposed colors (φ = 0). With a π/2 relative phase, the pump field exhibits a temporal asymmetry around the electric field maxima and the current density J(t) develops a low-frequency component due to the stepwise increase of the electron density. This component is then the major THz source [35].

Following the local current theory [23], ionization happens near the relative extrema of E(t) at the instants t1, t2, t3, . . . tn, from which the electron density and current can be approximated as Ne(t)nδNnHn(ttn) and J(t) ≃ JA(t) + JB(t) with

JA(t)=enδNnνf(t)Hn(ttn),JB(t)=enδNnettnτcνf(tn)Hn(ttn).
The quasi-step function is Hn(t)=12[1+erf(t/τn)], where the duration of the nth ionization event is τn=[3(UH/Ui)3/2|E(tn)|2/(|t2E(tn)|Ea)]1/2. Using Fourier transforms, we obtain in the low-frequency domain and in the non-collisional limit (see [23,36]):
[tJA](ω)ie22πmenδNn[Eω0(tn)+14E2ω0(tn)]ωω02,
[tJB](ω)e2πnδNnνf(tn)eiωtn,
where Eω0 (t) = ω0 (t)aω0 cos(ω0t) and E2ω0 (t) = 2ω0 (t)a2ω0 cos(2ω0t + φ).

Neglecting again the influence of the envelopes (ω0,2ω0 = 1), the ionization instants of a two-color pulse can be approximated by [23]

ω0tnnπ2a2ω0aω0(1)nsinφ
at leading order in a2ω0/aω0 ≪ 1. We assume equal density jumps
δNnNa(1eπW[E(t1)]τ1)δN,
occurring over a large number of ionization events N ≫ 1. In the THz frequency range ωω0 and using r ≪ 1, it is straightforward to evaluate
[tJA](ω)ie2a2ω042πmeNδNωω02cosφ,
[tJB](ω)3e2a2ω02πmeδNω0sin(Nωπ/2ω0)sin(ωπ/ω0)sinφ.
Expressed in wavelength, the spectrum of the electron current density then follows from
[tJ](λ)e2a2ω0(2π)3/2mecδN[i4Nλ024cosφ+3λ0sin(Nλ0π/2λ)sin(λ0π/λ)sinφ].
Equations (2830) show that t JA, scaling as λ02, and t JB, scaling as λ0, dominate for φ = 0 and φ = π/2, respectively. The ionization steps δN [Eq. (27)] increase, in the limit n ≪ 1, linearly with the ionization duration τnτ1. For a fixed pulse duration, the number of optical cycles is halved when one doubles the pump wavelength and since τnω01, one has τ2λ0/τλ0 ∼ 2. The number of ionization events decreases accordingly, i.e., N2λ0/Nλ0 = 1/2.

For a better understanding of t JA, it may be instructive to rewrite Eq. (24) in the form

[tJA](ω)iωe2πnδNnrf(tn),
where rf denotes the free electron position (rf = 0 at −∞):
rf(t)=tνf(t)dt.

Figure 4 illustrates the phase space (rf, vf). It provides a qualitative way to rapidly know if a given pulse configuration favors THz generation from JA or JB. Dots correspond to the minima and maxima of the laser field at the coordinates [rf (tn), vf (tn)]. There are constructive contributions if rf (tn) for [t JA] or vf (tn) for [t JB] are sign-definite. For one color [Fig. 4(a)], there is only one contribution of [t JA] which is destructive: vf (tn) is zero, while the symmetric extrema in the positions rf (tn) cancel each other due to their opposite signs. For two colors with a null relative phase [Fig. 4(b)], again destructive contributions exist in [t JA] and [t JB], but the configuration is more favorable to [t JA] for which rf (tn) cannot cancel out. For two colors and φ = π/2 [Fig. 4(d)], positive velocities vf (tn) > 0 enhance [t JB], whereas [t JA] vanishes with opposite rf (tn). This situation also applies to Fig. 4(c) where φ = π/4.

In Figs. 4(a) and 4(b), stricto-sensu, THz emission should not be zero due to the pulse envelope [23]. Indeed, with an envelope imposing a smooth profile over a finite pulse duration, the local minima and maxima of the laser field are not equal and do not exactly cancel each other at the coordinates [rf (tn), vf (tn)]. Considering the influence of bounded envelopes, Fig. 5 shows the ratio between the THz field induced by a two-color pump-pulse with fundamental wavelength at 1600 nm and one with fundamental wavelength at 800 nm. This ratio is evaluated through an ordinary least squares method applied to the THz field profiles calculated numerically from the LC model for ionizing beam intensities. This method mostly captures the ratio between the THz field maxima along the time axis. For comparison, the theoretical ratio |2λ0/λ0| inferred from the inverse Fourier transform of Eq. (30) is plotted as a black solid line. It provides a gain factor that varies between 4 (φ = 0) and 2 (φ = π/2) with π-periodicity. For Gaussian pulses [ ω0,2ω0(t)=exp(22β1ln2t2β/τω0,2ω02β)with β = 1], this behavior is verified by the LC results (red curves) of Fig. 5(a), despite minor variations caused by envelope effects. The ratio |2λ0/λ0| remains less sensitive to the pulse duration and the fundamental wavelength than to the relative phase φ. Maximum gain factor in the THz field amplitudes is obtained for φ ≈ 0, which underlines the role of the current density JA directly connected to the laser field. Opting next for 4th-order super-Gaussian profiles (β = 4), |2λ0/λ0| again varies with the relative phase, but it strongly evolves and even exceeds the value 5 for φπ/10 when decreasing the FWHM duration [Fig. 5(b)]. We attribute these changes to the steepness of the envelope, which makes the first ionization events not exactly located at the same times for 800-nm and 1600-nm pump pulses. For our laser parameters, the relative intensity ratio r appears to have a limited impact on the gain performances.

 

Fig. 5 LC computations: (a,b) Ratio of THz field strengths emitted by a two-color pulse with a 1600-nm pump over that emitted with a 800-nm pump, function of the relative phase between the fundamental and second harmonic in a 80-THz-wide window. (a) Gain factor for Gaussian pulses with various intensity ratios ra2ω02/aω02 and laser intensities I0 (see legend). Blue dotted lines show the gain factor for two different pulse durations at the same intensity. The black solid line shows the gain factor using the analytical model Eq. (30). (b) Same quantity for 4th-order super-Gaussian envelopes with different ratios r and intensities I0. (c,d) Evolution of the THz yield with the pump wavelength for the three relative phases 0, π/4 and π/2 using (c) Gaussian pulses and (d) 4th-order super-Gaussian pulses.

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Figures 5(c) and 5(d) illustrate the increase in the THz energy yield for 60-fs FWHM pump duration and intensities ∼ 200 TW/cm2 rather reached in focusing geometries [21]. Solid lines refer to the computed energy values, while the dashed lines are fitting curves in λα. We can observe that exponents α > 4 fit for small relative phases. A π/2 phase angle, however, renders the JB contribution dominant and thus decreases this exponent. So, even though λ-dependent scalings reported in [21] are possible, they are not generic as the gain factors are highly sensitive to the relative phase between the two colors, the shape of the pulse envelopes and their durations. Note from Figs. 5(c) and 5(d) that the THz pulse energy is much larger with a π/2 phase angle than with a null phase. This means that in the situation where JA is dominant (φ → 0), the overall THz spectrum is much smaller than when JB prevails for different phase values. It should be kept in mind that, as the relative phase φ is constant in the LC model, an important issue will be to figure out the changes in the conversion efficiency when this phase varies upon propagation, which is the purpose of the next section.

4. Comparison with unidirectional pulse propagation simulations

The previous properties are now checked by direct 3D numerical computations. Our reference model is the unidirectional pulse propagation equation (UPPE) [24,25] that governs the forward-propagating component of linearly polarized pulses

zE^=ik2(ω)kx2ky2E^+iμ0ω22k(ω)^NL,
where Ê(kx, ky, z, ω) is the Fourier transform of the laser electric field with respect to x, y, and t. The first term on the right-hand side of Eq. (33) describes linear dispersion and diffraction of the pulse. The term ℱ̂NL = NL + iĴ/ω + iĴloss/ω contains the third-order nonlinear polarization with Kerr index n2=3χ(3)/4n02c0 [n0 = n(ω0)], the electron current J and a loss term Jloss due to ionization [2, 3]. Compared with [25], the denominator of the nonlinear term reduces to 2k(ω), assuming ω2ℱ̂NL relevant only for k(ω)=n(ω)ω/ckx2+ky2.

The analysis presented below aims at testing the generic nature of our theoretical findings on the Raman nonlinearity and the effect of varying the pump wavelength against full 3D, linear and nonlinear propagation effects undergone by two-color pulses issued from different setups, subject to different medium parameters and evolving along various filament ranges. Both focused and collimated propagation geometries will be examined for Gaussian beams. We shall first validate our theoretical expectations using the simple QST model for a single species (O2) and classical values for the Kerr indices. Next, more elaborated ionization models and recently measured Kerr coefficients in the mid-infrared will be employed to countercheck our findings.

4.1. Validation of theoretical issues

Equation (33) is here solved for experimental configurations close to those examined in [21], i.e., for focused pulses with f -numbers > 10 (f -number refers to the ratio between the focal length and the FWHM input beam diameter). The initial relative phase φ is set equal to zero and the fundamental pump wavelengths of the two-color pulses are 800 nm and 1600 nm.

In a first set of simulations we choose f/# = 42 for the beam width w0 = 500 μm and focal length f = 2.5 cm. Our two-color pulses have 200 μJ in energy and the FWHM duration of the pump pulse is 60 fs. About 7% of the laser energy is contained in the second harmonic. Dispersion curve in air for the refractive optical index n(ω) is again taken from [34]. Kerr indices are chosen as n2 ≃ 1.2 × 10−19 cm2/W following [37, 38]. At atmospheric pressure, Na = 5.4 × 1018 cm−3 for O2 molecules and the critical power for self-focusing, defined by Pcrλ02/2πn0n2, is Pcr = 8.5 GW at 800 nm and 35.1 GW at 1600 nm. Although strongly focused, our ultrashort pulses promote single-ionization events for peak intensities < 300 TW/cm2 near focus due to local defocusing by the generated plasma. Therefore, we can here use the QST ionization rate (4) applied to oxygen molecules only.

Simulations have been performed with a time window of 1.22 ps, a temporal step Δt = 75 attoseconds and transverse resolution of Δx = Δy ≈ 3 μm. Figure 6 shows the peak electron density reached near focus, the variations of the relative phase between the fundamental and second harmonic along z [Fig. 6(a)], and the THz energy contained in our numerical box (3 × 3 mm2) [Fig. 6(b)]. THz radiation is collected within a 80-THz-large frequency window. Cyan/magenta curves ignore the delayed Raman nonlinearity; blue/red curves include it for comparison (xk = 0.5). There is a limited influence of the Kerr response in tight focusing regime, but its related THz conversion efficiency is clearly diminished by the delayed nonlinearity for the reasons given in Section 3. Concerning the wavelength dependency, the maximum intensity achieved near focus decreases with λ0, as the beam waist wfw0 f/z0 becomes proportional to the pump wavelength when the Rayleigh length z0=πw02/λ0 is much larger than the focal distance f [39]. Consequently, since the QST rate (4) does not depend on the pump wavelength, the peak electron density decreases in turn [Fig. 6(a)]. The relative phase φ covers the full interval [0, 2π] over the 4-cm-long propagation range. It experiences a Gouy phase shift up to π near focus, supplemented by another π phase shift induced by linear dispersion for the 800-nm pump [see Fig. 2(f)]. In Fig. 6(b) we observe a net increase of the maximum THz energy produced at zf when λ0 is augmented.

 

Fig. 6 3D UPPE simulations of focused two-color Gaussian pulses in ratio r = 7.4%. (a) Maximum electron density (left-hand side axis, solid curves) and relative phase between the two pulse components (right-hand side axis, dashed curves), (b) THz energy yield (ν ≤ 80 THz) for the pump wavelengths 800 nm (blue/cyan curves) and 1600 nm (red/magenta curves), with and without the Raman nonlinearity. (c) THz energy vs pump wavelength. Cyan diamonds: no Raman; blue squares: With Raman. Green crosses × report THz gain factors in filamentation regime with no Raman nonlinearity as promoted in Fig. 7; Green symbols + report gain factors in filamentation regime with Raman nonlinearity as given by Fig. 9. The red dots recall the experimental data of [21]. (d) Normalized on-axis THz spectral intensities [arb. u.] computed near focus.

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The experimental data points of [21] are recalled by the red dots in Fig. 6(c), which we compare with the THz pulse energy at focus. Despite differences between the original experiment and our laser parameters, the THz yield only evaluated from two pump wavelengths follows a comparable growth. Accounting for Raman scattering helps to reach a better agreement with the experimental data. For our THz window of 80 THz, a rough fitting curve indicates a growth rate in λα with α ≈ 3.5, i.e., 2 < α ≤ 4 in agreement with Fig. 5(c) and 5(d), keeping in mind the variations in the relative phase φ shown in Fig. 6(a). Shortening this window to 20 THz as measured in [21] does not noticeably change this scaling, as the THz spectra emitted around focus are self-contained in the frequency domain ν < 20 THz [Fig. 6(d)]. The influence of the plasma volume is here limited: Visual inspection of the numerical data indeed revealed plasma channels being of comparable dimensions when using a pump wavelength of either 800 nm or 1600 nm, i.e., the plasma volumes only vary within a factor 0.8 – 1.3 from density levels > 1015–17 cm−3.

We now employ Eq. (33) to describe THz generation by two-color filaments operating with two different pump wavelengths over long distances. The UPPE is integrated for two-color Gaussian pulses with input power Pin = 34 GW, beam waist w0 = 400 μm and FWHM durations τω0 = 40 fs (τ2ω0 = τω0/2, r = 3.4%) in a collimated propagation. Kerr indices are unchanged and we keep the quasi-static tunneling rate (4). For reasons of computational cost, the numerical resolution has been decreased to Δt = 99 attoseconds and Δx = Δy ≈ 9 μm, which was checked to introduce no significant variations in the THz spectra and fields. The selected THz window is still ν ≤ 80 THz.

Figures 7(a) and 7(b) illustrate the peak intensity and maximum electron density reached along meter-range distances in two-color filamentation regime. Light (cyan and magenta) curves show a propagation for which no delayed Kerr nonlinearity is accounted for (xk = 0). Dark (blue and red) curves include the Raman-delayed nonlinearity in the ratio xk = 0.5 [30,40,41]. From Fig. 7(a) it is clear that the Raman term weakens the contribution of the instantaneous Kerr response, which results in (i) a longer self-focusing distance, (ii) a decreased clamping intensity, and thereby (iii) an enhanced self-guiding range. Consistently, the peak plasma density decreases in turn and extends over longer distances. As expected, the bottom row of Figs. 7(a) and 7(b) displays a net decrease of the THz energy emitted along propagation. With a pump wavelength of 1600 nm, at equal energy content, the input power becomes closer to a single critical power in air and self-channeling with no delayed-Kerr response favors a more extended filamentation range compared with a 800-nm pump pulse. Peak densities decrease from 1017 cm−3 to 1016 cm−3, which should weaken the high gain factors achieved in focused geometry. Indeed, the THz yield is only stronger (without Raman), locally by a factor ∼ 1.52 at maximum emission, as indicated by the green crosses of Fig. 6(c). Performances in the THz gain factor with an increased pump wavelength in this collimated propagation thus appear weaker than in a focused geometry. Note that the THz energy with a 800-nm pump wave can escape early our numerical box (2.4 × 2.4 mm2), which explains the important decrease in the THz energy emission after propagating over tens of cm. From a physical point of view, this drop of THz energy is also due to a loss of asymmetry undergone by the 800-nm pump field over long distances. We attribute this property to the group-velocity mismatch between the ω and 2ω components [42]: Assuming an efficient coupling between the two colors over τω0/4, the walk-off length is found to be ∼ 39 cm for the 800-nm pump pulse and ∼ 1.64 m for the 1600-nm pump pulse. So the previous evaluation is only performed at the maximum of THz energy and is certainly not optimal for getting a precise estimate of the THz gain in a filament configuration. When adding the Raman-delayed nonlinearity, the available power contributing to the instantaneous Kerr response is subcritical (∼ 0.7), which prevents the two-color pulse from self-focusing and exceeding the ionization threshold. As a result, no plasma generation takes place and only a residual THz emission occurs due to four-wave mixing.

 

Fig. 7 3D UPPE simulations of two-color filaments. (a) Top: Maximum intensity (solid curves, left-hand side axis) and peak electron density (dashed curves, right-hand side axis) of a meter-long two-color filament with 800-nm (blue/cyan curves) and 1600-nm pump component (red/magenta curves) (r = 3.4%). Colored curves refer to wave propagation without (cyan/magenta curves) and with (blue/red curves) Raman-delayed Kerr nonlinearity. Bottom: Corresponding THz pulse energy yield accumulated along z inside a 80-THz-large frequency window. (c,d) On-axis THz fields and spectral intensities [arb. u.] near the distance of maximum THz energy yield.

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Figures 7(c) and 7(d) depict THz fields propagated over several tens of cm and their spectra for 800-nm and 1600-nm pump pulses. The selected distances correspond to the range of maximum THz energy shown in Figs. 7(a) and 7(d), bottom. One clearly sees that the Raman-delayed response contributes locally to diminish the THz conversion efficiency, because the pump dynamics is changed and in particular the peak intensity is reduced. In addition, a longer pump wavelength promotes the formation of a supercontinuum linking the tail of the fundamental pulse spectrum to the THz spectrum [Fig. 7(d)], which can justify a stronger influence of the current component JA. THz fields with ∼ 0.1 GV/m amplitudes are achieved at both pump wavelengths with a clear amplification at z = 60 cm from the 1600-nm pump pulse.

4.2. Generalization for different medium parameters

We now test our previous findings for more complex ionization rates applying to the two major air species and consider different bound electron responses.

We first choose the same f -number ∼ 14 as in Clerici et al.’s experiments [21]. For numerical reasons we limit the initial beam width to w0 = 150 μm for a focal length f = 2.5 mm. Our two-color pulses have 400 μJ in energy with 5.2% being injected into the second harmonic. These simulations include both Kerr and Raman nonlinearities and our selected THz window is again 80 THz. The simulations use a temporal step Δt = 75 attoseconds and a transverse resolution of Δx = Δy = 0.88 μm. For completeness we also included ionization of nitrogen molecules using either a QST rate (Ui = 15.6 eV, Z* = 1) or a field-dependent PPT rate for two species, adopting Talebpour et al.’s charge numbers ZO2*=0.53, ZN2*=0.9 [43]. When using a QST rate for both O2 and N2 molecules, the peak intensity and electron density reach 650 TW/cm2 and 2.7 × 1019 cm−3 (complete single ionization) near focus with a 800-nm pump, respectively [see Fig. 8(a)]. With the PPT rate, the effective charge numbers being less than unity promote weaker ionization rates [44], which increases the maximum pulse intensity at focus. Again a complete single ionization of both molecular species is achieved at 800 nm.

 

Fig. 8 3D UPPE simulations of focused two-color Gaussian pulses in ratio r = 5.2% for QST ionization (dashed curves) and PPT ionization (solid curves) of O2 and N2 molecules. (a) Peak electron density. The selected pump wavelengths are 0.8, 1.6 and 2 μm (see legend). (b) Maximum THz energy yield for ν ≤ 80 THz as a function of the pump wavelength for a focused beam and two species ionized with the QST rate (black curves) and with an instantaneous PPT rate (violet curves). Scaling curves in λα shown as dashed curves are evaluated through least-square fitting (see legend). The red dots recall the experimental data points of [21]. (c) On-axis THz spectral intensities [arb. u.] computed at focus. Inset shows maximum THz fields.

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Figure 8(b) compares the corresponding THz energy yields obtained from either a QST or an instantaneous PPT rate with both oxygen and nitrogen. Except at 800 nm with the PPT rate, the computed THz energy growth and values appear in good quantitative agreement with Clerici et al. [21]’s experimental results [compare solid curves and red dots of Fig. 8(b)]. Differences due to the choice of the ionization model are limited. A λ-dependent scaling of the THz yield appears closer to λ2 than λ4. Figure 8(c) displays the spectra at focus. It is interesting to observe that the computed THz spectra now shifts their maximum to ν ≃ 30 THz, and not to ν = 5 THz as reported in [21]. This discrepancy may be attributed to the fact that the ABCD technique used in [21] can barely measure frequencies above ∼ 20 THz (see also [13]). Inset details the growth of the maximum THz electric field, which increases quasi-linearly with the pump wavelength. Comparing Figs. 6(c) and 8(b) demonstrates how sensitive the gain curves and THz spectra can be when one varies the laser parameters in focusing geometries. It should be noticed that the plasma volume again appears of limited influence in the THz gain. The plasma volume measured from density levels Ne > 1017 cm−3 in Fig. 8 even slightly increases by a factor ∼ 1.7 to the benefit of the 800-nm pump. This confirms the weak impact of the plasma volume in the THz gain at longer wavelength and rather privileges THz emission by the plasma-air surfaces [16,29].

Finally, to evaluate the influence of the nonlinearity coefficients, we present in Fig. 9 the peak intensity and plasma density, THz energy, spectra and fields of the same femtosecond pulses as in Fig. 7 subject to stronger self-focusing with higher Raman-delayed responses, n2 = 3.79 × 10−19 cm2/W, xk = 0.79 as recently measured in [45, 46] for 800-nm pump pulses. With 1600-nm pump pulses, following [47], we selected the Kerr index values n2 = 3.72 × 10−19 cm2/W, xk = 0.78. For completeness, we employed an instantaneous PPT rate with effective charge numbers ZO2 = 0.53 and ZN2 = 0.9 [43]. Unlike in Fig. 7, the 1600-nm pump is here able to trigger a self-focusing sequence, starting with an input power ratio over critical equal to 3.1 that corresponds to an effective power ratio of about 2.5. Figure 9(b) shows the THz energy evolving with the propagation distance. Over the plasma zone (0.1 ≤ z ≤ 0.7 m), the laser-to-THz conversion efficiency with a 1600-nm pump wave compared to a 800-nm pump is smaller than in the previous filamentary configuration [see green symbols + in Fig. 6(c)], which can be attributed to the larger drop in the peak plasma densities reached in Fig. 9(a). The maximum THz yield achieved with the 1600-nm pump is smaller than that reached in Fig. 7. Figures 9(c) and 9(d) detail the THz fields and spectra at the distances of maximum THz energy emission. Computed for low frequencies ≤ 80 THz, on-axis THz fields created with the 800-nm pump prevail. On the whole, the main trend reported about Fig. 7 is retrieved: Compared to the THz gain factors achieved in a focused geometry, doubling the pump wavelength for two-color filaments propagating over meter-range distances in air may not significantly increase the THz conversion efficiency.

 

Fig. 9 3D UPPE computations of two-color filaments simulated with the Kerr indices and fractions of delayed nonlinearity reported in [45,47] for 800-nm (blue curves) and 1600-nm (red curves) pump pulses. (a) Peak intensities (left-hand side axis, solid curves) and maximum plasma densities (right-hand side axis, dashed curves). (b) THz energy in a 80-THz frequency window. (c) On-axis THz fields at z = 20 cm and z = 40 cm, and (d) corresponding spectral intensities [arb. u.].

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5. Conclusion

In summary, we have theoretically studied the influence of long pump wavelengths belonging to the range 0.8–2 μm in THz emissions caused by two-color laser pulses through air photoionization. We also cleared up the action of Raman-delayed and instantaneous Kerr nonlinearities of air molecules on the laser-to-THz conversion efficiency. Optical nonlinearities contribute to THz generation, in particular prior to ionization, but rotational Raman scattering leads to weaken the THz energy yield. At clamping intensity, direct laser-to-THz conversion via four-wave-mixing is weak compared to the photocurrent mechanism. However, Kerr-induced propagation effects such as cross-phase modulation and self-steepening have significant impact on THz generation. Furthermore, increasing the pump wavelength can dramatically enhance the THz energy yield. We showed that the THz energy gain factor cannot be quantitatively formulated with a simple power law in λα due to the influence of the relative phase between the two colors and their pulse envelopes. However, powers of growth rates between 2 and 5 can be justified from the local current model, mainly depending on the relative phase between the two colors. Scalings in ∼ λ2–3.5 have been extracted in focused propagation geometries through 3D comprehensive UPPE simulations, which faithfully reproduce experimental measurements of THz pulse energies. Similar gain factors can, however, barely be reached in a filamentation geometry that clamps the intensity at smaller values and features much lower peak plasma densities at longer wavelengths. These results should help anticipate the THz gain factors achieved with mid-infrared laser systems used in future experiments.

Funding

This work was supported by the ANR/ASTRID Project “ALTESSE” # ANR-15-ASTR-0009 and performed using HPC resources from PRACE (Grant # 2014-112576) and GENCI (Grant # 2016-057594). I.B. acknowledges support by the joint grant DFG-MO # 850/20-1 - RSF # 16-42-01060. S.S. acknowledges support by the Qatar National Research Fund through the National Priorities Research Program (Grant # NPRP 8-246-1-060).

References and links

1. S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005). [CrossRef]  

2. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007). [CrossRef]  

3. L. Bergé and S. Skupin, “Few-cycle light bullets created by femtosecond filaments,” Phys. Rev. Lett. 100, 113902 (2008). [CrossRef]   [PubMed]  

4. J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003). [CrossRef]   [PubMed]  

5. T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009). [CrossRef]  

6. J. Liu, J. Dai, S. L. Chin, and X.-C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photon. 4, 627 (2010). [CrossRef]  

7. C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).

8. C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007). [CrossRef]  

9. K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577 (2007). [CrossRef]   [PubMed]  

10. Y. S. You, T. I. Oh, and K. Y. Kim, “Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. Lett. 109, 183902 (2012). [CrossRef]   [PubMed]  

11. K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photon. 2, 605 (2008). [CrossRef]  

12. M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser & Photon. Rev. 1, 349 (2007). [CrossRef]  

13. V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016). [CrossRef]   [PubMed]  

14. I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010). [CrossRef]   [PubMed]  

15. A. Debayle, L. Gremillet, L. Bergé, and C. Köhler, “Analytical model for THz emissions induced by laser-gas interaction,” Opt. Express 22, 13691 (2014). [CrossRef]   [PubMed]  

16. I. Thiele, R. Nuter, B. Bousquet, V. Tikhonchuk, S. Skupin, X. Davoine, L. Gremillet, and L. Bergé, “Theory of terahertz emission from femtosecond-laser-induced microplasmas,” Phys. Rev. E 94, 063202 (2016). [CrossRef]  

17. D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. 25, 1210 (2000). [CrossRef]  

18. A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett. 38, 1906 (2013). [CrossRef]   [PubMed]  

19. L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013). [CrossRef]   [PubMed]  

20. J. R. Peñano, P. Sprangle, P. Serafim, B. Hafizi, and A. Ting, “Stimulated Raman scattering of intense laser pulses in air,” Phys. Rev. E 68, 056502 (2003). [CrossRef]  

21. M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013). [CrossRef]   [PubMed]  

22. A. Debayle, P. González de Alaiza Martínez, L. Gremillet, and L. Bergé, “Non-monotonic increase in laser-driven THz emissions through multiple ionization events,” Phys. Rev. A 91, 041801 (2015). [CrossRef]  

23. I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011). [CrossRef]  

24. M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002). [CrossRef]  

25. M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 7, 036604 (2004). [CrossRef]  

26. P. Sprangle, J. R. Peñano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004). [CrossRef]  

27. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, 1965).

28. A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

29. P. González de Alaiza Martínez, X. Davoine, A. Debayle, L. Gremillet, and L. Bergé, “Terahertz radiation driven by two-color laser pulses at near-relativistic intensities: Competition between photoionization and wakefield effects,” Scientific Reports 6, 26743 (2016). [CrossRef]   [PubMed]  

30. T. A. Pitts, T. S. Luk, J. K. Gruetzner, T. R. Nelson, A. McPherson, S. M. Cameron, and A. C. Bernstein, “Propagation of self-focusing laser pulses in atmosphere: experiment versus numerical simulation,” J. Opt. Soc. Am. B 21, 2008 (2004). [CrossRef]  

31. J. P. Palastro, T. M. Antonsen Jr., and H. M. Milchberg, “Compression, spectral broadening, and collimation in multiple, femtosecond pulse filamentation in atmosphere,” Phys. Rev. A 86, 033834 (2012). [CrossRef]  

32. J. Wu, Y. Tong, M. Li, H. Pan, and H. Zeng, “THz generation by a two-color pulse in prealigned molecules,” Phys. Rev. A 82, 053416 (2010). [CrossRef]  

33. P. González de Alaiza Martínez, “Generation of intense terahertz sources by ultrashort laser pulses,” PhD Dissertation Thesis, Université Paris-Saclay NNT # 2016SACLS350, Chap. 3 (2016).

34. E. R. Peck and K. Reeder, “Dispersion of Air,” J. Opt. Soc. Am. 62, 958–962 (1972). [CrossRef]  

35. M. Li, W. Li, Y. Shi, P. Lu, H. Pan, and H. Zeng, “Verification of the physical mechanism of THz generation by dual-color ultrashort laser pulses,” Appl. Phys. Lett. 101, 161104 (2012). [CrossRef]  

36. P. González de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting Terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015). [CrossRef]   [PubMed]  

37. V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components,” Opt. Express 17, 13429–13434 (2009); See also erratum in Opt. Express 18, 3011–3012 (2010). [CrossRef]   [PubMed]  

38. W. Ettoumi, Y. Petit, J. Kasparian, and J. P. Wolf, “Generalized Miller formulae,” Opt. Express 18, 6613–6620 (2010). [CrossRef]   [PubMed]  

39. L. Bergé, J. Rolle, and C. Köhler, “Enhanced self-compression of mid-infrared laser filaments in argon,” Phys. Rev. A 88, 023816 (2013). [CrossRef]  

40. S. Champeaux and L. Bergé, “Postionization regimes of femtosecond laser pulses self-channeling in air,” Phys. Rev. E 71, 046604 (2005). [CrossRef]  

41. S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, “(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments,” Phys. Rev. E 77, 036406 (2008). [CrossRef]  

42. O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011). [CrossRef]  

43. A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999). [CrossRef]  

44. R. Nuter and L. Bergé, “Pulse chirping and ionization of O2 molecules for the filamentation of femtosecond laser pulses in air,” J. Opt. Soc. Am. B 23, 874–884 (2006). [CrossRef]  

45. J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012). [CrossRef]  

46. E. W. Rosenthal, J. P. Palastro, N. Jhajj, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Sensitivity of propagation and energy deposition in femtosecond filamentation to the nonlinear refractive index,” J. Phys. B: At. Mol. Opt. Phys. 48, 094011 (2015). [CrossRef]  

47. S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Measurements of the nonlinear refractive index of air constituents at mid-infrared wavelengths,” Opt. Lett. 40, 5794–5797 (2015). [CrossRef]   [PubMed]  

References

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  1. S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005).
    [Crossref]
  2. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
    [Crossref]
  3. L. Bergé and S. Skupin, “Few-cycle light bullets created by femtosecond filaments,” Phys. Rev. Lett. 100, 113902 (2008).
    [Crossref] [PubMed]
  4. J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
    [Crossref] [PubMed]
  5. T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
    [Crossref]
  6. J. Liu, J. Dai, S. L. Chin, and X.-C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photon. 4, 627 (2010).
    [Crossref]
  7. C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).
  8. C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
    [Crossref]
  9. K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577 (2007).
    [Crossref] [PubMed]
  10. Y. S. You, T. I. Oh, and K. Y. Kim, “Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. Lett. 109, 183902 (2012).
    [Crossref] [PubMed]
  11. K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photon. 2, 605 (2008).
    [Crossref]
  12. M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser & Photon. Rev. 1, 349 (2007).
    [Crossref]
  13. V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
    [Crossref] [PubMed]
  14. I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
    [Crossref] [PubMed]
  15. A. Debayle, L. Gremillet, L. Bergé, and C. Köhler, “Analytical model for THz emissions induced by laser-gas interaction,” Opt. Express 22, 13691 (2014).
    [Crossref] [PubMed]
  16. I. Thiele, R. Nuter, B. Bousquet, V. Tikhonchuk, S. Skupin, X. Davoine, L. Gremillet, and L. Bergé, “Theory of terahertz emission from femtosecond-laser-induced microplasmas,” Phys. Rev. E 94, 063202 (2016).
    [Crossref]
  17. D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. 25, 1210 (2000).
    [Crossref]
  18. A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett. 38, 1906 (2013).
    [Crossref] [PubMed]
  19. L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
    [Crossref] [PubMed]
  20. J. R. Peñano, P. Sprangle, P. Serafim, B. Hafizi, and A. Ting, “Stimulated Raman scattering of intense laser pulses in air,” Phys. Rev. E 68, 056502 (2003).
    [Crossref]
  21. M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
    [Crossref] [PubMed]
  22. A. Debayle, P. González de Alaiza Martínez, L. Gremillet, and L. Bergé, “Non-monotonic increase in laser-driven THz emissions through multiple ionization events,” Phys. Rev. A 91, 041801 (2015).
    [Crossref]
  23. I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
    [Crossref]
  24. M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
    [Crossref]
  25. M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 7, 036604 (2004).
    [Crossref]
  26. P. Sprangle, J. R. Peñano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004).
    [Crossref]
  27. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, 1965).
  28. A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).
  29. P. González de Alaiza Martínez, X. Davoine, A. Debayle, L. Gremillet, and L. Bergé, “Terahertz radiation driven by two-color laser pulses at near-relativistic intensities: Competition between photoionization and wakefield effects,” Scientific Reports 6, 26743 (2016).
    [Crossref] [PubMed]
  30. T. A. Pitts, T. S. Luk, J. K. Gruetzner, T. R. Nelson, A. McPherson, S. M. Cameron, and A. C. Bernstein, “Propagation of self-focusing laser pulses in atmosphere: experiment versus numerical simulation,” J. Opt. Soc. Am. B 21, 2008 (2004).
    [Crossref]
  31. J. P. Palastro, T. M. Antonsen, and H. M. Milchberg, “Compression, spectral broadening, and collimation in multiple, femtosecond pulse filamentation in atmosphere,” Phys. Rev. A 86, 033834 (2012).
    [Crossref]
  32. J. Wu, Y. Tong, M. Li, H. Pan, and H. Zeng, “THz generation by a two-color pulse in prealigned molecules,” Phys. Rev. A 82, 053416 (2010).
    [Crossref]
  33. P. González de Alaiza Martínez, “Generation of intense terahertz sources by ultrashort laser pulses,” PhD Dissertation Thesis, Université Paris-Saclay NNT # 2016SACLS350, Chap. 3 (2016).
  34. E. R. Peck and K. Reeder, “Dispersion of Air,” J. Opt. Soc. Am. 62, 958–962 (1972).
    [Crossref]
  35. M. Li, W. Li, Y. Shi, P. Lu, H. Pan, and H. Zeng, “Verification of the physical mechanism of THz generation by dual-color ultrashort laser pulses,” Appl. Phys. Lett. 101, 161104 (2012).
    [Crossref]
  36. P. González de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting Terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
    [Crossref] [PubMed]
  37. V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components,” Opt. Express 17, 13429–13434 (2009); See also erratum in Opt. Express 18, 3011–3012 (2010).
    [Crossref] [PubMed]
  38. W. Ettoumi, Y. Petit, J. Kasparian, and J. P. Wolf, “Generalized Miller formulae,” Opt. Express 18, 6613–6620 (2010).
    [Crossref] [PubMed]
  39. L. Bergé, J. Rolle, and C. Köhler, “Enhanced self-compression of mid-infrared laser filaments in argon,” Phys. Rev. A 88, 023816 (2013).
    [Crossref]
  40. S. Champeaux and L. Bergé, “Postionization regimes of femtosecond laser pulses self-channeling in air,” Phys. Rev. E 71, 046604 (2005).
    [Crossref]
  41. S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, “(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments,” Phys. Rev. E 77, 036406 (2008).
    [Crossref]
  42. O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
    [Crossref]
  43. A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999).
    [Crossref]
  44. R. Nuter and L. Bergé, “Pulse chirping and ionization of O2 molecules for the filamentation of femtosecond laser pulses in air,” J. Opt. Soc. Am. B 23, 874–884 (2006).
    [Crossref]
  45. J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).
    [Crossref]
  46. E. W. Rosenthal, J. P. Palastro, N. Jhajj, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Sensitivity of propagation and energy deposition in femtosecond filamentation to the nonlinear refractive index,” J. Phys. B: At. Mol. Opt. Phys. 48, 094011 (2015).
    [Crossref]
  47. S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Measurements of the nonlinear refractive index of air constituents at mid-infrared wavelengths,” Opt. Lett. 40, 5794–5797 (2015).
    [Crossref] [PubMed]

2016 (3)

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

I. Thiele, R. Nuter, B. Bousquet, V. Tikhonchuk, S. Skupin, X. Davoine, L. Gremillet, and L. Bergé, “Theory of terahertz emission from femtosecond-laser-induced microplasmas,” Phys. Rev. E 94, 063202 (2016).
[Crossref]

P. González de Alaiza Martínez, X. Davoine, A. Debayle, L. Gremillet, and L. Bergé, “Terahertz radiation driven by two-color laser pulses at near-relativistic intensities: Competition between photoionization and wakefield effects,” Scientific Reports 6, 26743 (2016).
[Crossref] [PubMed]

2015 (4)

A. Debayle, P. González de Alaiza Martínez, L. Gremillet, and L. Bergé, “Non-monotonic increase in laser-driven THz emissions through multiple ionization events,” Phys. Rev. A 91, 041801 (2015).
[Crossref]

P. González de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting Terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

E. W. Rosenthal, J. P. Palastro, N. Jhajj, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Sensitivity of propagation and energy deposition in femtosecond filamentation to the nonlinear refractive index,” J. Phys. B: At. Mol. Opt. Phys. 48, 094011 (2015).
[Crossref]

S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Measurements of the nonlinear refractive index of air constituents at mid-infrared wavelengths,” Opt. Lett. 40, 5794–5797 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (4)

L. Bergé, J. Rolle, and C. Köhler, “Enhanced self-compression of mid-infrared laser filaments in argon,” Phys. Rev. A 88, 023816 (2013).
[Crossref]

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett. 38, 1906 (2013).
[Crossref] [PubMed]

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[Crossref] [PubMed]

2012 (4)

M. Li, W. Li, Y. Shi, P. Lu, H. Pan, and H. Zeng, “Verification of the physical mechanism of THz generation by dual-color ultrashort laser pulses,” Appl. Phys. Lett. 101, 161104 (2012).
[Crossref]

J. P. Palastro, T. M. Antonsen, and H. M. Milchberg, “Compression, spectral broadening, and collimation in multiple, femtosecond pulse filamentation in atmosphere,” Phys. Rev. A 86, 033834 (2012).
[Crossref]

Y. S. You, T. I. Oh, and K. Y. Kim, “Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. Lett. 109, 183902 (2012).
[Crossref] [PubMed]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).
[Crossref]

2011 (2)

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

2010 (4)

J. Wu, Y. Tong, M. Li, H. Pan, and H. Zeng, “THz generation by a two-color pulse in prealigned molecules,” Phys. Rev. A 82, 053416 (2010).
[Crossref]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

J. Liu, J. Dai, S. L. Chin, and X.-C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photon. 4, 627 (2010).
[Crossref]

W. Ettoumi, Y. Petit, J. Kasparian, and J. P. Wolf, “Generalized Miller formulae,” Opt. Express 18, 6613–6620 (2010).
[Crossref] [PubMed]

2009 (2)

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components,” Opt. Express 17, 13429–13434 (2009); See also erratum in Opt. Express 18, 3011–3012 (2010).
[Crossref] [PubMed]

2008 (3)

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photon. 2, 605 (2008).
[Crossref]

L. Bergé and S. Skupin, “Few-cycle light bullets created by femtosecond filaments,” Phys. Rev. Lett. 100, 113902 (2008).
[Crossref] [PubMed]

S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, “(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments,” Phys. Rev. E 77, 036406 (2008).
[Crossref]

2007 (5)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577 (2007).
[Crossref] [PubMed]

M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser & Photon. Rev. 1, 349 (2007).
[Crossref]

2006 (1)

2005 (2)

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005).
[Crossref]

S. Champeaux and L. Bergé, “Postionization regimes of femtosecond laser pulses self-channeling in air,” Phys. Rev. E 71, 046604 (2005).
[Crossref]

2004 (3)

T. A. Pitts, T. S. Luk, J. K. Gruetzner, T. R. Nelson, A. McPherson, S. M. Cameron, and A. C. Bernstein, “Propagation of self-focusing laser pulses in atmosphere: experiment versus numerical simulation,” J. Opt. Soc. Am. B 21, 2008 (2004).
[Crossref]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 7, 036604 (2004).
[Crossref]

P. Sprangle, J. R. Peñano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004).
[Crossref]

2003 (2)

J. R. Peñano, P. Sprangle, P. Serafim, B. Hafizi, and A. Ting, “Stimulated Raman scattering of intense laser pulses in air,” Phys. Rev. E 68, 056502 (2003).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

2002 (1)

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[Crossref]

2000 (1)

1999 (1)

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999).
[Crossref]

1972 (1)

1966 (1)

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Aközbek, N.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005).
[Crossref]

Akturk, S.

C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).

André, Y. B.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Andreeva, V. A.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett. 38, 1906 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

Antonsen, T. M.

J. P. Palastro, T. M. Antonsen, and H. M. Milchberg, “Compression, spectral broadening, and collimation in multiple, femtosecond pulse filamentation in atmosphere,” Phys. Rev. A 86, 033834 (2012).
[Crossref]

Babushkin, I.

P. González de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting Terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[Crossref] [PubMed]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Becker, A.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005).
[Crossref]

Bergé, L.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

I. Thiele, R. Nuter, B. Bousquet, V. Tikhonchuk, S. Skupin, X. Davoine, L. Gremillet, and L. Bergé, “Theory of terahertz emission from femtosecond-laser-induced microplasmas,” Phys. Rev. E 94, 063202 (2016).
[Crossref]

P. González de Alaiza Martínez, X. Davoine, A. Debayle, L. Gremillet, and L. Bergé, “Terahertz radiation driven by two-color laser pulses at near-relativistic intensities: Competition between photoionization and wakefield effects,” Scientific Reports 6, 26743 (2016).
[Crossref] [PubMed]

A. Debayle, P. González de Alaiza Martínez, L. Gremillet, and L. Bergé, “Non-monotonic increase in laser-driven THz emissions through multiple ionization events,” Phys. Rev. A 91, 041801 (2015).
[Crossref]

P. González de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting Terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

A. Debayle, L. Gremillet, L. Bergé, and C. Köhler, “Analytical model for THz emissions induced by laser-gas interaction,” Opt. Express 22, 13691 (2014).
[Crossref] [PubMed]

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[Crossref] [PubMed]

L. Bergé, J. Rolle, and C. Köhler, “Enhanced self-compression of mid-infrared laser filaments in argon,” Phys. Rev. A 88, 023816 (2013).
[Crossref]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

L. Bergé and S. Skupin, “Few-cycle light bullets created by femtosecond filaments,” Phys. Rev. Lett. 100, 113902 (2008).
[Crossref] [PubMed]

S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, “(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments,” Phys. Rev. E 77, 036406 (2008).
[Crossref]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

R. Nuter and L. Bergé, “Pulse chirping and ionization of O2 molecules for the filamentation of femtosecond laser pulses in air,” J. Opt. Soc. Am. B 23, 874–884 (2006).
[Crossref]

S. Champeaux and L. Bergé, “Postionization regimes of femtosecond laser pulses self-channeling in air,” Phys. Rev. E 71, 046604 (2005).
[Crossref]

Bernstein, A. C.

Borodin, A. V.

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett. 38, 1906 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

Bourayou, R.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Bousquet, B.

I. Thiele, R. Nuter, B. Bousquet, V. Tikhonchuk, S. Skupin, X. Davoine, L. Gremillet, and L. Bergé, “Theory of terahertz emission from femtosecond-laser-induced microplasmas,” Phys. Rev. E 94, 063202 (2016).
[Crossref]

Cabrera-Granado, E.

P. González de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting Terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

Cameron, S. M.

Caspani, L.

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

Champeaux, S.

S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, “(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments,” Phys. Rev. E 77, 036406 (2008).
[Crossref]

S. Champeaux and L. Bergé, “Postionization regimes of femtosecond laser pulses self-channeling in air,” Phys. Rev. E 71, 046604 (2005).
[Crossref]

Châteauneuf, M.

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

Chen, Y.

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

Cheng, Y.-H.

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).
[Crossref]

Chin, S. L.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett. 38, 1906 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

J. Liu, J. Dai, S. L. Chin, and X.-C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photon. 4, 627 (2010).
[Crossref]

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005).
[Crossref]

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999).
[Crossref]

Clerici, M.

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

Cook, D. J.

Couairon, A.

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

D’Amico, C.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).

Dai, J.

J. Liu, J. Dai, S. L. Chin, and X.-C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photon. 4, 627 (2010).
[Crossref]

Davoine, X.

I. Thiele, R. Nuter, B. Bousquet, V. Tikhonchuk, S. Skupin, X. Davoine, L. Gremillet, and L. Bergé, “Theory of terahertz emission from femtosecond-laser-induced microplasmas,” Phys. Rev. E 94, 063202 (2016).
[Crossref]

P. González de Alaiza Martínez, X. Davoine, A. Debayle, L. Gremillet, and L. Bergé, “Terahertz radiation driven by two-color laser pulses at near-relativistic intensities: Competition between photoionization and wakefield effects,” Scientific Reports 6, 26743 (2016).
[Crossref] [PubMed]

Debayle, A.

P. González de Alaiza Martínez, X. Davoine, A. Debayle, L. Gremillet, and L. Bergé, “Terahertz radiation driven by two-color laser pulses at near-relativistic intensities: Competition between photoionization and wakefield effects,” Scientific Reports 6, 26743 (2016).
[Crossref] [PubMed]

A. Debayle, P. González de Alaiza Martínez, L. Gremillet, and L. Bergé, “Non-monotonic increase in laser-driven THz emissions through multiple ionization events,” Phys. Rev. A 91, 041801 (2015).
[Crossref]

A. Debayle, L. Gremillet, L. Bergé, and C. Köhler, “Analytical model for THz emissions induced by laser-gas interaction,” Opt. Express 22, 13691 (2014).
[Crossref] [PubMed]

Dubois, J.

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

Elsaesser, T.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Esaulkov, M. N.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett. 38, 1906 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

Ettoumi, W.

Faccio, D.

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

Faucher, O.

Franco, M.

C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Frey, S.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Giguère, M.

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

Glownia, J. H.

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photon. 2, 605 (2008).
[Crossref]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577 (2007).
[Crossref] [PubMed]

González de Alaiza Martínez, P.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

P. González de Alaiza Martínez, X. Davoine, A. Debayle, L. Gremillet, and L. Bergé, “Terahertz radiation driven by two-color laser pulses at near-relativistic intensities: Competition between photoionization and wakefield effects,” Scientific Reports 6, 26743 (2016).
[Crossref] [PubMed]

P. González de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting Terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

A. Debayle, P. González de Alaiza Martínez, L. Gremillet, and L. Bergé, “Non-monotonic increase in laser-driven THz emissions through multiple ionization events,” Phys. Rev. A 91, 041801 (2015).
[Crossref]

P. González de Alaiza Martínez, “Generation of intense terahertz sources by ultrashort laser pulses,” PhD Dissertation Thesis, Université Paris-Saclay NNT # 2016SACLS350, Chap. 3 (2016).

Gordon, D.

S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, “(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments,” Phys. Rev. E 77, 036406 (2008).
[Crossref]

Gremillet, L.

P. González de Alaiza Martínez, X. Davoine, A. Debayle, L. Gremillet, and L. Bergé, “Terahertz radiation driven by two-color laser pulses at near-relativistic intensities: Competition between photoionization and wakefield effects,” Scientific Reports 6, 26743 (2016).
[Crossref] [PubMed]

I. Thiele, R. Nuter, B. Bousquet, V. Tikhonchuk, S. Skupin, X. Davoine, L. Gremillet, and L. Bergé, “Theory of terahertz emission from femtosecond-laser-induced microplasmas,” Phys. Rev. E 94, 063202 (2016).
[Crossref]

A. Debayle, P. González de Alaiza Martínez, L. Gremillet, and L. Bergé, “Non-monotonic increase in laser-driven THz emissions through multiple ionization events,” Phys. Rev. A 91, 041801 (2015).
[Crossref]

A. Debayle, L. Gremillet, L. Bergé, and C. Köhler, “Analytical model for THz emissions induced by laser-gas interaction,” Opt. Express 22, 13691 (2014).
[Crossref] [PubMed]

Gruetzner, J. K.

Hafizi, B.

P. Sprangle, J. R. Peñano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004).
[Crossref]

J. R. Peñano, P. Sprangle, P. Serafim, B. Hafizi, and A. Ting, “Stimulated Raman scattering of intense laser pulses in air,” Phys. Rev. E 68, 056502 (2003).
[Crossref]

Herrmann, J.

P. González de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting Terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[Crossref] [PubMed]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Hertz, E.

Hochstrasser, R. M.

Hosseini, S. A.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005).
[Crossref]

Houard, A.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).

Husakou, A.

P. González de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting Terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

Jhajj, N.

E. W. Rosenthal, J. P. Palastro, N. Jhajj, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Sensitivity of propagation and energy deposition in femtosecond filamentation to the nonlinear refractive index,” J. Phys. B: At. Mol. Opt. Phys. 48, 094011 (2015).
[Crossref]

Kandidov, V. P.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005).
[Crossref]

Kapetanakos, C. A.

P. Sprangle, J. R. Peñano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004).
[Crossref]

Kasparian, J.

W. Ettoumi, Y. Petit, J. Kasparian, and J. P. Wolf, “Generalized Miller formulae,” Opt. Express 18, 6613–6620 (2010).
[Crossref] [PubMed]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Kim, K. Y.

Y. S. You, T. I. Oh, and K. Y. Kim, “Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. Lett. 109, 183902 (2012).
[Crossref] [PubMed]

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photon. 2, 605 (2008).
[Crossref]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577 (2007).
[Crossref] [PubMed]

Köhler, C.

P. González de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting Terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

A. Debayle, L. Gremillet, L. Bergé, and C. Köhler, “Analytical model for THz emissions induced by laser-gas interaction,” Opt. Express 22, 13691 (2014).
[Crossref] [PubMed]

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[Crossref] [PubMed]

L. Bergé, J. Rolle, and C. Köhler, “Enhanced self-compression of mid-infrared laser filaments in argon,” Phys. Rev. A 88, 023816 (2013).
[Crossref]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Kolesik, M.

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 7, 036604 (2004).
[Crossref]

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[Crossref]

Kosareva, O. G.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett. 38, 1906 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005).
[Crossref]

Kress, M.

M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser & Photon. Rev. 1, 349 (2007).
[Crossref]

Kuehn, W.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, 1965).

Lavorel, B.

Le Bloas, J.

C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).

Légaré, F.

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

Li, M.

M. Li, W. Li, Y. Shi, P. Lu, H. Pan, and H. Zeng, “Verification of the physical mechanism of THz generation by dual-color ultrashort laser pulses,” Appl. Phys. Lett. 101, 161104 (2012).
[Crossref]

J. Wu, Y. Tong, M. Li, H. Pan, and H. Zeng, “THz generation by a two-color pulse in prealigned molecules,” Phys. Rev. A 82, 053416 (2010).
[Crossref]

Li, W.

M. Li, W. Li, Y. Shi, P. Lu, H. Pan, and H. Zeng, “Verification of the physical mechanism of THz generation by dual-color ultrashort laser pulses,” Appl. Phys. Lett. 101, 161104 (2012).
[Crossref]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, 1965).

Liu, J.

J. Liu, J. Dai, S. L. Chin, and X.-C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photon. 4, 627 (2010).
[Crossref]

Liu, W.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005).
[Crossref]

Liu, Y.

C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).

Löffler, T.

M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser & Photon. Rev. 1, 349 (2007).
[Crossref]

Loriot, V.

Lotti, A.

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

Lu, P.

M. Li, W. Li, Y. Shi, P. Lu, H. Pan, and H. Zeng, “Verification of the physical mechanism of THz generation by dual-color ultrashort laser pulses,” Appl. Phys. Lett. 101, 161104 (2012).
[Crossref]

Luk, T. S.

Luo, Q.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005).
[Crossref]

Makarov, V. A.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett. 38, 1906 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

Marceau, C.

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

McPherson, A.

Méjean, G.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Milchberg, H. M.

E. W. Rosenthal, J. P. Palastro, N. Jhajj, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Sensitivity of propagation and energy deposition in femtosecond filamentation to the nonlinear refractive index,” J. Phys. B: At. Mol. Opt. Phys. 48, 094011 (2015).
[Crossref]

S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Measurements of the nonlinear refractive index of air constituents at mid-infrared wavelengths,” Opt. Lett. 40, 5794–5797 (2015).
[Crossref] [PubMed]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).
[Crossref]

J. P. Palastro, T. M. Antonsen, and H. M. Milchberg, “Compression, spectral broadening, and collimation in multiple, femtosecond pulse filamentation in atmosphere,” Phys. Rev. A 86, 033834 (2012).
[Crossref]

Mlejnek, M.

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[Crossref]

Moloney, J. V.

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 7, 036604 (2004).
[Crossref]

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[Crossref]

Morandotti, R.

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

Morgner, U.

P. González de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting Terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

Mysyrowicz, A.

C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Nelson, T. R.

Nuter, R.

I. Thiele, R. Nuter, B. Bousquet, V. Tikhonchuk, S. Skupin, X. Davoine, L. Gremillet, and L. Bergé, “Theory of terahertz emission from femtosecond-laser-induced microplasmas,” Phys. Rev. E 94, 063202 (2016).
[Crossref]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

R. Nuter and L. Bergé, “Pulse chirping and ionization of O2 molecules for the filamentation of femtosecond laser pulses in air,” J. Opt. Soc. Am. B 23, 874–884 (2006).
[Crossref]

Oh, T. I.

Y. S. You, T. I. Oh, and K. Y. Kim, “Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. Lett. 109, 183902 (2012).
[Crossref] [PubMed]

Ozaki, T.

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

Palastro, J. P.

E. W. Rosenthal, J. P. Palastro, N. Jhajj, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Sensitivity of propagation and energy deposition in femtosecond filamentation to the nonlinear refractive index,” J. Phys. B: At. Mol. Opt. Phys. 48, 094011 (2015).
[Crossref]

J. P. Palastro, T. M. Antonsen, and H. M. Milchberg, “Compression, spectral broadening, and collimation in multiple, femtosecond pulse filamentation in atmosphere,” Phys. Rev. A 86, 033834 (2012).
[Crossref]

Pan, H.

M. Li, W. Li, Y. Shi, P. Lu, H. Pan, and H. Zeng, “Verification of the physical mechanism of THz generation by dual-color ultrashort laser pulses,” Appl. Phys. Lett. 101, 161104 (2012).
[Crossref]

J. Wu, Y. Tong, M. Li, H. Pan, and H. Zeng, “THz generation by a two-color pulse in prealigned molecules,” Phys. Rev. A 82, 053416 (2010).
[Crossref]

Panov, N. A.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett. 38, 1906 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

Peccianti, M.

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

Peck, E. R.

Peñano, J.

S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, “(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments,” Phys. Rev. E 77, 036406 (2008).
[Crossref]

Peñano, J. R.

P. Sprangle, J. R. Peñano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004).
[Crossref]

J. R. Peñano, P. Sprangle, P. Serafim, B. Hafizi, and A. Ting, “Stimulated Raman scattering of intense laser pulses in air,” Phys. Rev. E 68, 056502 (2003).
[Crossref]

Perelomov, A. M.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Petit, Y.

Pitts, T. A.

Popov, V. S.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Prade, B.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).

Reeder, K.

Reimann, K.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Rodriguez, G.

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photon. 2, 605 (2008).
[Crossref]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577 (2007).
[Crossref] [PubMed]

Rodriguez, M.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Rolle, J.

L. Bergé, J. Rolle, and C. Köhler, “Enhanced self-compression of mid-infrared laser filaments in argon,” Phys. Rev. A 88, 023816 (2013).
[Crossref]

Rosenthal, E. W.

E. W. Rosenthal, J. P. Palastro, N. Jhajj, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Sensitivity of propagation and energy deposition in femtosecond filamentation to the nonlinear refractive index,” J. Phys. B: At. Mol. Opt. Phys. 48, 094011 (2015).
[Crossref]

Roskos, H. G.

M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser & Photon. Rev. 1, 349 (2007).
[Crossref]

Salmon, E.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Sauerbrey, R.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Savel’ev, A. B.

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

Schmidt, B. E.

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

Schroeder, H.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005).
[Crossref]

Serafim, P.

J. R. Peñano, P. Sprangle, P. Serafim, B. Hafizi, and A. Ting, “Stimulated Raman scattering of intense laser pulses in air,” Phys. Rev. E 68, 056502 (2003).
[Crossref]

Shalaby, M.

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

Shi, Y.

M. Li, W. Li, Y. Shi, P. Lu, H. Pan, and H. Zeng, “Verification of the physical mechanism of THz generation by dual-color ultrashort laser pulses,” Appl. Phys. Lett. 101, 161104 (2012).
[Crossref]

Shipilo, D. E.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

Shkurinov, A. P.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, “Transformation of terahertz spectra emitted from dual-frequency femtosecond pulse interaction in gases,” Opt. Lett. 38, 1906 (2013).
[Crossref] [PubMed]

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

Skupin, S.

I. Thiele, R. Nuter, B. Bousquet, V. Tikhonchuk, S. Skupin, X. Davoine, L. Gremillet, and L. Bergé, “Theory of terahertz emission from femtosecond-laser-induced microplasmas,” Phys. Rev. E 94, 063202 (2016).
[Crossref]

P. González de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting Terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[Crossref] [PubMed]

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

L. Bergé and S. Skupin, “Few-cycle light bullets created by femtosecond filaments,” Phys. Rev. Lett. 100, 113902 (2008).
[Crossref] [PubMed]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

Solyankin, P. M.

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

Sprangle, P.

S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, “(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments,” Phys. Rev. E 77, 036406 (2008).
[Crossref]

P. Sprangle, J. R. Peñano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004).
[Crossref]

J. R. Peñano, P. Sprangle, P. Serafim, B. Hafizi, and A. Ting, “Stimulated Raman scattering of intense laser pulses in air,” Phys. Rev. E 68, 056502 (2003).
[Crossref]

Talebpour, A.

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999).
[Crossref]

Taylor, A. J.

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photon. 2, 605 (2008).
[Crossref]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577 (2007).
[Crossref] [PubMed]

Terent’ev, M. V.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Théberge, F.

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005).
[Crossref]

Thiele, I.

I. Thiele, R. Nuter, B. Bousquet, V. Tikhonchuk, S. Skupin, X. Davoine, L. Gremillet, and L. Bergé, “Theory of terahertz emission from femtosecond-laser-induced microplasmas,” Phys. Rev. E 94, 063202 (2016).
[Crossref]

Thomson, M. D.

M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser & Photon. Rev. 1, 349 (2007).
[Crossref]

Tikhonchuk, V.

I. Thiele, R. Nuter, B. Bousquet, V. Tikhonchuk, S. Skupin, X. Davoine, L. Gremillet, and L. Bergé, “Theory of terahertz emission from femtosecond-laser-induced microplasmas,” Phys. Rev. E 94, 063202 (2016).
[Crossref]

C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).

Tikhonchuk, V. T.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Ting, A.

S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, “(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments,” Phys. Rev. E 77, 036406 (2008).
[Crossref]

J. R. Peñano, P. Sprangle, P. Serafim, B. Hafizi, and A. Ting, “Stimulated Raman scattering of intense laser pulses in air,” Phys. Rev. E 68, 056502 (2003).
[Crossref]

Tong, Y.

J. Wu, Y. Tong, M. Li, H. Pan, and H. Zeng, “THz generation by a two-color pulse in prealigned molecules,” Phys. Rev. A 82, 053416 (2010).
[Crossref]

Volkov, R. V.

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

Wahlstrand, J. K.

E. W. Rosenthal, J. P. Palastro, N. Jhajj, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Sensitivity of propagation and energy deposition in femtosecond filamentation to the nonlinear refractive index,” J. Phys. B: At. Mol. Opt. Phys. 48, 094011 (2015).
[Crossref]

S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Measurements of the nonlinear refractive index of air constituents at mid-infrared wavelengths,” Opt. Lett. 40, 5794–5797 (2015).
[Crossref] [PubMed]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).
[Crossref]

Wang, T.-J.

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

Wille, H.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Woerner, M.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

Wolf, J. P.

W. Ettoumi, Y. Petit, J. Kasparian, and J. P. Wolf, “Generalized Miller formulae,” Opt. Express 18, 6613–6620 (2010).
[Crossref] [PubMed]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Wöste, L.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Wu, J.

J. Wu, Y. Tong, M. Li, H. Pan, and H. Zeng, “THz generation by a two-color pulse in prealigned molecules,” Phys. Rev. A 82, 053416 (2010).
[Crossref]

Yang, J.

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999).
[Crossref]

You, Y. S.

Y. S. You, T. I. Oh, and K. Y. Kim, “Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. Lett. 109, 183902 (2012).
[Crossref] [PubMed]

Yu, J.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Zahedpour, S.

S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Measurements of the nonlinear refractive index of air constituents at mid-infrared wavelengths,” Opt. Lett. 40, 5794–5797 (2015).
[Crossref] [PubMed]

E. W. Rosenthal, J. P. Palastro, N. Jhajj, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Sensitivity of propagation and energy deposition in femtosecond filamentation to the nonlinear refractive index,” J. Phys. B: At. Mol. Opt. Phys. 48, 094011 (2015).
[Crossref]

Zeng, H.

M. Li, W. Li, Y. Shi, P. Lu, H. Pan, and H. Zeng, “Verification of the physical mechanism of THz generation by dual-color ultrashort laser pulses,” Appl. Phys. Lett. 101, 161104 (2012).
[Crossref]

J. Wu, Y. Tong, M. Li, H. Pan, and H. Zeng, “THz generation by a two-color pulse in prealigned molecules,” Phys. Rev. A 82, 053416 (2010).
[Crossref]

Zhang, X.-C.

Appl. Phys. Lett. (2)

T.-J. Wang, Y. Chen, C. Marceau, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “High energy terahertz emission from two-color laser-induced filamentation in air with pump pulse duration control,” Appl. Phys. Lett. 95, 131108 (2009).
[Crossref]

M. Li, W. Li, Y. Shi, P. Lu, H. Pan, and H. Zeng, “Verification of the physical mechanism of THz generation by dual-color ultrashort laser pulses,” Appl. Phys. Lett. 101, 161104 (2012).
[Crossref]

Can. J. Phys. (1)

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: Physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005).
[Crossref]

J. Infrared Milli. Terahz. Waves (1)

O. G. Kosareva, N. A. Panov, R. V. Volkov, V. A. Andreeva, A. V. Borodin, M. N. Esaulkov, Y. Chen, C. Marceau, V. A. Makarov, A. P. Shkurinov, A. B. Savel’ev, and S. L. Chin, “Analysis of dual frequency interaction in the filament with the purpose of efficiency control of THz pulse generation,” J. Infrared Milli. Terahz. Waves 32, 1157–1167 (2011).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

J. Phys. B: At. Mol. Opt. Phys. (1)

E. W. Rosenthal, J. P. Palastro, N. Jhajj, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Sensitivity of propagation and energy deposition in femtosecond filamentation to the nonlinear refractive index,” J. Phys. B: At. Mol. Opt. Phys. 48, 094011 (2015).
[Crossref]

Laser & Photon. Rev. (1)

M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser & Photon. Rev. 1, 349 (2007).
[Crossref]

Nat. Photon. (2)

J. Liu, J. Dai, S. L. Chin, and X.-C. Zhang, “Broadband terahertz wave remote sensing using coherent manipulation of fluorescence from asymmetrically ionized gases,” Nat. Photon. 4, 627 (2010).
[Crossref]

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photon. 2, 605 (2008).
[Crossref]

New J. Phys. (2)

I. Babushkin, S. Skupin, A. Husakou, C. Köhler, E. Cabrera-Granado, L. Bergé, and J. Herrmann, “Tailoring terahertz radiation by controling tunnel photoionization events in gases,” New J. Phys. 13, 123029 (2011).
[Crossref]

C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M. Franco, B. Prade, A. Couairon, V. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” New J. Phys. 10, 013015 (2007).

Opt. Commun. (1)

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. A (5)

L. Bergé, J. Rolle, and C. Köhler, “Enhanced self-compression of mid-infrared laser filaments in argon,” Phys. Rev. A 88, 023816 (2013).
[Crossref]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).
[Crossref]

A. Debayle, P. González de Alaiza Martínez, L. Gremillet, and L. Bergé, “Non-monotonic increase in laser-driven THz emissions through multiple ionization events,” Phys. Rev. A 91, 041801 (2015).
[Crossref]

J. P. Palastro, T. M. Antonsen, and H. M. Milchberg, “Compression, spectral broadening, and collimation in multiple, femtosecond pulse filamentation in atmosphere,” Phys. Rev. A 86, 033834 (2012).
[Crossref]

J. Wu, Y. Tong, M. Li, H. Pan, and H. Zeng, “THz generation by a two-color pulse in prealigned molecules,” Phys. Rev. A 82, 053416 (2010).
[Crossref]

Phys. Rev. E (6)

J. R. Peñano, P. Sprangle, P. Serafim, B. Hafizi, and A. Ting, “Stimulated Raman scattering of intense laser pulses in air,” Phys. Rev. E 68, 056502 (2003).
[Crossref]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. E 7, 036604 (2004).
[Crossref]

P. Sprangle, J. R. Peñano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004).
[Crossref]

I. Thiele, R. Nuter, B. Bousquet, V. Tikhonchuk, S. Skupin, X. Davoine, L. Gremillet, and L. Bergé, “Theory of terahertz emission from femtosecond-laser-induced microplasmas,” Phys. Rev. E 94, 063202 (2016).
[Crossref]

S. Champeaux and L. Bergé, “Postionization regimes of femtosecond laser pulses self-channeling in air,” Phys. Rev. E 71, 046604 (2005).
[Crossref]

S. Champeaux, L. Bergé, D. Gordon, A. Ting, J. Peñano, and P. Sprangle, “(3+1)-dimensional numerical simulations of femtosecond laser filaments in air: Toward a quantitative agreement with experiments,” Phys. Rev. E 77, 036406 (2008).
[Crossref]

Phys. Rev. Lett. (9)

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[Crossref] [PubMed]

Y. S. You, T. I. Oh, and K. Y. Kim, “Off-axis phase-matched terahertz emission from two-color laser-induced plasma filaments,” Phys. Rev. Lett. 109, 183902 (2012).
[Crossref] [PubMed]

V. A. Andreeva, O. G. Kosareva, N. A. Panov, D. E. Shipilo, P. M. Solyankin, M. N. Esaulkov, P. González de Alaiza Martínez, A. P. Shkurinov, V. A. Makarov, L. Bergé, and S. L. Chin, “Ultrabroad terahertz spectrum generation from an air-based filament plasma,” Phys. Rev. Lett. 116, 063902 (2016).
[Crossref] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[Crossref] [PubMed]

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

L. Bergé and S. Skupin, “Few-cycle light bullets created by femtosecond filaments,” Phys. Rev. Lett. 100, 113902 (2008).
[Crossref] [PubMed]

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[Crossref]

M. Clerici, M. Peccianti, B. E. Schmidt, L. Caspani, M. Shalaby, M. Giguère, A. Lotti, A. Couairon, F. Légaré, T. Ozaki, D. Faccio, and R. Morandotti, “Wavelength scaling of terahertz generation by gas ionization,” Phys. Rev. Lett. 110, 253901 (2013).
[Crossref] [PubMed]

P. González de Alaiza Martínez, I. Babushkin, L. Bergé, S. Skupin, E. Cabrera-Granado, C. Köhler, U. Morgner, A. Husakou, and J. Herrmann, “Boosting Terahertz generation in laser-field ionized gases using a sawtooth wave shape,” Phys. Rev. Lett. 114, 183901 (2015).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[Crossref]

Science (1)

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Scientific Reports (1)

P. González de Alaiza Martínez, X. Davoine, A. Debayle, L. Gremillet, and L. Bergé, “Terahertz radiation driven by two-color laser pulses at near-relativistic intensities: Competition between photoionization and wakefield effects,” Scientific Reports 6, 26743 (2016).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, “Ionization of atoms in an alternating electric field,” Sov. Phys. JETP 23, 924–934 (1966).

Other (2)

P. González de Alaiza Martínez, “Generation of intense terahertz sources by ultrashort laser pulses,” PhD Dissertation Thesis, Université Paris-Saclay NNT # 2016SACLS350, Chap. 3 (2016).

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, 1965).

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Figures (9)

Fig. 1
Fig. 1 (a) Transverse and (b) longitudinal fields computed at z = 1 cm from Eqs. (6) and (7) (1D model), and filtered in a 80-THz window for a 800+400-nm pulse with I0 = 100 TW/cm2, φ = π/2 and r = 15%. The red dashed curve displays the THz field computed with the plasma response only (P); the solid curve corresponds to both Kerr (instantaneous) and plasma responses (K+P). Inset in (b) details the THz spectrum of the longitudinal field.
Fig. 2
Fig. 2 1D simulations [Eq. (6)]: (a) Transverse THz field for two-color 800+400-nm pulses (r = 15%) at z = 1 cm by plasma alone (P, red dashed curves), the Kerr response alone (K, blue dash-dotted curves) and both nonlinearities (K+P, black solid curves) at 25 TW/cm2 with φ = 0. (b) Corresponding spectra. (c) Transverse THz field at z = 1 cm by two-color pulses with 100 TW/cm2 intensity and φ = π/2. These fields are filtered in the frequency window ν < 80 THz. (d) Corresponding spectra. (e,f) Evolution of the relative phase φ versus z in the forward component of the electric field for (e) I0 = 25 TW/cm2 and (f) I0 = 100 TW/cm2, including or not linear dispersion (D, see legend). The phase jump near z = 1 and 7 mm is due to sharp distortions of the pulse profile induced by plasma generation.
Fig. 3
Fig. 3 Eq. (8) including PNL and discarding the z-derivatives: (a) THz spectra as functions of the fraction xk of Raman nonlinearity with no ionization. (b) Corresponding local fields produced by four-wave mixing and filtered in a 80-THz-wide window. (c,d) THz spectra computed by plugging the temporal profiles of two-color pulses obtained from the 3D unidirectional propagator Eq. (33) into the source terms t J and/or t 2 P NL, isolated or summed up with (R) or without the Raman contribution (see legend) for the 800-nm pump pulses simulated in (c) Fig. 6 at the distance z = 2.5 cm and (d) Fig. 7(a) at the distance z = 20 cm.
Fig. 4
Fig. 4 The LC phase space: Velocity of free electrons created from t = −∞ as function of their position. Dots locate the minima (red dots) and maxima (black dots) of the laser field. (a) Single color. (b) Two colors with zero relative phase. (c) Two colors with a relative phase of π/4. (d) Two colors with a relative phase of π/2. Squares indicate the location of the strongest extrema for which δNn exceeds the others by more than one order of magnitude.
Fig. 5
Fig. 5 LC computations: (a,b) Ratio of THz field strengths emitted by a two-color pulse with a 1600-nm pump over that emitted with a 800-nm pump, function of the relative phase between the fundamental and second harmonic in a 80-THz-wide window. (a) Gain factor for Gaussian pulses with various intensity ratios r a 2 ω 0 2 / a ω 0 2 and laser intensities I0 (see legend). Blue dotted lines show the gain factor for two different pulse durations at the same intensity. The black solid line shows the gain factor using the analytical model Eq. (30). (b) Same quantity for 4th-order super-Gaussian envelopes with different ratios r and intensities I0. (c,d) Evolution of the THz yield with the pump wavelength for the three relative phases 0, π/4 and π/2 using (c) Gaussian pulses and (d) 4th-order super-Gaussian pulses.
Fig. 6
Fig. 6 3D UPPE simulations of focused two-color Gaussian pulses in ratio r = 7.4%. (a) Maximum electron density (left-hand side axis, solid curves) and relative phase between the two pulse components (right-hand side axis, dashed curves), (b) THz energy yield (ν ≤ 80 THz) for the pump wavelengths 800 nm (blue/cyan curves) and 1600 nm (red/magenta curves), with and without the Raman nonlinearity. (c) THz energy vs pump wavelength. Cyan diamonds: no Raman; blue squares: With Raman. Green crosses × report THz gain factors in filamentation regime with no Raman nonlinearity as promoted in Fig. 7; Green symbols + report gain factors in filamentation regime with Raman nonlinearity as given by Fig. 9. The red dots recall the experimental data of [21]. (d) Normalized on-axis THz spectral intensities [arb. u.] computed near focus.
Fig. 7
Fig. 7 3D UPPE simulations of two-color filaments. (a) Top: Maximum intensity (solid curves, left-hand side axis) and peak electron density (dashed curves, right-hand side axis) of a meter-long two-color filament with 800-nm (blue/cyan curves) and 1600-nm pump component (red/magenta curves) (r = 3.4%). Colored curves refer to wave propagation without (cyan/magenta curves) and with (blue/red curves) Raman-delayed Kerr nonlinearity. Bottom: Corresponding THz pulse energy yield accumulated along z inside a 80-THz-large frequency window. (c,d) On-axis THz fields and spectral intensities [arb. u.] near the distance of maximum THz energy yield.
Fig. 8
Fig. 8 3D UPPE simulations of focused two-color Gaussian pulses in ratio r = 5.2% for QST ionization (dashed curves) and PPT ionization (solid curves) of O2 and N2 molecules. (a) Peak electron density. The selected pump wavelengths are 0.8, 1.6 and 2 μm (see legend). (b) Maximum THz energy yield for ν ≤ 80 THz as a function of the pump wavelength for a focused beam and two species ionized with the QST rate (black curves) and with an instantaneous PPT rate (violet curves). Scaling curves in λα shown as dashed curves are evaluated through least-square fitting (see legend). The red dots recall the experimental data points of [21]. (c) On-axis THz spectral intensities [arb. u.] computed at focus. Inset shows maximum THz fields.
Fig. 9
Fig. 9 3D UPPE computations of two-color filaments simulated with the Kerr indices and fractions of delayed nonlinearity reported in [45,47] for 800-nm (blue curves) and 1600-nm (red curves) pump pulses. (a) Peak intensities (left-hand side axis, solid curves) and maximum plasma densities (right-hand side axis, dashed curves). (b) THz energy in a 80-THz frequency window. (c) On-axis THz fields at z = 20 cm and z = 40 cm, and (d) corresponding spectral intensities [arb. u.].

Equations (33)

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( t + ν c ) J = e 2 m e N e E + Π ,
Π = e m e J × B + ( J ) ( J e N e ) + J e N e ( J ) ,
t N e = W ( E ) ( N a N e ) ,
W [ E ( t ) ] = 4 ( U i / U H ) 5 2 ν a | E ( t ) / E a | exp ( 2 ( U i / U H ) 3 2 3 | E ( t ) / E a | ) ,
( t 2 + c 2 × × + ω pe 2 ) E + ν c ( t E + c 2 t × × E ( t ) d t ) = Π ε 0 ,
ν c ( t 2 c 2 z 2 ) E x ( t ) d t + ( t 2 c 2 z 2 + ω pe 2 ) E x = Π x ε 0 ,
( t 2 + ν c t + ω pe 2 ) E ˜ z = Π z ε 0 .
[ t 2 c 2 z 2 + t ( t + ν c ) 1 ω pe 2 ] E ˜ x = 1 ε 0 t J L .
( t 2 + ν c t + ω pe 2 ) E ˜ z = e m e ε 0 c J L E L .
P NL ( t ) = ( 1 x k ) 0 χ ( 3 ) E x 3 ( t ) + x k 3 2 0 χ ( 3 ) ( h * E x 2 ) ( t ) E x ( t ) ,
h ( t ) = Θ ( t ) τ 1 2 + τ 2 2 τ 1 τ 2 2 sin ( t / τ 1 ) e t / τ 2 .
E L ( t , z = 0 ) = 2 I 0 c ε 0 [ 1 r e 2 ln 2 ( t τ p ) 2 cos ( ω 0 t ) + r e 8 ln 2 ( t τ p ) 2 cos ( 2 ω 0 t + φ ) ] ,
E ( t ) = ω 0 ( t ) a ω 0 cos ( ω 0 t ) + 2 ω 0 ( t ) a 2 ω 0 cos ( 2 ω 0 t + φ ) ,
P inst dc = ( 1 x k ) 3 4 0 χ ( 3 ) a ω 0 2 a 2 ω 0 cos φ .
P Raman = x k 3 2 0 χ ( 3 ) E ( t ) 0 + τ 1 2 + τ 2 2 τ 1 τ 2 2 e τ / τ 2 sin ( τ τ 1 ) E 2 ( t τ ) d τ .
P Raman dc = x k 3 2 0 χ ( 3 ) a ω 0 2 a 2 ω 0 [ T 1 cos φ + T 2 sin φ ] ,
T 1 = τ 1 2 + τ 2 2 4 ( τ 2 2 + τ 1 2 ( 1 4 τ 2 2 ω 0 2 ) α ( τ 1 , τ 2 , ω 0 ) + 2 τ 1 ω 0 ( τ 2 2 τ 1 2 ( 1 + τ 2 2 ω 0 2 ) ) β ( τ 1 , τ 2 , ω 0 ) ) ,
T 2 = τ 1 2 + τ 2 2 4 ( 4 τ 1 2 τ 2 ω 0 α ( τ 1 , τ 2 , ω 0 ) + 2 τ 1 τ 2 1 ( τ 2 2 + τ 1 2 ( 1 + τ 2 2 ω 0 2 ) ) β ( τ 1 , τ 2 , ω 0 ) ) ,
α ( τ 1 , τ 2 , ω 0 ) = ( τ 1 2 + τ 2 2 ) 2 + ( 2 τ 1 τ 2 ω 0 ) 2 ( 2 τ 1 2 2 τ 2 2 + 4 τ 1 2 τ 2 2 ω 0 2 ) ,
β ( τ 1 , τ 2 , ω 0 ) = ( τ 1 2 + τ 2 2 ) 2 + ( τ 1 τ 2 ω 0 ) 2 ( 2 τ 1 2 2 τ 2 2 + τ 1 2 τ 2 2 ω 0 2 ) .
P NL dc 3 4 0 χ ( 3 ) a ω 0 2 a 2 ω 0 [ 1 x k ( 1 2 T 1 ) ] cos φ .
ν f ( t ) = e m e e t τ c t E ( t ) e t τ c d t
J A ( t ) = e n δ N n ν f ( t ) H n ( t t n ) , J B ( t ) = e n δ N n e t t n τ c ν f ( t n ) H n ( t t n ) .
[ t J A ] ( ω ) i e 2 2 π m e n δ N n [ E ω 0 ( t n ) + 1 4 E 2 ω 0 ( t n ) ] ω ω 0 2 ,
[ t J B ] ( ω ) e 2 π n δ N n ν f ( t n ) e i ω t n ,
ω 0 t n n π 2 a 2 ω 0 a ω 0 ( 1 ) n sin φ
δ N n N a ( 1 e π W [ E ( t 1 ) ] τ 1 ) δ N ,
[ t J A ] ( ω ) i e 2 a 2 ω 0 4 2 π m e N δ N ω ω 0 2 cos φ ,
[ t J B ] ( ω ) 3 e 2 a 2 ω 0 2 π m e δ N ω 0 sin ( N ω π / 2 ω 0 ) sin ( ω π / ω 0 ) sin φ .
[ t J ] ( λ ) e 2 a 2 ω 0 ( 2 π ) 3 / 2 m e c δ N [ i 4 N λ 0 2 4 cos φ + 3 λ 0 sin ( N λ 0 π / 2 λ ) sin ( λ 0 π / λ ) sin φ ] .
[ t J A ] ( ω ) i ω e 2 π n δ N n r f ( t n ) ,
r f ( t ) = t ν f ( t ) d t .
z E ^ = i k 2 ( ω ) k x 2 k y 2 E ^ + i μ 0 ω 2 2 k ( ω ) ^ NL ,

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