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Abstract
The miscellaneous applications of terahertz have called for an urgent demand of a super intense terahertz source. Here, we demonstrate the capability of femtosecond laser-driven wires as an efficient ultra-intense terahertz source using 700 mJ laser pulses. When focused onto a wire target, coherent THz generation took place in the miniaturized gyrotron-like undulator where emitted electrons move in the radial electric field spontaneously created on wire surface. The single-cycle terahertz pulse generated from the target is measured to be radially polarized with a pulse energy of a few milijoule. By further applying this scheme to a wire-tip target, we show the near field of the 500 nm radius apex could reach up to 90 GV/m. This efficient THz energy generation and intense THz electric field mark a substantial improvement toward ultra-intense terahertz sources.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) wave lying in the 0.1-10 THz range of electromagnetic spectrum has been intensively pursued during the last few decades as an ideal tool in various applications ranging from material to biomedical science. This new intriguing spectrum can be further developed in the high energy scope, where brand-new research areas still await explorations [1] such as THz-induced nonlinear effects in crystal or liquids [2,3], THz acceleration of electron bunches [4–6], THz-driven high-order harmonics generation (HHG) [7,8] and THz manipulation of the transient state of matters [9–11]. In particular, the recent developments in THz acceleration has put an ever-pressing demand on radially polarized, high energy THz sources to fuel the electrons into the relativistic regime. In order to fully explore these fields, THz pulses with above milijoule (mJ)-level energies or peak electric field strengths in excess of GV/m order are highly desirable.
Present available intense THz sources exist by means of relativistic electrons from accelerator [12], nonlinear optical crystals [13–16] and laser plasma interactions [17]. In the accelerator-based system featured by coherent radiation, relativistic electrons reside in a pulse length shorter than radiation wavelength thereby permitting the radiation intensity to scale quadratically with the bunch charge. This merit of coherent radiation has shown tremendous potential toward intense radiation with great tunability: THz pulse energy up to ∼600 µJ [12] and peak electric field of 1 MV/cm [18] has been reported from accelerator-based sources. However, in most laboratory experiments where table-top THz sources are favored, accelerators are generally large, costly and far from accessible. With nonlinear optical crystals, on the other hand, THz pulse energy approaching ∼900 µJ and 400µJ has been reported from centimeter-size organic crystal and LiNbO3 crystal respectively [13,19]. But their access to higher THz energy requires bigger crystals. In the ultra-intense laser intensity regime, tremendous improvements have been achieved by laser interaction with thin foils [20–23]. In the recent work by A. Gopal for example, over 1.5 MV/cm radially polarized THz field strength has been demonstrated on a 1J/30fs laser system [22]. And an astonishing record of THz burst energy up to 50 mJ was also reported by irradiating ∼60 J laser pulse on copper foil [23]. These THz sources are attractive for their compactness and incredible potential for developing higher power sources. But the transition radiation or sheath acceleration radiation that underlies this source generally would lead to a broadband spectrum (several THz). Furthermore, these sources also suffer from a low laser-to-THz conversion efficiency (generally below 0.1%) and large divergence angle compared to that of the optical crystals.
An alternatively method based on femtosecond laser-driven metal wires has been developed recently that produce coherent THz radiations in a way conceptually mimics a gyrotron-like undulator used in accelerators but with miniaturized size [24]. Specifically, about 28 µJ THz in the 0.1-3 THz range had been generated by a ∼3 mJ laser pulse irradiating a 50 µm diameter metal wire. It demonstrated approximate 1% energy conversion efficiency, a value comparable to that of optical crystals. In addition, the waveguide nature of the metal wires [25,26] further facilitates the transmission of generated THz and is significantly beneficial for applications that require coupling of THz waves to sub-wavelength scales. Nevertheless, the prospect of upscaling this scheme as intense THz sources remains to be determined.
In the present study, we demonstrate milijoule THz pulses generation from metal wires exposed to sub-joule level femtosecond laser at single shot mode. The radiated THz pulse energy exhibited a conversion efficiency approaching 0.5% that outperforms those performed at same laser energy scale. It should be noted that, the working principle of this system is also suitable for wire-like tips. By irradiating a wire with sharp tip at end, we show that electric field amplitude can exceed 90 GV/m at the tip end, which is, to the best of our knowledge, the highest electric field generated in the terahertz range.
2. Results
The experiments are performed on two different Petawatt facilities at Shanghai Institute of Optics and Fine Mechanics (SIOM) and Shanghai Superintense Ultrafast Laser Facility (SULF), with similar laser parameters [27,28]. A schematic of the experimental setup is sketched in Fig. 1. In our experiment, p-polarized high-intensity laser pulse (central wavelength 800 nm, 32 fs FWHM duration and 1 Hz repetition rate) of 700 mJ pulse energy splitted from the main pulse was focused to a spot radius of 6 µm (FWHM) by an f/5.5 off-axis parabolic mirror, resulting in a peak intensity of approximate 1.95×1019 W/cm2 on the target at an incident angle of 45°. In order to prevent fracture of the target, the laser system was operated in single-shot mode. A translation motor held one end of the target and pulled the wire along its axis after each shot to avoid cumulative energy deposition on the same spot.
Fig. 1. Schematic of the experimental setup for: (a) THz excitation on a tip target and the electro-optic measurement of the emitted THz spectrum; (b) THz excitation on a wire target and energy measurement with a Golay cell detector. Two pinholes separated with 1 mm distance were used for the wire to thread through and ensure a sharp emitting angle. The experiments were performed in a vacuum chamber with pressure of 10−3 Pa.
As shown in Fig. 1, two different wire-like targets were employed in our experiment. The first target we adopted is a 500-µm diameter tungsten wire with a sharp tip on one side (shown in Fig. 1(a)), which is widely used as a standard probe tool for scanning tunneling microscopy. It has a tip radius of 500 nm and a 500 µm diameter shaft connected via a taper of 10° half-opening angle. The pump pulse irradiates on the wire part of the target (about 10 mm distance to the tip end). Meanwhile, a p-polarized probe pulse splitted from the main pulse was negatively chirped via a grating pair and travels parallel to the wire axis. Their centers were separated by 5 mm distance. The emitted THz spectrum was recorded by 0.4-mm-thick GaP <110> crystal placed 12 mm behind the tip together with a polarizer prism and spectrometer. To avoid the possible damage from large number of guided electrons in the forward direction, a 1 mm-thick Teflon plate with a small aperture that allows the probe to pass through was placed in front of the crystal to spatially separate electrons. In the second experiment, we probe the generated THz energy by extending the wire target to the window of vacuum chamber with an over 10 cm long, 200 µm diameter tungsten wire as THz waveguide (shown in Fig. 1(b)). In this case the wire target was threaded through the Teflon plate and tightened by a small weight. Emitted THz energy was measured by a Golay cell detector.
Using the setup in Fig. 1(a), we characterized the emitted THz power spectrum and transient electric field through THz-induced electro-optic effect in the GaP crystal [29]. In the measurement, the probe pulse was linearly chirped and a temporal waveform of the THz field was linearly encoded onto the spectrum of the probe pulse [30]. Thus, we can be informed of the THz waveform by decoding the modulation on the laser spectrum. The typical results in Fig. 2(a) indicate a quasi-single-cycle THz pulse with center frequency located at 0.18 THz and FWHM bandwidth of 0.2 THz. The maximum peak electric field observed on GaP crystal in our experiment is 21 MV·m−1. Considering no focusing is applied in detection, the field is remarkably strong in comparison to the common implementations of electro optic sampling (EOS) where focused THz field is measured. Interestingly, such strong electric field may also give rise to nonlinear effects like harmonics generation in the GaP crystal, as some visible frequency spikes also appear in the frequency spectrum. Such phenomenon deserves further study with optimized experimental setup. Here, by evaluating the radiation’s spatial distribution from the end of the 500 $\mu $m tip target (described in the simulation part), the simulation results based on the electric field from Fig. 1(a) yield a summed THz energy in the whole space up to 2.0 mJ (among which 75% are in the forward direction). While for the 200 wire target, the energy is justified by the measured value with Golay cell in the wire experiment in Fig. 1(b). The whole space energy emitted from the target is 3.4 mJ (among which 88%, i.e. ∼3mJ is in the forward direction), corresponding to an energy conversion efficiency of 0.5%. In this measurement, Golay cell is used to measure the THz energy in the forward direction (∼3mJ) and the backward energy is calculated from a ratio obtained from the simulation. Energy difference in these two targets partially arises from the wire diameter influence on electron behavior [31], where thicker wires owns lower initial field strength and blocks more electrons due to the wider diameter. The wire-like shape also influences the power flow distribution emitted from the antenna, as described in the simulation part.
Fig. 2. (a) Emitted THz power spectrum and electric field waveform (inset) measured with setup 1(a). (b) Forward THz energy as a function of rotation angle α of a wire grid polarization placed before the Golay Cell detector in Fig. 1(b). The green and red lines respectively represent the measured THz energy without or with a metallic plate inserted after THz filter and block the left half area of the filter. The blue dotted line is cos2α fit with a -22°shift.
Polarization of the emitted THz pulse was measured by inserting a wire grid polarizer in front of the Golay cell in Fig. 1(b). We recorded the detected energy as a function of the azimuthal rotating angle α of the polarizer (α=0° corresponds to polarization in p-direction. The polarizer rotates clock-wise when viewed from Golay cell). As illustrated by the green line in Fig. 2(b), the measured THz energy seems to be α-independent, which may refer to circularly or radially polarization. This is further examined by placing a metallic shield plate which covers the left half area of the THz filter in Fig. 1(b). The results with the shield are shown by the red line in Fig. 2(b) and fitted by a cos square function displayed by the dotted blue line. The fact that a small shift angle presented in the cos square function indicates a spatially inhomogeneous radially polarized field where the downward component is stronger in vertical direction. This is in accordance to the Sommerfeld surface wave characteristics on a wire whereas the stronger downward component could be attributed to the fraction of energy guided downstream the curve presented at the end of the wire.
3. Simulation and discussion
To interpret our experimental results, we first consider the laser interaction process with the wire-like target using three-dimensional (3D) particle-in-cell (PIC) code EPOCH [32]. In the simulation, a 32 fs (FWHM) p-polarized laser pulse with intensity of 2×1019 W/cm2 (or normalized intensity a0=eE0/mecω0=3, where e is electron charge, E0 is laser electric field amplitude, me is electron mass, c is speed of light and ω0 is center frequency of the laser pulse) is incident from x-z plane with focal spot size of 7.5λ (λ=0.8 µm is the laser wavelength) at 45° incident angle. The target with 200 µm diameter and 18 µm lengths is assumed to have an exponential gradient of: $n(r )= 100{n_c} \times \exp [{ - {{(r - {r_0})}^2}/{{(0.5{\lambda })}^2}} ]{\; \; }({\; }r < {r_0})$, where ${n_c} = {m_e}\omega _0^2/4\pi {e^2}$ is the critical density of plasma, ${r_0}$ is the target radius and $r = \sqrt {{x^2} + {y^2}} $.
The results in Fig. 3(a) summarize the initial electron characteristics after laser irradiation, showing substantial portion of the emitted electrons carry momentum in the + z direction and flew upward or downward out of the laser incidence plane with the majority pointing +30° and +60° angle relative to the wire axis. A total charge over 0.7 nC is observed with a cutoff energy reaching 14.3 MeV. In a broader time scale, the escape of some energetic charges would give rise to a charge-neutralizing disturbance on wire, consequently excites a time-varying radial electric field on surface. By assuming the electric field form of: $E({r,t} )= {E_{initial}}({{r_0}/r} )\exp ({ - t/\tau } )\cdot \overrightarrow {{e_r}} ,\; (r \ge {r_0})$ [33], where ${r_0}$ is the target radius, $r = \sqrt {{x^2} + {y^2}} $, $\tau $ is relaxation time of the field and $\overrightarrow {{e_r}} $ is the unit vector of radial direction, we set the initial radial field amplitude derived from the PIC simulation results with E0=2.5×109 V/m and assumed $\tau = $65 ps. Thus, the THz radiation in the complex process of laser-plasma interaction is reduced to solve electron motions in classical electrodynamics. A few typical electron trajectories that circle along the wire are shown in Fig. 3(b).
Fig. 3. THz generation in the laser-wire interaction. (a) Electron characteristics after laser irradiation. The insets show respectively the momentum spectrum along x, y and z direction and its direction distribution in the laser incidence plane, where the magnitude represents electron number. (b) Electron trajectories from a portion of the emitted electrons that could sustain helical motion along the target. (c) The generated THz spectrum from electron helical motion.
We can infer the period of electron circular motion from electron trajectories in Fig. 3(c). When a 200 µm diameter wire target is applied, electrons near 1 ± 0.5 MeV energy range are more inclined to circle around the wire, corresponding to a circling period of 1-2 mm at initial. With this periodic movement and sub-wavelength undulation cycle length, amplified coherent synchrotron radiation could take place as demonstrated by [24]. The radiation spectrum was calculated follow the general Liénard–Wiechert potential [34] given by:
Femtosecond-laser-driven wire-based electron undulator has thus far sufficiently provided coherent THz source on the wire-like targets. But estimation of radiated THz energy still requires access to the radiation pattern from the THz surface waves at the terminal point of the wire-like target. To investigate the power flow in our experiment, we employed simulation with CST Microwave Studio [37], with which THz surface waves are assumed to have a Gaussian profile with 0.200 ${\pm} $ 0.125 THz spectrum range. The radiation patterns are calculated in the frequency domain. Figure 4(a) shows the 0.18 THz frequency power flow from a 10-mm long wire-like tip identical to the shot condition in Fig. 2(a). While a multi-direction power flow is presented from the result, most energy resides in the two lobes tilted 17° to the target axis. By substituting the experimentally measured value, we thus evaluated the emitted energy in whole space using the following equation:
Fig. 4. Simulated THz radiation pattern from tip and wire targets. (a) Radiation power pattern from the tip target. The blue line indicates the main lobe direction (which is 17° when 0.18 THz frequency is simulated). The inset represents a frame of electric vector distribution in the transverse cross section. (b) Left: 3D profile of the 0.18 THz frequency radiation power emitted from a 200 µm diameter, 60 mm long wire with a 1 mm diameter semicircle presented at end. Right: A slice distribution of the radiation intensity cutted at $\varphi $ = 90° (y-z plane), showing asymmetric energy distribution caused by the wire curvature. (c) Simulated electric field evolution (in y-z plane) respectively from the tip target (upper row) and wire (lower row, without curvature at wire end) in time domain. The t=0 has been set to the time when the field front arrives the waveguide end.
For wire targets with a length over 10 cm, however, performing three-dimensional simulation at such large scale is limited possible due to computation limitations. Whereas the emission of THz from metal antenna and conical structures has been intensively investigated [35,38,39], we took a shorter model to examine the impact of wire curvature presented at the end of the wire. The wire has been modelled with perfectly electric conducting (PEC) material of 200 µm diameter and 60 mm length, whose end is connected with a 1-mm-diameter semicircle (curved in y-z plane and pointed to –y direction). With simulated radiation power flow pattern shown in Fig. 4(b), we confirmed an asymmetrical energy flow introduced by the curvature. At 0.18 THz frequency, the energy ratio between the lower lobe, upper lobe (sliced by at $\varphi $ = 90° or y-z plane) and lobe in x-y plane (sliced by at $\varphi $ = 0°) is 1:0.7:0.88. Therefore, a simple estimation would result in a α=±arctan(1-0.7/0.88)=±19° polarization slant to horizontal direction if energy in + x or -x space is blocked. This result may reasonably explain the shift angle presented in our experimental results when fitted to a cos2 function, with the slight 3° difference possibly arises from Teflon plate level adjustment. And the forward radiation in the wire case contains 88% of the total energy.
Another intriguing problem we concerned is how electric field evolves on these targets. To gain insight, we performed time domain simulations with the tip target and a more general wire target without the curved tail at the wire end. The results in Fig. 4(c) show a few selected electric field distributions at three different time delays that are typified by the THz surface waves propagation (t=2ps); THz emission (t=14ps) and the radiation propagation (t=40ps) processes. Here for better comparison of these two targets, an identical THz energy is assumed on the two targets. Hence, according to Gauss’s flux theorem, the surface electric field of the THz surface wave on the 200 µm diameter wire is stronger than that on the 500 µm diameter wire part of the tip target at t=2ps. Afterwards, as the THz surface wave propagates toward the target end, it is clear the surface waves are spatially concentrated at the tapered part of the tip and eventually forms an enhanced field in close vicinity to the tip apex. The peak field amplitude at the tip is 25 times higher than the peak electric field on a 200 µm diameter wire (at the edge of wire end) and 200 times to that of its own 500-µm-diameter wire surface. This field enhancement features a promising direction for future usage of laser-driven taper wires as intense near-field THz source for matter control. In the longer distance range (Fig. 4(c)), however, THz distribution are shaped by the whole antenna shape other than the sub-wavelength structure at tip end. The spatial extent of electric field from tip target exhibits larger emitting angle compared to wire target. We estimated the field strength on the tip in our experiment using the result from simulation, and inferred a peak field amplitude of 90 GV/m in our experiment. Considering the tip geometry’s influence on field enhancement effect, much higher field could be expected by replacing the 500 nm radius tip apex with a shaper one [40,41].
The high energy conversion efficiency, radially polarization characteristic and good transmission property of the wire-based THz source has provided plenty advantages for applications like acceleration and HHG generation. However, for practical application of this THz source, good stability or endurance of this system becomes an imperative requirement in developing a steadfast THz source. In the present work, due to the high laser peak intensity on wire surface, the system is operated in single-shot. And the wire is moved 700 µm after each shot toward the opposite propagation direction of THz surface wave, so the laser beam and THz surface wave could always play on clean surfaces. Hence, the same target could be repetitively used if it could survive a single shot (in our case the minimum wire diameter that satisfies this requirement is 200-µm diameter). In our experiment for example, the available shot numbers on 200-µm diameter wire is limited by the travel range of our motor rather than other factors. Specifically, the 40 mm travel range grants about 40 shots on a same wire target. The measured root mean square energy fluctuation is about 18% on this same target. Because the energy jitter arises mainly from the later shots, it is likely the energy jitter arises from the displacement between the target and the beam focus, which situation could be ameliorated by careful adjusting the setup. If the longitudinal motion of the wire could be delicately aligned to be the same as its axis, we can even boldly expect a stable wire-based THz source at a constant repetition with alluring application promises.
4. Conclusions
In summary, we have experimentally demonstrated over 3 mJ THz pulse generation by irradiating a 700 mJ femtosecond laser pulse onto wire-like targets. The energy conversion efficiency of 0.5% signifies the currently highest THz pulse energy when pumped by equivalent laser energy level. Besides, owing to the THz generation mechanism, higher efficiency could be expected with further investigation on the electron behavior reliance on experimental conditions such as wire material and laser contrast ratio. The emitted quasi single-cycle THz pulse is measured to be radially polarized and centered at 0.2 THz. Associate with the experimental results, we have interpreted the observed THz characteristics in terms of laser-wire interaction process, coherent radiation generation and THz surface wave emission where the curvature at wire-end has been taken into consideration and explained the polarization shift observed in experiment. When a wire-tip target is employed in contrast to wire, field enhancement in the near field of the tip apex was found to produce a 200 times enhancement to the 500 µm diameter wire surface. We show by time domain field simulation that the 21 MV/m field amplitude measured at 13 mm from the tip indicates a 90 GV/m field in close vicinity of the 500 nm radius apex. The strong THz energy as well as the enhanced near field thus efficiently provide a powerful means toward the diverse applications where ultra-high intensity THz or extremely strong electric THz field is highly desired.
Funding
National Natural Science Foundation of China (11425418, 11874372, 11922412, 11974251); Shanghai Rising-Star Program; Strategic Priority Research Program (B) (XDB16); Shanghai Commission of Science and Technology (19PJ1410500); 100 Talents Program of CAS; Science and Technology on Plasma Physics Laboratory; Youth Innovation Promotion Association of the Chinese Academy of Sciences; Key Research Program of Frontier Sciences (ZDBS-LY-SLH018).
Acknowledgments
We would like to express our gratitude to Dr. Hui Zhang, Dr. Tongjun Xu and Dr.Jiancai Xu for providing some experimental materials and their support of our experiment.
Disclosures
The authors declare no conflicts of interest.
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