1. Introduction

Over the last years a huge progress in the generation of sub-10fs pulses, direct out of the oscillator or by external pulse compression was made. Whereas the direct generation is limited to the tuning range of titanium sapphire and nJ pulse energy, compression was shown also in the near ultraviolet (>300nm), the visible and for more energetic pulses (µJ-mJ). Generation of energetic sub-10 fs pulses was demonstrated by self phase modulation in gas filled hollow waveguides [1], broadband parametric amplification [2] and spectral broadening of a probe pulse in impulsively excited gaseous media also filled in a hollow waveguide [3]. One of the advantages of the latter technique is the possibility to compress single pulses with control of the sign of the induced phase modulation by the delay of the probe pulse with respect to the pump pulse as it was theoretical shown in [4] and experimental proven [3].

In the ultraviolet (UV), which is very important for example for investigation of small molecules and biological specimen, the dispersion and nonlinear losses of nonlinear crystals like BBO and LBO limit the phase-matching bandwidth and pump power. Therefore it is not possible to combine nonlinear frequency conversion with pulse shortening as this was successfully demonstrated for the visible [2]. At present the methods to get broadband conversion to the UV are sophisticated phase-matching schemes with angular dispersion [5, 6] and four wave mixing in gas-cells (air) [7] which is less efficient. If the nonlinear mixing is performed in hollow waveguides the generated ultraviolet pulses are additional cross phase modulated by the strong pump pulses leading to additional spectral broadening. This combination enabled to generate 8 fs pulses at 266 nm [8]. The generation of high harmonics has proven to provide even sub-fs pulses [9] in the EUV range but has also for lower orders very low conversion efficiency.

Here we present a new approach for generation of energetic sub-30 fs ultraviolet pulses based on a combination of conversion to the UV by efficient second order nonlinear processes and additional pulse compression by impulsively excited rotational wave-packets in nitrogen. In order to increase the overall compression we also use hollow waveguides to lengthen the region of efficient impulsive excitation and probe pulse modulation. The basic idea for our experiment was proposed in [4]. The specific requirements for the UV/VUV spectral range, detailed aspects of compression and pumping and limitations are theoretical analyzed in [10]. In the present work we have to consider rotational wave-packets and not only the excitation of two dominant rotational levels. For nitrogen at room temperature the impulsive excitation leads to wave-packet like recurrences of fast temporal changes of the refracting index as a result of the dynamical alignment. Probe-pulse compression by such rotational wave-packets excited with ultrashort pulses at 800nm was first demonstrated in [11] in CO₂. The probe pulses at 400 nm were compressed down to 30 fs. A theoretical analysis of limits for pulse shortening with nitrogen was published in [12]. Since in that paper the excitation condition and preparation of nitrogen were much different to our experiment we also describe very briefly an analytical model for the analysis of our data and further optimization of the pulse compression.

The compression at 266 nm demonstrated here is also possible for pulses at wavelengths less than 205 nm where second harmonic generation with angular dispersion and higher order phase-matched sum frequency mixing are not applicable.

2. Experimental setup

Figure 1 shows a schematic of our experimental setup. All pulses were derived from a high power fs-amplifier (SPITFIRE) providing 45 fs at 800 nm with up to 2 mJ single pulse energy at 1kHz repetition rate. For the generation of the third harmonic (THG) 400 µJ were used. A 0.3 mm thick BBO crystal was used for the second harmonic generation (SHG). The sum frequency of the second harmonic pulses with the fundamental at 800 nm in a 0.1 mm BBO (oo-e) provided 4 µJ pulses with sub-50 fs pulse duration, measured by the same XFROG scheme used also for the determination of the compressed pulse duration (see below). For the nonlinear conversion the fundamental beam was down collimated to match the aperture of the nonlinear crystals which was 5×5 mm.

Since not all of the metallic mirrors used were optimized for high UV-reflection only 2 µJ of the THG were available at the entrance of the hollow waveguide. The waveguide holder was made from a glass cylinder with adapters for the windows and with a flange for filling and exhausting. Because the capillary had an outer diameter of only 0.3 mm it was additionally supported by a glass tube with an inner diameter of 0.4 mm, fixed by two plastic rings in the large glass cylinder. The inner diameter of the hollow waveguide was 128 µm. For our experiments we used a length of 25 cm. All experiments were performed at room temperature.

Up to 800 µJ of the fundamental radiation were available as a pump for the excitation of the gas in the waveguide. The delay between the pump pulse and the 266 nm pulse could be controlled by the optical delay line D1. A third part of the amplified pulses at 800 nm served as a predefined gate pulse for the XFROG measurement of the UV-pulses. Its exact shape and phase was measured by a commercial SPIDER device. The nonlinear process used for the XFROG was sum frequency mixing of 800 nm and 266 nm in a 10 µm thick BBO crystal. Measurement of the XFROG trace was performed stepwise by changing the position of optical delay D2 (for a fixed D1 position). The UV-spectrometer (McPherson Model 234/302 equipped with an ANDOR CCD camera) for registration of XFROG spectra and the spectral shape at 266 nm was connected to a computer which controlled also the delay lines D1 and D2. The data were evaluated by the FROG program supplied by FEMTOSOFT Inc.

 

Fig. 1. Experimental setup; D1, D2 optical delay lines; DM1 dielectric mirror for overlapping of the fundamental and the THG; P1, P2 CaF₂ prism; L1 MgF₂ lens, CM1 curved mirror, focal length 20cm, HWG hollow waveguide holder with MgF₂ windows; XTAL 10 µm BBO crystal. All mirrors shown as filled in black color and CM1 were metal coated (UV enhanced Al).

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3. Results

The adequate gas for ultraviolet pulse shortening by impulsive Raman excited temporal changes of the refractive index should fulfill the following requirements: a) good transmission in the UV; b) high Raman polarizability and c) vibrational or rotational periods somewhat longer than the pulse to be shortened. Theoretical investigations have shown that para-hydrogen [10] and nitrogen [12] are suitable for the compression of UV pulses down to sub-10 fs duration. Because para-hydrogen is very expensive and complicated to handle we have looked for alternatives and found that deuterium should also be appropriate. In the initial experiments we investigated nitrogen as well as deuterium; the former is a good candidate for excitation of rotational wave-packets whereas the latter should exhibit the inclusion of only few rotational levels for our bandwidth limited 50 fs pump pulses.

To compare these two gases we first measured the spectral changes of the UV pulses depending on the delay to the pump pulse. The results are shown in Fig. 2. Close to time delay zero one can see the spectral changes caused by direct cross phase modulation of the pump-and probe pulses in the cell and the material of the windows.

 

Fig. 2. Contour plot of spectra of the UV-pulses versus delay, 500 mbar N₂ (left) and 530 mbar D₂ (right), note the different time scales. The pump energy was 400 µJ at the entrance of the hollow waveguide having a diameter of 128 µm and a length of 25 cm.

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As expected nitrogen exhibits well separated recoveries of the wave-packet while deuterium modulates the probe spectrum sinusoidal-like with small distortions. More important is, however, the amount of the spectral broadening or shift, which is apparently larger for nitrogen.

Figure 3 shows in more detail the spectra measured with N₂ at a delay of approximately 4.1 ps. Time t0 is set by the first sign of spectral shifting. A more accurate value for the actual delay of the pump and probe pulses cannot be given because of the difficulty in defining the zero time delay. In the diagram we have shown the broadest spectra and the points of largest spectral shift which is also remarkable. It is interesting to note that close to the reversal points of the spectral changes the probe pulse spectra are shifted and only slightly broadened (see Fig. 3, spectra t0+140fs and t0+240fs). In principle this can be used for tuning in a range of about four times of the bandwidth of the input pulse simply by adjusting the pump power at a fixed delay D1.

 

Fig. 3. Selected probe pulse spectra from the recovery at 4.1 ps (Fig. 2) in comparison to the input spectrum, 500 mbar N₂, 128 µm capillary, 25 cm long.

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The compression setup with the highest throughput efficiency is a prism compressor consisting of two prisms in a double pass configuration. Unfortunately this setup has a fixed relation of the second and third order dispersion and therefore allows no perfect removal of the chirp. In order to avoid two-photon absorption in the prism material we chose for our setup Brewster cut CaF₂ prisms with apex separation of 22 cm. The compression was optimized by variable insertion of the second prism into the beam path. After some iteration steps we got 28 fs pulses at 266 nm with an energy of about 0.5 µJ. The energy before compression was about 1 µJ, the main loss in the compressor was caused by the retro-reflecting metal mirror between the two passes.

 

Fig. 4. XFROG trace (left), and intensity and phase (right) of the shortest UV-pulse with a duration of 23 fs obtained with a 128 µm waveguide, 25 cm long.

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With higher pressure in the waveguide we observed further spectral broadening and yet shorter pulses. The XFROG trace and the pulse shape for the shortest pulses with a duration of 23 fs is depicted in Fig. 4. In this case the N₂ pressure was 800 mbar and the energy of the compressed pulse was also about 0.5 µJ.

4. Theoretical model and comparison with the experimental observations

Pulse compression by impulsively excited wave-packets in N₂ has been theoretically studied in Ref. [12] for an 800 nm input pump and probe pulse. In this work the Schrödinger equation for a diatomic molecule in a laser field was numerically solved for a pump pulse specially shaped for maximum alignment of the cooled gas and a phase controlled input probe for pre-compensation of the dispersion of the output window. In the following we use an alternative approach for short pump pulses which is numerically less time consuming.

The interaction of a strong pump pulse with a diatomic molecule can be described by the Schrödinger equation of a rigid rotator in a time-dependent field (see, e.g., [12, 13] and references therein). If the pump pulse duration is much shorter than the dominant period within the excited rotational wave-packet, the solution after the pulse can be presented in the operator form as Ψ(θ,φ,τ)=exp(-iBJ ²τ)exp(iPcos²θ) Y_J,M(θ,φ), where B is the rotational constant, J is the operator of rotational angular momentum, θ is the angle between the molecular axis and the direction of field polarization, φ is the azimuthal angle, P=Δα∫A²(t)dt/4 the normalized pulse fluence, Y_J,M(θ,φ) is the spherical harmonic function with the initial rotational quantum numbers J, M, A(t) is the amplitude of the pump pulse, Δα=α_‖-α_⊥ is the polarizability anisotropy (α_‖ and α_φ are the components of the polarizability parallel and perpendicular to the molecular axis).

An explicit analytical expression of Ψ(θ,φ,τ) for this representation has been derived in [13]. Utilizing the solution of the Schrödinger equation at time τ after the pulse, we can find the polarization P_R for a weak delayed UV probe pulse. The propagation of the probe pulse is then described by the so-called reduced Maxwell equation which neglects backward propagating waves but does not assume the slowly varying envelope approximation (see e.g.[14]), ∂E_pr/∂z=-((n-1)/c)∂[a(η) E_pr (z,η)]/∂η, where E_pr is the field strength of the probe wave, n is the linear refractive index defined in atomic units by n=1+2πNα_av, α _av=(α _‖+2α _⊥)/3 is the average (isotropic) polarizability, N is the number density of N₂ molecules and a(η)=1+(Δα/α_av)(<cos²θ(η)>-1/3). Here <…> implies averaging over both coherent rotational excitation and the initial Boltzmann distribution at room temperature. Neglecting the influence of linear dispersion this first-order partial differential equation can be solved by the method of characteristics with an analytical solution given in [14]. With this solution we find a relation of the carrier frequency ω to its initial value ω0 given for small propagation lengths z by the expression ω/ω₀≅1-(Δα/α_av) ((n-1)z/c)∂<cos² θ(τ)>/∂τ. For the calculation of the alignment function <cos² θ(τ)> we consider the broad initial thermal rotational distribution (T=300K) of ¹⁴N² for pump pulse parameters as used in the experiments. Precisely, we have taken into account all initially populated rotational quantum numbers J up to J=26 covering 99.9 % of the thermal rotational distribution. We assume that both pump and probe beams are characterized by a Bessel-like lateral field distribution of the EH11 mode in the hollow waveguide. The normalized pump pulse fluence P for a pump pulse energy inside the waveguide of 100 µJ (which corresponds the measured output pulse energy in the experiment), a hollow waveguide diameter of 128 µm and Δα(800 nm)=4.6 a.u. (cf. [15] and references therein) is approximately P=2. Now the alignment function <cos² θ(τ)> for an arbitrary time τ after the pump pulse can be obtained carrying out thermal averaging. The result is seen on the left side of Fig. 5. Because we neglect centrifugal distortion effects the dynamical alignment is periodic with a revival period T_rev=8.4 ps. The computed evolution of <cos² θ(τ)> shows a recovery near τ=T_rev/2 and two smaller recoveries near τ=T_rev/4 and τ=3T_rev/4. This behavior arises from the statistical averaging over the broad initial rotational distribution. For J given, the dynamical alignment is roughly sinusoidally modulated with a period depending on J. After thermal averaging constructive interference takes place near τ=k T_rev/2 (k integer). Summing only either over all even or all odd J values constructive interference appears for τ=k T_rev/4. Thus, the recoveries in the vicinity of τ=T_rev/4 and τ=3T_rev/4 arise from the even-odd alternation of the rotational levels in ¹⁴N₂ due to the nuclear spin statistics. The corresponding result for the carrier frequency is shown on the right side of Fig. 5. Comparing with the experimental result in the left side in Fig. 2, one can see that both the typical recovery behavior with a period of 8.4 ps and the specific shape of the central frequency change in dependence on the time delay are well reproduced by our theoretical model.

 

Fig. 5. Left side - Calculated evolution of the alignment function <cos²θ> in N₂ at the time τ after the pump pulse Right side - Calculated change of the probe wavelength due to phase modulation.

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Next we calculate the spectrum, the spectral phase and the temporal shape of the compressed probe pulse after chirp compensation for a given optimal pump- probe delay time and Δα(267 nm)=5.1 a.u. (in accordance with the calculations using the CC3 model [16]), a pressure of 500 mbar, a waveguide length of 25 cm and a Gaussian probe pulse shape of 50 fs duration (FWHM) at the input.

 

Fig. 6. Power spectrum (red curve) and spectral phase (blue curve) of a probe pulse with 50 fs duration at delay τ=4.133 ps.

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In Fig. 6 the red curve shows the spectrum of the probe pulse at the output for a delay of τ=4.133 ps, where the temporal modulation of the refractive index change is near the maximum. In this case the spectrum is almost symmetrically broadened around the input frequency as shown in the red curve of Fig. 6. The spectral phase represented in the blue curve in Fig. 6 shows a continuous behavior with a positive almost linear derivative. The compressed pulse after linear chirp compensation has a FWHM of 14 fs. Note that for a delay of τ=4.267 ps at the minimum of the alignment the same spectrum is found as in the red curve in Fig. 6, but in this case the spectral phase has a negative second derivative. This behavior offers the possibility to compensate the chirp caused by the Raman response by a normal dispersive element. In our setup and without pre-compensation of the input pulses this effect is hidden by the large amount of material dispersion of the windows of the hollow waveguide holder and the lens for recollimation.

Comparing the theoretical results with the experimental observations we see that pulse compression in our model is slightly overestimated. The difference could be caused by several uncertainties in the assumed medium and pump pulse parameters, the absolute delay time used in the experiment, the influence of dispersion and other effects not accounted for in our analytical model. Nevertheless we can state, that our theoretical model describes the experimental results for N₂ in a satisfactory way.

5. Summary

In summary we demonstrated, for the first time to our knowledge, ultrashort pulse compression directly in the ultraviolet spectral region. Our technique is based on phase modulation in an impulsively Raman excited gas and allows additional spectral shift of the pulses by more than 4 times the bandwidth of the input pulses. The shortest pulse we obtained had a duration of 23 fs at a pulse energy of 0.5 µJ. Yet shorter pulses seem to be possible at higher pressure and a combination of a prism compressor with a deformable mirror for higher order chirp compensation. Initial measurements with higher pump energy in a single pulse indicated increasing losses in the waveguide so that probably pulse trains should be used to get higher excitation of the gas without ionization.

The advantage of our method is the broad spectral range where it is applicable; the lower limit is given by the transparency range of the gas used.