A nonlinear filter using rotation of the polarization ellipse in air is investigated. Scheme to enhance the temporal contrast is developed for a double-CPA multi-terawatt Ti:sapphire laser. It supports an energy level of millijoule and has a high efficiency. The method allows suppression of the ASE pedestal, pre- and post-pulses by 3 orders of magnitude and also steepens the pulse front. For the physical interpretation of the results, numerical simulation of the filtering is performed.
©2004 Optical Society of America
Modern Ti:sapphire laser technology allows one to develop laser systems supporting multi-terawatt power level [1–5]. It also allows controlling the spectral phase of the recompressed pulse which makes it possible to reach recompression with nearly transform-limited pulse duration and steep laser pulse fronts. In combination with a high quality of the laser beam, this allows one to reach intensities of 1019–1020 W/cm2. Typically the Ti:sapphire lasers have an amplified spontaneous emission (ASE) background ranging between 10-7–10-5 of the peak laser intensity. The principal source determining high ASE level of Ti:sapphire lasers is a front-end, especially the first amplifier (multi-pass or regenerative). It has the highest amplification (106–108) in the laser system and weak seed energy. Low energy level of the master oscillator, losses in the stretcher, additional implementation of means for spectral phase correction etc. result in a low starting signal level and thus high noise (ASE) in the amplifier. The presence of the ASE pedestal limits performance of the laser systems and does not allow pre-pulse-free interaction of short laser pulses with matter.
The ASE pedestal typically has a duration of several nanoseconds. There are several ways to overcome the problem. A modern Pockels cells having a sub-nanosecond optical window (Kentech instruments for instance) can subtract a substantial part of the ASE pedestal as well as possible short pre- and post-pulses [6,7]. But, within the duration of the stretched pulse, the pedestal overlays the phase-modulated pulse and thus the ASE cannot be reduced by this method. New schemes of more powerful oscillators  and multi-pass amplifiers , which can allow reduction of the ASE-level, are discussed and reported in the literature. Direct pre-amplification of short laser pulse preceding the first amplifier allows one to improve the laser ASE contrast . Recently utilization of an OPCPA technique for the front end of a Petawatt Nd:glass laser allowed the authors to reduce intensity of pre-pulses to a level of ~ 10-8 . Another possible solution of the temporal contrast problem is realization of a laser system with two chirped pulse amplification stages, including an intermediate pulse recompression and implementing nonlinear methods to subtract the ASE pedestal (double CPA, DCPA). In this case choosing of the right method to filter the short pulse plays the key role.
The general requirements to the system for nonlinear temporal pulse cleaning follow from the schemes of the Ti:sapphire lasers. Since the ASE - associated problem arises in the first stage it is reasonable to temporally ‘clean’ the pulse just after this stage. Typically the first amplifier delivers pulses at the millijoule level. Thus the filtering system has to support this energy level, have a uniform spatial mode for further amplification, allow at least 1000 times suppression of the low intensity signal (to be able to reach the ASE contrast level of 1010) and have high transmittance (higher than 10%). Based on these criteria we tested various schemes for nonlinear pulse filtering including a saturable absorber  and a nonlinear Sagnac interferometer . We found that the first method does not allow combination of the high ASE suppression with high pulse transmission. The Sagnac interferometer has a drawback associated with the fact that the beams in the two arms of the interferometer have different phase, amplitude and in most cases a mode size. This leads to formation of the output beam mode that is not suitable for further amplification.
The experiments on temporal pulse filtering using the technique of nonlinear ellipse rotation  (NER) in a hollow waveguide filled with a noble gas done by D.Homoelle  and colleagues have demonstrated very promising results satisfying nearly all of the above mentioned parameters, especially a good spatial mode, which is very important for the practical use of the laser beam. Unfortunately, similar to experiments using NER in optical fibers , the technique does not support the millijoule energy level required for the DCPA. Improvement of the NER filtering method to make it suitable for the DCPA laser was done within the European SHARP -project in MBI (reported here) and in LOA Palaiseu .
2. Experimental setup
The experimental scheme is presented in Fig. 1, where the front end of the MBI DCPA laser is shown. It consists of a maser oscillator, a stretcher, a multi-pass amplifier and a compressor. The master oscillator (Femtolasers) delivers 20-fs transform-limited pulses. The stretcher is based on a cylindrical mirror telescope and temporally expands the optical pulses to ~ 300 ps duration. This part of the installation is shared with our 100 - Hz Ti:sapphire laser system, thus it enables relatively high losses, leading to ~ 20 mW power seeded into the amplifier. A single pulse is picked out of the pulse train by the Pockels cell and gets amplified in the multi-pass amplifier to 1–2 mJ. The amplifier is pumped from both sides by altogether 65 mJ of a frequency-doubled pulse of a YAG laser running at 10 Hz. The cavity consists of two spherical mirrors with a hole to let the pump beam go through. The mirrors have slightly different curvature radii of 1000mm and 984 mm. The mirror aperture of 90 mm allowed us to reach up to 12 passes through the active medium. However, at the given pump energy, 9 passes through the active medium were sufficient to reach the energy level of 2 mJ. After the fourth pass in the cavity, the pulse goes through an additional Pockels cell, which allows us to partly suppress the ASE - pedestal. After amplification, the pulse passes through an additional Pockels cell. Both Pockels cells have optical windows of ~ 5 ns and do not have influence on the ASE pedestal in the vicinity of the laser pulse. The amplified pulse is injected after that into the compressor. The compressor consists of a pair of diffraction gratings with a constant of 1400 lines/mm. It has a throughput of ~50% and recompresses the pulse to nearly the transform-limited value. Thus the recompressed pulse has a duration of ~ 40 fs and an energy of ~1 mJ. This pulse is then injected into the nonlinear temporal filter suppressing the ASE pedestal and pre-pulses.
The nonlinear filter consists of a set of two crossed polarizers, two achromatic λ/4 plates and a cavity consisting of two mirrors similar to the cavity of the multi-pass amplifier. The first λ/4 plate makes the beam slightly elliptical to ensure the nonlinear effect. It is oriented so that its fast axis is turned 22.5° from the input polarization plane. The second one compensates for the polarization ellipse induced by the first plate. The injected elliptically polarized beam gets focused with a f = 750 mm lens to the confocal point of the mirrors. Similar to the cavity of the multi-pass amplifier the scheme allows up to 12 passes through the cavity. During each roundtrip the beam gets focused near the confocal point of the cavity. Difference in the focal lengths of the mirrors allows one to slightly decrease the beam size after each pass and thus to increase the waist length. Assuming that the cavity mirrors and the out-coupler do not additionally change the polarization state of the laser beam, the low-intensity pulse passing through the system gets turned away from the optical axis by the second crossed polarizer (s-beam in Fig. 1). After passing through the cavity the beam accumulates an additional phase ΔΦnl ≈ n 2 Iz, which depends on the intensity and the interaction length. Since the nonlinear interaction takes place at high intensity and thus within the beam waists, the scheme implementing multi-passing allows one to tune flexibly the total length of the nonlinear interaction and thus the transmission efficiency. It allows a total length of the waist of several tens of cm.
3. Experimental results
3.1 Filtering efficiency
In the experiments we examined the characteristics relevant to application of the filter to DCPA. They are the mode, spectrum, efficiency and ASE suppression as a function of the pulse chirp. Since our scheme allows working in a single-pass configuration we started the experiments from a single pass set-up. To reach a phase shift in air close to π, which is associated with substantial pulse filtering within a single pass, one needs to focus the beam to an intensity close to 1014 W/cm2. This is beyond the level of plasma formation in air and leads to several non-desirable consequences. Strong ionization of air in the beam waist leads to self-guiding of femtosecond laser pulses as observed earlier . The beam starts to collapse which leads to a substantial reduction of the beam mode and of the conversion coefficient. With a single pass configuration, prolongation of the laser pulse (chirping) did not lead to a substantial improvement, because reduction of the pulse intensity below the ionization level did not allow to reach the nonlinear phase substantial for efficient pulse filtering. We found that under these conditions it is impossible to get reproducible pulse spectrum and mode. We did not reach a filter transmission higher than 10%.
The best experimental results were obtained with the four-pass arrangement. The following results correspond to this arrangement. We found a very strong dependence of the filtered beam properties on the input pulse chirp. The chirp sign and the amplitude were varied by changing of the grating distance in the compressor. The near-field distributions of the short filtered pulse depending on the input pulse chirp are presented in Fig. 2. The three cases correspond to the following parameters of the incident pulse. Positively chirped pulse of ~ 200 fs duration [Fig. 2(a)], fully recompressed pulse of 40 fs [Fig. 2(b)], and negatively chirped pulse of 400 fs [Fig. 2(c)]. The case of the fully recompressed pulse showed a strong filamentation of the beam associated with ionization of the gas and formation of a two-ring structure in the near-field distribution, which matches the incident beam diameter. This reproduces results obtained with a single-pass scheme. The case of the negatively chirped pulse also shows a slight beam mode reduction. In both cases the filtering efficiency did not exceed 15%. With our laser parameters, the best filtering throughput as well as the best mode and spectrum were reached with a slightly positively chirped pulse [Fig. 2(a)] (intensity ~ 1013 W/cm2). The ratio between the energy of the ‘clean’ and residual pulses obtained in our experiments for the optimized case amounts to > 50%. One needs to mention that one of the most important features of this nonlinear temporal cleaning method is the high quality of the spatial mode. Figure 2(a) reproduces the typical near field distribution of a filtered beam. We found that positions of the beam waists of a propagating through the multi-pass cavity beam must not overlap. Efficient temporal and spatial cleaning of the pulse takes place also without a pinhole. This has a clear reason. The phase shifts required for efficient NER arise mostly in places, where the intensity has a maximum. Under our experimental conditions this corresponds to regions with the highest intensity in the far field (beam waists). Since the NER filter selects the most intense part of the far field distribution, it does the same as the spatial filter with the only difference, that not a pinhole but the NER performs the selection. Thus the cleaning takes place in temporal and spatial domains simultaneously.
3.2 Spectral reshaping
The spectra of laser pulses passing through the nonlinear filter are presented in Fig. 3. Similar to Fig. 2 the three cases of different chirp sign are shown. One can see that in both cases of the chirped pulses the filtered clean beam experiences a blue shift and narrowing. Starting from the 30 nm FWHM pulse, the filtered pulses have spectral width of 20 nm (positive chirp) and 12 nm (negative chirp). In addition, for the positively chirped pulse the front (red wing) is filtered out. The filtered out pulse is modulated, which demonstrates phase modulation taking place in the process of nonlinear filtering. The case corresponding to the recompressed pulse [Fig. 3(b)] shows strong modulation of the pulse spectrum in both the clean and the filtered out beams associated with self phase modulation, which changes strongly from shot to shot.
3.3 Contrast enhancement
The contrast enhancement was examined with a third order cross-correlator developed in the frame of the SHARP-project . The cross-correlator allows one to measure the pulse shape over > 10 orders of magnitude of the pulse intensity. Unfortunately, the dynamic range of the device strongly depends on the incident pulse intensity. The full dynamic range of 10 orders of magnitude was experimentally realized with pulses of ~ 1.5 mJ energy and 40 fs duration. The cross-correlator linearity and dynamic range were cross checked with other similar devices developed within the SHARP-project. Typically, the ASE pedestal of the multi-pass amplifier did not exceed the value of 10-7 of the peak intensity. To make the effect of filtering more visible, in the experiments we specially reduced the pulse coupling in the multi-pass amplifier to allow a pedestal level close to 10-6 of the main peak. Slight chirping of the pulse required for the optimal filtering in addition to limited filter transmission has resulted in a reduction of the intensity entering the cross-correlator. Amplitudes of the second and third harmonic signals generated in the correlator dropped down and the noise appearing in the temporal scans increased. Thus a dynamic range of only ~ 107 was available for the characterization of the filtered pulse. Since the ASE level of the incoming pulse had an amplitude slightly higher than the dynamic range of the correlator, we could not observe the enhancement of the ASE contrast directly (see Fig. 4).
The temporal shapes of the laser pulses in front (blue) and behind the filtering system (red) are presented in Fig. 4. We estimated the attenuation of low-intensity part of the laser pulse in the following way. An etalon was installed between the compressor and the filtering system to produce a post-pulse. Reduction of this post-pulse intensity after passing through the filter was taken as a measure of the filter contrast enhancement. The corresponding post-pulse appearing at ~ 15 ps after the main pulse is visible in the incoming correlation. The pulse vanishes in the correlation of the temporally filtered pulse. This gives an estimate of the filter attenuation of ~ 103. An additional influence of the filtering can be observed at the fronts of the filtered pulse, which become more steep.
Analysis of our experimental results shows that the scheme presented here allows one to suppress low-intensity pulses and the ASE -pedestal at least by a factor of 1000. Maximal contrast enhancement that can be achieved is limited by the polarizing quality of the optical components used in the setup. The achromatic λ/4 wave plates are required to reach a phase shift uniform over the pulse spectrum, or at least over 50 nm. An additional polarization test of dielectric coated mirrors placed between the wave pates has to be performed. In fact the contrast enhancement in our experiments was limited by the quality of the dielectric coated mirror, which was at nearly normal incidence (out-coupler of the filter cavity in Fig. 1), This restricted the low-intensity attenuation to 1000. We tested the polarizing properties of the optical components used in our system with the beam of the master oscillator (~ 60 nm FWHM). The set of crossed calcite wedges used as polarizers, including cavity mirrors and an out-coupler, allowed us to reach the attenuation factor of 3.8∙10-6. The achromatic λ/4 wave plates (CVI) used in the filter reduced the attenuation to 2∙10-5.
3.4 Compressibility and shot to shot stability
We checked temporal compressibility of the filtered pulse and found the following. Since a 10 Hz Ti: sapphire laser was used in our experiments, the shot to shot energy variation was not better than 10%. For the case of optimum filtering, reduction of the spectral width and variation of the seed energy resulted mostly in fluctuations of the transmitted pulse spectrum, leading to ±15fs oscillations of the pulse duration around the average value of 50 fs.
4. Numerical simulations
For better understanding of the experimental results, we have performed a numerical modeling of the pulse cleaning process. Since we mainly aim to understand the temporal and spectral changes caused by the filtering, we have not considered the influence of nonlinear effects on the evolution of the transverse structure of the beam, such as filament formation. The effects of group-velocity dispersion are included approximately, by introducing a corresponding additional chirp to the input pulse. The chirp corresponds to a propagation of 2 m in air, which is the optical path in our system, with a group-velocity dispersion coefficient β”=0.2 fs2/cm. The field of the output beam is found using a time-dependent field transmission coefficient T(t) given by, e.g., 
Here Δϕ(t) = ω(Δn K (t)+Δn R (t)+Δn P (t)) z/c is the phase shift, caused by Kerr nonlinearity, Raman nonlinearity, and a plasma contribution, which is the same for both polarizations. The phase difference of the two linear polarizations is denoted by Δψ(t) = ω(Δn K (t)/3+Δn R (t)/3)z/c, and α0=π/8 is the angle which characterizes the input polarization. Here z is the effective nonlinear propagation distance, i.e., the total length of the beam waists, which is assumed to be 12 cm. The individual contributions to the phase shift are given by
Here I(t) is the pulse intensity, f = 0.5 is the fraction of the Raman response in the nonlinearity, n2 = 3.2×10-7 cm2/TW is the nonlinear refraction coefficient of air, T1 = 76 fs the Raman relaxation time and ωR = 0.016 fs-1 the Raman frequency, A = + )/ω R normalization factor, is the electron density, β MPI=4.46×102 cm-3/fs (cm2/TW)7 is the multiphoton ionization coefficient, K=7 is the multiphoton ionization order, e is the electron charge and me is the electron mass.
The results of the numerical calculations are presented in Fig. 5 for the positively chirped input pulse with parameters corresponding to the case of Fig. 3(a). In Fig. 5(a) the comparison of the input (red) and cleaned (green) temporal shapes shows suppression of the temporal wings of the pulse. The suppression of the wings is around 3∙103 for a relative intensity of ~10-3, in agreement with the suppression of the post-pulse shown in Fig. 4. The transmission is higher at the back front of the pulse. The spectrum of the transmitted pulse, as shown by the green line in Fig. 5(b), is shifted to short wavelengths. Both of these spectra for positive-chirp pulse exhibit qualitative agreement with the corresponding experimental spectra shown in Fig. 3(a). The reason for the higher transmission for the short-wavelength components is the delayed nonlinear contribution ΔnR of the Raman effect, which increases the phase shift between the two polarizations at the trailing edge of the pulse. Thus the back front of the pulse, which contains shorter wavelengths for the positive chirp as shown by the blue curve in Fig. 5(a), experiences a higher transmission coefficient. The overall shift of the spectrum after the passage through air (before the filter) toward shorter wavelengths is due to the plasma contribution ΔnP(t) to the phase of the pulse, which creates time-dependent phase modulation and thus changes the spectrum.
For the case of the unchirped input illustrated in Fig. 3(b) and Fig. 6, the phase modulation Δϕ(t) is much larger than in the previous case due to the stronger nonlinearity. This results in a complicated dependence of the instantaneous wavelength on the time, and correspondingly to the complicated spectral structure with several peaks and strong broadening as shown in Fig. 6(b) and also experimentally observed in Fig. 3(b). The spectral shift toward the shorter wavelength due to plasma contribution is also clearly present. The agreement between the theory and experiment in this case is worse because the filamentation effects, not accounted for in the model, notably influence the propagation for the compressed and therefore intense pulse. We have also performed the numerical calculations for the negative-chirp case illustrated in Fig. 3(c) (theoretical curve not shown), and found qualitative agreement.
In conclusion we have demonstrated that the method for short pulse filtering based on nonlinear rotation of the polarization ellipse in gases can be realized at a millijoule level with high efficiency. It satisfies most of the requirements for implementation at the double CPA laser systems and allows one to improve the ASE temporal contrast at least by a factor of 1000. The reported set-up is used as a front end of the MBI double CPA laser system, which allows reaching the ASE contrast of > 1010 . We believe that driving the temporal filter with a kHz laser having higher energy stability from shot to shot can substantially reduce the temporal fluctuations observed in our experiments. The spectral narrowing associated with using air as a nonlinear medium can probably be also improved using other gases.
The work was supported by the European Community - Access to Research Infrastructure action of the Improving Human Potential Program (SHARP - project, Contract Nr.: HPRI-CT-2001-50037), as well as by Deutsche Forschungsgemeinschaft.
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21. M.P. Kalashnikov, E. Risse, and H. Schönnagel, Max-Born-Institute Berlin, are preparing a manuscript to be called “Double-CPA laser : way to temporally clean pulses”.