CEP after prism + chirped mirrors compressor

The commercial Femtopower front-end of the laser system is CEP stabilized

The initial CEP drift with the fast and slow feedback active was measured to be 176 mrad for a time of 30 minutes. The integration time on the spectrometer was 1 ms, 20 consecutive spectra are averaged for CEP measurement. After reducing the jitter of the acoustic wave of the AOPDF in the laser system (see next section) we decreased this noise to 100 mrad for a measurement of several hours Fig. 6.23. The same measurement was repeated to characterize the CEP drift between the 4 mJ pulses with the fast loop activated. The measurement trace presented frequent random jumps of the CEP and it was impossible to stabilize the CEP drift with the slow feedback loop. These random variations of the CEP between pulses can not be compensated with the slow feedback loop. We believe that this CEP drift was added by the compressor and in particular by the prisms (the chirped mirrors have been tested separately after the Femtopower without degradation of the CEP). Due to its large dimension (3 meters between the two triplets of prism) the compressor was not sufficiently isolated from the dispersion fluctuation caused by the movement of air between the prism. Probably with a correctly designed cover this problem can be solved. We did not continued in this direction because the propagation in the prisms also strongly degrades the spatial quality of the beam and thus its M2 . We thus tried a second configuration where the amplified pulses are compressed in a hybrid compressor consisting of transmission gratings and chirped mirrors. The good CEP stabilization we obtained in this configuration and its robustness convinced us to adopt this solution. 

Transmission grating + chirped mirror compressor

The laser setup with the transmission gratings + chirped mirrors compressor is shown in Fig. 6.24. The compressor is composed of two 600 lines/mm, fused silica holographic gratings (Wasatch Photonics). Substituting the prisms with the gratings implies some changes in the laser configuration, primarily due to the fact that the stretcher and compressor are not matched anymore. The prism compressor introduces negative third order dispersion (−95760fs3 ) and this compensates the positive third order dispersion of the bulk stretcher and the material in the amplifier (91064fs3 ). In the case of a grating compressor, the third order dispersion is positive and it is therefore added to the value of the stretcher and the material in the amplifier. Furthermore the value of the third order dispersion is directly proportional to the value of the second order dispersion. We decided to compensate all the third order phase with the Dazzler. This is possible only making a trade-off with the negative chirp introduced by the compressor. With a distance between the gratings of 70 mm for an angle of incidence of 13.9 °, the spectral phase added by the compressor is ϕ (2) = −50000fs2 and ϕ (3) = 70000fs3 . Again the final compression is then achieved after 32 bounces through the negatively chirped mirrors pair. The pulses are thus initially stretched to 7 ps. Decreasing the pulse stretching compared to the previous configuration limits the output pulse energy to 4 mJ. The spectral phase added by the Dazzler in the two compression configurations is reported in Tab. 6.25. The overall transmission of the compression stage is 53 % (60 % for the gratings compressor). Using grooved gratings instead of holographic gratings this efficiency can be increased to 83 %. Temporal and spectral characterization of the 2.1 mJ output pulses was achieved using an home made SPIDER, Fig. 6.26(a),(b), after a DazScope optimization. The spectrum does not exhibit any significant distortions over 100 nm bandwidth. The measured spectral duration is 25 fs, close to the Fourier transform limit. Furthermore, the proposed compression scheme preserves a good spatial quality. (M2 = 1.2). The Gaussian spatial intensity distribution of the focused beam is represented in Fig. 6.26(c). A few µJ are split off and sent into the collinear f-2f interferometer APS 800, Menlo System to monitor the relative CEP drift of the amplified pulses. Fig. 6.27(a) represents single shot fringe pattern registered at the output of the interferometer (2000 shots, the integration time of the spectrometer is 1 ms). No feedback loop is activated for this acquisition. The visible and wellcontrasted interference figure demonstrates the effective CEP stabilization of the laser pulses. This observation is corroborated by the measurement of the corresponding CEP drift on a short time scale (one minute) (Fig. 6.27(b)). The parameters of the APS are: acquisition time=1 ms, cycle loop time =100 ms, 20 consecutive spectra are averaged for CEP measurement. To evaluate the long term stability, the slow drift introduced by the amplifier is then pre-compensated by a feedback loop to the oscillator locking electronics using the measured CEP. Fig. 6.27(c) shows the typical CE phase stabilization of the system with feedback control. The RMS phase error over tens of minutes is 250 mrad. Furthermore we discovered that part of this noise was added by the jitter of the acoustic-wave of the Dazzler (section 6.9). The added CEP noise is in fact linearly proportional to the acoustic wave jitter. In this first configuration the acoustic rms jitter was measured to be 180-300 ps with a corresponding added CEP noise of 120-220 mrad. Decreasing the acoustic rms jitter to 70 ps noise reduces the added rms phase noise to less than 50 mrad. In this second configuration the measured RMS phase error is 180 mrad (Fig. 6.28) for a measurement of several (3) hours. Comparing this result to the measurement just after the Femtopower (after the Dazzler upgrading) we see that an additional CEP noise close to 80 mrad is added by the second amplifier and the grating compressor. Small distance between the gratings reduces the sensitivity to beam pointing and air currents in the compressor. In our case, the reduced groove density of gratings and the lower incident angle decrease CEP fluctuations associated with variations of gratings separation (thermal of mechanical drift). Previous studies have theoretically and experimentally demonstrated that the CEP drift stabilization in gratings-based setup may require interferometric control of the effective gratings separation, which nevertheless this introduce additional experimental complexity. In our configuration we overcome this limitation. 

Influence of the B integral on the CEP

The drawback of the small stretching factor of the pulses in the laser system, is the accumulation of a nonlinear phase induced by SPM during amplification. This nonlinear phase is evaluated measuring the B integral of the laser chain. I have shown in section 6.3 how the AOPDF can be used to measure and pre-compensate this spectral phase (DazScope) to avoid its adverse effect on the pulse compression. The B integral is also correlated to the added CEP noise. The intensity fluctuation of the amplified pulse shifts the CEP due to the nonlinear refractive index change. This shift can vary randomly from pulse to pulse and therefore can not be 139 compensated with an active phase stabilization loop. The refractive index change due to the nonlinear refractive index (∆n = n2I) is n = n0 + n2I. The length corresponding to a 2π shift of the CEP is given by: L2π,nl = 1/(d∆n/dλ) = 1/((dn2/dλ)I). (6.8) To make the situation simpler, we assume the intensity I constant over the length L; then the product of the intensity and the length is given by IL=λ n0Btot/2πn2. Where Btot, the B integral, is given by expression Btot = 2π/(λn0) R L 0 n2Idz. In this case, the CEP shift due to the nonlinear index is given by: δθnl = 2πL/L2π,nl = λn0 n2 dn2 dλ ! Btot. (6.9) The intensity fluctuation of ∆I results in the fluctuation of the CEP shift of ∆ϕ0 = δθnl∆I. The list of n0, n2, dn2 dλ and δθnl at Btot = 1, and the CEP fluctuation for a 1 % intensity fluctuation, is given in Tab. 6.29. For 1 % intensity fluctuation, the CEP fluctuation is on the order of 10−3 rad at Btot = 1.

Measuring the B integral

The B integral of a laser chain can be measured by injecting the amplifier with two delayed pulses and measuring the output replicas of these pulses with a high dynamic range correlator. To understand how two pulses can generate several replicas after amplification and compression 140 I first give here a short theoretical introduction. The most intuitive way to understand this temporal ”diffraction” is to consider it as a four-wave mixing (FWM) process [2]. As shown in Fig. 6.30, the delay between pulses is chosen so that the pulses partially overlap after the stretching. At any particular position in the overlapped part of the two pulses the instantaneous optical carrier frequencies are ω1 and ω2 (ω1>ω2). Since the pulses are stretched, the instantaneous carrier frequencies are ω1(τ ) = ω0 + b(τ + td/2) and ω2(τ ) = ω0 + b(τ − td/2), where td is the relative delay. The frequency difference is then δω = ω1 − ω2 = btd. The third order nonlinear polarization, PNL = χ (3) h E˜ 1(ω1) + E˜ 2(ω2) i hE˜∗ 1 (−ω1) + E˜∗ 2 (−ω2) i × h E˜ 1(ω1) + E˜ 2(ω2) i (6.10) gives FWM, SPM and XPM. In particular, the terms E˜ 1(ω1)E˜∗ 2 (−ω2)E˜ 1(ω1) and E˜ 2(ω2)E˜∗ 1 (−ω1)E˜ 2(ω2) are the FWM process of interest, giving the new frequencies 2ω1−ω2, and 2ω2−ω1. We see that 2ω1 − ω2 = ω1 + btd, so it is constantly blue shifted from ω1(τ ). Likewise, 2ω2 − ω1 = ω2 − btd is red shifted from ω2(τ ). When the chirped pulses are recompressed in the compressor, ω1 + δω = ω1 + btd is advanced by td relative to the ω1. Because the unshifted frequencies ω1 collapse to τ = 0 to form the compressed pulse, the blue shifted frequencies will collapse at τ = −td to form the pre-pulse. The same applies to the red shifted post-pulse. The partial overlap causes the bandwidth of the new pulses to be narrower, indeed no time casuality is violated. Another valid approach to understand the process is to look at the process as non linear propagation of the composite pulse, which contains the beat pattern. In this picture the new frequencies are generated as a result of SPM. The new frequencies are defined by: δω ∝ dI(τ )/dτ . 141 Because of the many rapid intensity oscillations due to the beating, new frequencies are generated efficiently. In particular blue shifted frequencies are generated in the rising fronts and red shifted frequencies in the decreasing front. All the new frequencies generated will interfere in the compressor to give the additional pulses. In particular the amplitude of these replicas compared to the main peak depends of the amount of B integral of the chain. A fit algorithm can then searches for a B integral parameter that minimizes a least-square error function calculated for the temporal sidebands. In our case two delayed pulses with the same amplitude are generated using the Dazzler present in the first amplifier (so strictly speaking we measure the B integral accumulated after the fourth pass of the first amplifier). The transfer function for generating these pulses is the same as that the one introduced in section 2.3.4 discussing the Phazzler. To measure the output replicas with sufficient dynamic range we used a third order correlator (Sequoia, Amplitude Technologies). In the absence of B-integral, the simulated third order cross correlation shows only three peaks and the energy ratio between the two pulses drives the symmetry of the resulting trace. This point is an important experimental control element; in particular, the relative injection-efficiency of the pulses into the amplifier, whose accurate control is experimentally challenging, can be evaluated that way. In the fit, the energy split ratio is adjusted numerically to fit any experimental asymmetry. In the presence of B-integral, side bands appear and the number and magnitude of the sidebands is adjusted to match the experimental data, using B as fit parameter. A typical measured trace is shown in Fig. 6.31. The multiples replicas separated by the temporal delay Td are clearly visible. An unexpected asymmetry is visible in the recorded traces. A possible explanation relies on the theory presented previously and is confirmed by the simulation of the replication process. When the spectrum of each individual pulse is numerically isolated, one sees that there is a sizeable frequency shift of the replicas when the pulse-to-pulse delay is comparable to the stretched-pulse width. Experimentally, the delay between the pulses was set to 1 ps, which leads to a frequency shift of 15 nm between the two first replicas at the two side of the main pulses. Such a frequency shift certainly impacts on the conversion efficiency of the measurement setup because of the finite spectral acceptance of the thick frequency mixing crystals in the cross-correlator. The fitted B integral in this case is 1.5 radians. The output energy was reduced in this measurement to avoid any damages in the Ti:Sa crystal. We can then estimate a B-integral of 3 radians at full energy. From Tab. 6.29, the contribution to the CEP noise considering an intensity fluctuation of 2 % is then < 50 mrad.

 Control of the CEP with the Dazzler

Without feedback loop, the CEP drift of the amplified pulses was small enough over several minutes to demonstrate, for the first time, that CEP control could also be performed using the AOPDF inserted in the Femtopower. We do this by controlling the CEP of the acoustic waves in the AOPDF. This first experiment was done before the reduction of the jitter of the acoustic-wave. The physics of AOPDF is based on a stringent acousto-optic phase-matching relationship between the acoustic and optical wave vectors. As for any phase-matching relationship, this relationship has its counterpart in terms of spectral phase and the acoustic and optical spectral phases are directly linked by the expression : ϕopr,in(ωopr) + ϕacc,in(ωacc) − ϕopr,dif f (ωopr) = π/2 (6.11) where, ϕopr,in and ϕopr,dif f are the spectral phase of the input and diffracted optical pulses, and ϕacc,in(ωacc) , is the spectral phase of the acoustic pulse. In this configuration, the electronic generator of the AOPDF is able to control the absolute phase of the acoustic wave within 160 mrad (rms time jitter between the trigger and the RF clock), which translates into the optical domain as follows: the CEP of the diffracted pulse can be changed with respect to the CEP of the input pulse by an arbitrary amount with 160 mrad (π /20) accuracy. Fig. 6.32 shows the effect of successive CEP jumps of -π, +π, -π, +π/2, +π/2, +π/2, +π/2 applied by the AOPDF, thereby demonstrating the ability of the AOPDF to exert control over the output CEP. Note here, that the feedback control was turned off to avoid automatic correction of the CEP jumps 143 by the oscillator locking electronics. These phase steps were performed at a low repetition rate, i.e. not limited by the refresh rate of the AOPDF. By pre-computing and pre-loading a set of RF waves with different CEP values (e.g. 64 waves covering the 0-2π interval) in SRAM memories, the RF generator is able to change the CEP phase drift at high repetition rate. A demonstration of this achievement is shown in Fig. 6.33 which shows the CEP measured function of time. The word ”LOA-ENSTA” was written changing the CEP between successive shots. The vertical segments were obtained by choosing random values of CEP. The baseline (-2.5rad) shows the low CE phase drift of the system during this experiment. This control of the CEP opens the path to closed-loop CEP drift corrections at high repetition rates without any moving parts or retroaction on the oscillator. This is the subject of the next section.