Adaptive compression of tunable pulses from a non-collinear-type OPA to below 16 fs by feedback-controlled pulse shaping

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1 Appl. Phys. B 70 [Suppl.], S125 S131 (2000) / Digital Object Identifier (DOI) /s Applied Physics B Lasers and Optics Adaptive compression of tunable pulses from a non-collinear-type OPA to below 16 fs by feedback-controlled pulse shaping D. Zeidler, T. Hornung, D. Proch, M. Motzkus Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, Garching, Germany Received: 1 October 1999/Revised version: 6 March 2000/Published online: 24 May 2000 Springer-Verlag 2000 Abstract. The self-controlled compression of widely tunable pulses in the visible generated by a non-collinear-type optical parametric amplifier is accomplished by a pulse shaper based on a 4f setup with a pixeled mask in the Fourier plane which is controlled by an evolutionary algorithm in a feedback loop. Pulse durations below 16 fs are achieved by shaping the pulses such that their second-harmonic signal is maximized. The optimization process generally requires less than five minutes. It is shown that the algorithm eventually determines the shaper settings which produce the global optimum for the SH signal. Moreover, pulses having propagated through a disturbing medium which introduced additional group velocity dispersion have been recompressed to below 16 fs. An acceptable value for the phase difference between two adjacent pixels of the liquid crystal mask is experimentally found to be 1.6. The described setup provides a powerful tool for delivering ultrashort tunable pulses to any location within an experiment, as well as tailored sub-20-fs pulses for optimal control studies. PACS: 42.65Re; v; g The rapid development of femtosecond laser technology has opened access to unforeseen applications in molecular and chemical physics. The high temporal resolution not only permits the real time observation of chemical reactions from bond breaking to new bond formation [1, 2] but also allows a manipulation of the dynamics such that the system is steered towards a desired reaction channel. This active control of a chemical or physical process is one of the paramount ambitions in physical chemistry. To achieve this goal, several control schemes have been developed which operate either in the frequency domain [3] with cw lasers or in the time domain [4] with broadband ultrashort lasers. A modification of the latter approach based on feedback-controlled shaping of ultrashort pulses was proposed by Judson and Rabitz [5]. Corresponding author. (Fax: / , mcm@mpq.mpg.de) The fundamental notion of this optimal control scheme is to take advantage of the temporal coherence property of the interference of light with the matter waves and thereby guide the system from the initial to the target state via a coherent bridge being built by the laser pulse. The tools for the experimental realization comprise a source of ultrashort laser pulses, a computer-controlled pulse shaper, and an optimization algorithm. The ultrashort laser pulse excites a sample, while some final state of the system (for example a product channel) is monitored. The amplitude of this probe signal serves as feedback for the optimization algorithm which controls the shaper and proposes a new pulse. The feedback signal from this modified pulse is again measured and relayed to the algorithm which proposes yet another pulse, and so forth until some convergence criterion is met. The crucial technological aspect is to generate arbitrarily shaped electrical control fields. In recent years, the temporal shaping of short pulses by complex filtering of their spectrum in the Fourier domain has proven to be a powerful and widely used technique to generate arbitrarily modulated pulses. Filtering in these devices can be effected continuously, for example by acousto-optical modulators (AOM) [6, 7], or discretely, for example by pixeled liquid crystal (LC) masks [8 12]. In the latter case, the steering parameters are the driving voltages fed to the individual LC pixels. Other techniques for generating shaped pulses have been proposed as well [13, 14]. The optimization algorithm not only has to cope with a possibly large number of parameters to be optimized, but also with inevitable experimental noise. Evolutionary strategies [15] and genetic algorithms [16] have proven robustness in finding the global optimum under experimental conditions [17]. Since no a-priori knowledge of the physical system is necessary, this feedback scheme consisting of fs laser, shaper, and algorithm should be applicable to all kinds of physical, chemical or even complex biological systems which are almost intractable on a quantum mechanical level. First examples of such optimizations were reported by the groups of Gerber [18] and Wilson [19] who reported on the dissociation of a complex organometallic compound and on the fluores-

2 S126 cence excitation of a dye molecule, respectively. Both experiments used a Ti:sapphire laser as the source for ultrashort pulses. Many physical and chemical systems which could be of interest in coherent control studies call for wavelengths outside the range of Ti:sapphire lasers and their harmonics. An instrument that is able to generate widely tunable tailored pulses is thus highly desirable. The concept of optical parametric amplification (OPA) allows to generate laser pulses that may be continuously tuned over a wide wavelength range. The shortest feasible pulse length obtained from commonly used OPA designs is typically determined by the pulse length of the pump laser. Control schemes as have been mentioned rely on an interference between distinct excitation pathways in a molecule. Their coherent excitation hence stipulates a broadband light source which makes short pulses mandatory. In this paper we demonstrate that a non-collinear OPA [20 23] as the pump source in the above described experimental environment provides a promising tool for coherent control studies. We combine the three above-mentioned techniques pulse shaping, feedback-controlled algorithm, non-collinear OPA design to actively shape tunable pulses on the sub- 20-fs timescale. The advantages and limits of adaptive shaping with special respect to the optimization algorithm will be discussed. As a first application of this tool, the optimization of the second harmonic (SH) of the ultrashort pulses for pulse compression [24 27] to below 16 fs is performed. The compression of broadband spectra produced by optical parametric amplifiers with non-collinear-type phasematching to pulse durations below 20 fs has commonly been achieved by prisms, gratings, and mirrors. For compensation of phases of order higher than two, a combination of these elements has to be used, which involves tedious and lengthy adjustment efforts. The task that remains, however, is that of maintaining the quality while delivering the short pulses to the experiment. This calls for the compensation of the group velocity dispersion (GVD) of second and higher orders introduced by dispersive elements installed in the beam path behind the compressor, such as cell windows, wave plates, cuvettes filled with solvents, etc. The main advantages of our setup are the swiftness of the automated compression procedure (typically less than five minutes) and the capability to compensate phase distortions of arbitrary appearance. Since a non-collinear OPA affords control of the central wavelength by variation of a single delay parameter without any further adjustments, we dispose of a tool which for the first time permits to perform automated spectral scans in the visible with sub-20-fs pulses. Fig. 1. a Spectra generated by changing the delay between pump and seed pulse. b Typical autocorrelation trace generated by a prism compressor amplifier system (CPA-1000, Clark-MXR Inc.). The parametric crystal is cut at θ = 27 and pumped with the frequencydoubled pulses (400 nm) atanenergyof20 30 µj. Temporal broadening of the signal due to idler walk-off is minimized by setting the angle between pump and seed beam such that the deviation between the projection of the group velocity (GV) of the idler onto the signal direction and the GV of the signal is minimized inside the BBO crystal. Representative spectra produced by solely varying the delay between pump and seed pulse are shown in Fig. 1. A non-collinear OPA emits strongly chirped output pulses and compressors based on prisms, gratings, or chirped mirrors must be installed in order to obtain short pulses. For the compensation of chirps raised by quadratic and cubic phases, combinations of prisms and gratings [23] or prisms and mirrors [22], respectively, have been used. With a conventional prism compressor, we routinely achieve pulse durations well below 20 fs. This figure is considered as a benchmark for the performance of our adaptive compressor setup. The autocorrelation measurements were performed in a non-collinear arrangement, either with a 10-µm BBO crystal, or with a 2-photon SiC diode [30], and yielded comparable values. Pulse durations were calculated by fitting the parameters of an assumed sech 2 pulse to the experimental data points. Figure 2 illustrates the design principles of the non-collinear OPA. This particular version 1 Experimental setup 1.1 Non-collinear type OPA The broadband spectra in the visible which are a requirement for short-pulse generation are obtained by amplification of a white-light continuum in a 2-mm BBO I crystal in a non-collinear beam geometry [21 23, 28, 29]. The continuum (seed) is produced in a 1-mm-thick sapphire plate from a small fraction of the fundamental pulses (800 nm, 100 fs, 1kHz) supplied by a commercial Ti:Sa regenerative Fig. 2. Setup of the two-color non-collinear-type OPA

3 S127 represents a compact (footprint approx cm 2 ) dual OPA which comprises two independently tunable broadband sources capable of generating sub-20-fs pulses. An input power of 400 µj easily produces 6 µj per pulse depending on the output wavelength. 1.2 Broadband pulse shaper We employ a pulse shaper based on a 4f setup (Fig. 3) which actively modulates the spectrum in the Fourier (frequency) domain to compensate for the phase of the OPA output. Basically, the design comprises two gratings which angularly disperse and recombine the pulses, and two focusing elements to accomplish the Fourier imaging. A LC mask is mounted in the Fourier plane [8 12]. An essential requirement for high-quality shaping is an accurate Fourier transformation from the time into the frequency domain and back. The pulses must pass the shaping unit undisturbed as long as no filtering is performed. Great care must thus be taken to avoid clipping of the spectrum at the aperture of the LC mask. Imaging distortion by chromatic aberration must be avoided since this will preclude a joint focus of the different colors at the second grating. Effects induced by an extended focus cannot be compensated by a suitable phase function. Therefore, lenses without chromatic correction are unacceptable for Fourier imaging. Our setup features a pair of 1/d = 600 /mm gratings and f = 150 mm cylindrical mirrors, as shown in Fig. 3 [31, 32]. Cylindrical optics are used to reduce the power density impinging on the LC mask and thus prevent damage. The offaxis angles are kept as small as possible (< 12 in the present case) to alleviate imaging aberrations introduced by the focusing mirrors. The LC mask (CRI SLM 256) consists of a stack of two arrays of N = 128 pixels which can independently influence attenuation and phase of the incident spectrum. The width of each pixel is 97µm, their mutual separation measures 3 µm. The overall accepted bandwidth of this shaper is (d/ f) N 100 µm 140 nm which is above that of the pulses generated by the OPA (see Fig. 1). To ensure that the shaper acts as a zero-dispersion compressor as long as the LC mask is inactive, we installed a pair of prisms before the shaper to compress the pulses close to OPA LC optimization algorithm f=200mm PMT FM AC BBO filter Fig. 3. Setup of the computer-controlled compressing unit. A flipping mirror (FM) steers the pulses either to the BBO crystal or to the autocorrelator (AC) the Fourier limit (< 20 fs) and then propagated them through the shaper. The device was then adjusted for shortest output pulses (again < 20 fs), indicating that it introduced no phase onto the spectrum. This alignment is crucial if a meaningful comparison between experimental and theoretical results is to be made in case the shaper is not used simply for compression, but rather serves to manipulate the pulse by introducing well-defined phase functions in control experiments. All experiments presented here have been performed at a fixed central wavelength to ease comparisons between individual datasets. Within the range of the accepted bandwidth, the central wavelength may be tuned without having to realign the shaper. Large changes of the central wavelength, of course, require a readjustment of the shaper. A mask dimensioned to accommodate the entire tuning range of the OPA would obsolete any alignment corrections. 1.3 Feedback loop To test the performance of the setup we removed the prism sequence. The uncompressed output pulses from the OPA centered around 620 nm are fed into the properly aligned shaper. Pulse compression is achieved by adjusting the LCD values in a feedback loop. The shaped output is focused by a spherical mirror ( f = 200 mm), frequency doubled (BBO, 10 µm) and recorded by a photomultiplier tube (PMT). A spectral filter (UG-11) in front of the PMT blocks the fundamental pulses. The PMT signal serves as feedback for an algorithm which controls the LC voltages (Fig. 3) [24 27]. Their adjustment for maximum second-harmonic (SH) signal represents an optimization problem which is tackled within a global optimization strategy. Other observables such as the spectral blueshift of the focused pulses [33] have also been used in iterative pulse compression schemes. Because we applied phase-only filtering, the energy of the pulses leaving the shaper is constant, and therefore, high SH intensity is indicative of short pulses. Pulse compression down to 11 fs by SH optimization has been demonstrated recently [27]. 1.4 Evolutionary algorithm Finding an extremum of a function depending on many variables is a problem that has been under investigation since the invention of differential calculus. The primary task of any optimization algorithm is to start from an ensemble of suitably chosen initial parameters and then to suggest a revised set which drives the critical observable towards the desired optimum, i.e. to generate new search directions in the (multidimensional) parameter space. Starting from this new parameter set, the procedure is reiterated until some convergence criterion is satisfied. Up to the early 60s, only deterministic schemes were used to this end. Later, algorithms using generators based on random schemes for new search directions, such as evolutionary strategies [15], genetic algorithms [16], and simulated annealing methods entered into competition with the classical deterministic schemes. Out of the large number of optimization algorithms which have been developed up to date, those based on indeterministic search generators have proven to be robust against inevitable experimental noise.

4 S128 We have implemented an evolutionary strategy which uses 48 vectors of parameters for the LCD voltages. These represent one generation. For each generation, the fitness value (SH signal) is measured for every setting of the mask. A new generation is built from the previous by mutation, which means changing the vector elements by some random value, and by recombination, i.e. by mixing of the vector elements of two parent vectors. Only those vectors corresponding to the highest SH values in the old generation serve as parents to produce the new generation. By successive repetition of this scheme, only those vectors which result in high SH values will survive and produce offspring ( survival of the fittest ). The initial generation is randomly chosen. Since mutation serves as dominant search operator, the extent of random change of each parameter must be intelligently restricted. Excessive step length will cause the new search points to be widespread in parameter space and no convergence will be achieved. Very small changes, on the other hand, will allow only very slow convergence, which is undesirable under practical aspects. We have hence implemented an adaptive step length control [15] which ties the amount of change to the number of foregoing mutations which had proven successful (i.e. produced a better SH value). The uncompressed output pulses of a non-collinear OPA are known to be mostly linearly chirped. It is hence suggestive to restrict the algorithm mainly to a search for polynomial phase functions. We thus chose a representation of the phase function, Fig. 4. a Autocorrelation trace behind shaper after phase optimization. b Phase values calculated from the coefficients retrieved by the algorithm. The phase was taken modulo 2π since this has no effect on the output pulse. c Comparison between uncompressed ( ) and compressed ( ) pulses Φ n = K k=2 ( ) n k N0 c k, n = 0,, N 1 = 127, (1) N with quadratic terms as lowest polynomial order k since constant (k = 0) or linear (k = 1) phase terms only produce a phase- or time-shift, respectively. The parameters c k and N 0 are optimized by the algorithm. Because the spectrum of the OPA is widely tunable, N 0 has been included as parameter to ensure that the offset of the phase function coincides with the center of the spectrum after the optimization has been accomplished. Alternative concepts of parametrization such as linear approximation or cubic splines were tested as well but resulted in many more loops of the algorithm while eventually achieving comparable pulse durations. 2 Adaptive pulse shaping As illustrated in Fig. 4, the shaping apparatus compressed the OPA pulses from about 260 fs to below 16 fs. The optimization procedure was confined to the search for second and cubic order phases, i.e. K = 3in(1).Figure5shows that the terminal value of the SH signal was approached after about 25 generations. At a pulse repetition rate of 1kHzand averaging over 50 pulses the adaptive compressor thus compensates the chirp and produces short output pulses in less than five minutes. This figure should be still reducible with a biased initial population taking advantage of a-priori physical knowledge such as the supposed sign of the chirp to be compensated. Fig. 5. Evolution of the averaged ( ) and best ( ) SH signal of each generation (equivalent to 48 trials) during the optimization process. A normalized value of 1 corresponds to the SH intensity when no additional phase is introduced by the mask, i.e. when all LC voltages are turned off A major problem in experiments that use ultrashort pulses is their faithful delivery to the location where the actual experiment is performed, especially when the ultrafast dynamics of molecules in liquid solvents is to be investigated. Usually, a collection of dispersive elements (cell windows, wave plates, polarizers, solvent-filled cuvettes, etc.) causing phase distortions of second and higher order is installed between the compressor exit and the position where the pulses are required to be short. We have mimicked this situation by installing an ethanol-filled 1-mm-path-length cuvette between shaper exit and SH crystal which broadened the output pulses. We then reapplied the algorithm and again obtained a pulse duration below 16 fs (see Fig. 6). An analogous experiment with a polarizer in the beam path which introduced a considerable chirp resulted only in sub-20-fs pulses (see Fig. 7) as will be discussed in the next chapter. As before, the optimization in both experiments was confined to the search for second and third order phases.

5 S129 Fig. 6. a Autocorrelation trace after phase optimization. An ethanol-filled cuvette has been placed between shaper exit and SH crystal. b Phase function retrieved by the algorithm thus be well below π. Figure 8 shows these differences for all three optimizations. With the polarizer in front of the SH crystal, the phase difference Φ attains 2.2, whereasit remains below 1.6 in all other cases. Since Φ should remain well below π, Nyquist s theorem may already be violated for Φ 2.2. Experimental evidence of this in the case of a linear phase function is the appearance of replica pulses. In the case of nonlinear phase functions, the effect is somewhat less trivial. Experimentally, a temporal smearing out of the pulse shape is observed which is responsible for a decrease of the SH signal. We believe that the algorithm found an optimal solution for the coefficients even when the dispersion to be compensated became excessive. Applying a phase function for which Φ was below its critical value proved insufficient to compensate the phase. Thus no short pulses were obtained and the SH signal remained below the expected value. On the other hand, applying the phase function necessary to obtain the shortest pulse would have violated Nyquist s theorem resulting in a temporal smearing out of the pulses and therefore, again in a SH signal lower than possible. The algorithm presumably applied only as much chirp as to compromise between these two scenarios. As net effect a residual phase remained after the optimization process which caused a longer pulse duration. For those cases where short pulses were obtained, Fig. 8 indicates that an estimate for an acceptable phase difference between two adjacent pixels is 1.6. LC Fig. 7. a Autocorrelation trace after phase optimization. A Glan Thompson polarizer has been placed between shaper exit and SH crystal. b Phase function retrieved by the algorithm 3 Limits of adaptive phase compensation The question arises why pulse restoration partly failed when a polarizer was moved into the beam path (Fig. 7), i.e. when a large amount of chirp had to be compensated. Two conceivable arguments come to mind: (a) shapers with a discrete phase filter cannot synthesize any deliberate amount of chirp and, (b) the algorithm may have missed the globally optimal solution. The pixelized mask used in our setup causes a discretely modulated spectrum which gives rise to special features that have to be taken into account. This has been discussed in detail elsewhere [9, 11, 12]. Nyquist s sampling theorem states that a periodic function must be probed at least twice per period, or twice over a phase interval of 2π. With reference to a phase function that is to be imposed onto a spectrum, a phase interval of 2π hence must be sampled by at least two pixels. The absolute value of the phase difference Φ between two adjacent pixels must Fig. 8a,b. Phase differences Φ = Φ n Φ n 1 between two adjacent pixels (a) and phase functions Φ n (b) retrieved by the algorithm (bottom) forthree different optical paths (: air, : ethanol-filled cuvette, : Glan Thompson polarizer)

6 S130 masks with a larger number of pixels should be able to improve the maximum amount of chirp that can be introduced onto a spectrum because more pixels then would cover the same spectral range. Reducing the amount of chirp to be compensated by precompressing the OPA pulses with an additional prism pair and using the shaper only to remove residual phase would bypass this limitation as well. Indeed, we use this additional prism pair when the capability of producing arbitrarily shaped pulses in real experiments on molecules is essential, though it has the disadvantage that these extra elements introduce losses (though small) and additional parameters which need manual adjustment. Since the demonstration of the limits of adaptive shaping is one of the prime purposes of this article, results concerning simple removal of residual phase are not presented here. The process of finding an optimum (for example, a maximum) within a merit function of many parameters largely depends on the structure of this function. The particular function may possibly have many local maxima separated by deep valleys, so that the optimization routine may be fooled by getting stuck in such a local sub-optimal maximum. To gain an insight on the structure of the merit function and to offer evidence that the algorithm has indeed found the global optimum, we performed a two-dimensional scan of the SH signal intensity vs. the second and third order phase coefficients c 2 and c 3 without any material in the beam path (see Fig. 9). Obviously, the function I SH = f(c 2, c 3 ) is unimodal with its maximum at c ± 10 and c ± 25 which comes close to the values c 2 = 162 and c 3 = 109 determined by the algorithm for identical experimental conditions. Thus, the algorithm has found the global optimum of the SH value although under idealized noiseless mathematical aspects in this case it was a trivial task. In this special optimization case and with this special parametrization a simple algorithm such as a Gauss Seidel strategy [15] should have been sufficient and should have found the optimal solution within a few seconds. We would like to emphasize that all this results from the special parametrization of the phase function which strongly reduced the number of free parameters and, furthermore, decoupled the parameters. With other parametrizations the merit function could have had a totally different structure. We would therefore not use deterministic algorithms in optimizations with unknown and possibly multimodal merit functions, since these algorithms may be sensitive to experimental noise [17]. With other parametrizations of the phase function, we found that the convergence speed as well as the final SH value was dependent on the internal strategy parameters of the algorithms. As a rule of thumb, we found that the more complex the optimization, for example the more parameters to optimize, the more careful the optimum has to be approached by a proper choice of internal strategy parameters mentioned above. This has been investigated in detail and will be published elsewhere [34]. 4 Conclusions The fast adaptive compression of tunable pulses in the visible to below 16 fs in the presence of additional dispersive material in the beam path before the autocorrelation measurement has been demonstrated. The scheme uses a combination of non-collinear OPA design, pulse shaper, and learning algorithm. Short pulses at locations wherever they may be required in the experiment can be produced automatically in less than five minutes. It has been shown that the algorithm found the global optimum solution for the mask settings. An acceptable limit for the phase difference between two adjacent pixels is experimentally found to be 1.6. Given the virtue that the center wavelength of the non-collinear OPA can be adjusted via a single delay without further adjustments, our setup is a powerful tool for spectroscopy experiments with ultrafast pulses. After all, the modulation of broadband spectra in the visible is a prerequisite for coherent control. Even more promising is the fact that our setup is also capable of attenuating the amplitude of each spectral component. Thus, even nasty spectra with side wings should be compressable almost to the Fourier limit by cutting off the unwanted spectral components, so that less effort has to be invested to generate smooth spectra. This will be the subject of future investigations. Acknowledgements. The authors thank K.-L. Kompa for continuous support of this project, T. Lang, R. 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