1. Introduction

Femtosecond pulse shaping technique has been playing a central role in physical chemistry and quantum control [1–4]. Currently the most successful and widely used shaping method is based on spatial light modulators, where the spectrum of the pulse is spatially dispersed and modulated independently [5–8]. Since its introduction to visible and near-infrared pulses, there has been increasing interest in applying this pulse shaping technique to other spectral regions [9,10]. In particular, the control of molecular excited state processes such as photo-dissociation, fragmentation, and fluorescence are best implemented using shaped pulses at ultraviolet (UV) wavelengths, because many atomic or molecular electronic transitions occur in the UV region. Liquid crystal modulator based pulse shapers suffer from the absorption starting below about 450 nm, and acousto-optic modulators made from TeO₂ are limited by the low damage threshold. Recently a pulse shaper that directly shapes UV pulses was reported [9].

On the other hand, theoretical predictions for the appropriate pulse shapes for quantum control experiments usually have large errors, due to the complicated nature of molecular Hamiltonians. Judson and Rabitz first proposed the use of a genetic algorithm in a learning loop to adaptively control the laser field [11]. The genetic algorithm simulates an evolution process, and drives the laser field to enhance the desired outcome while suppressing the undesired ones. Their work has stimulated much effort to build adaptively controlled pulse shapers, as well as many experiments using adaptively controlled pulses [12–16].

In this work, we demonstrate the application of an adaptive feedback algorithm to control a femtosecond UV pulse shaper. Our pulse shaper design is largely based on previous work on pulse shapers employing acousto-optic modulators (AOM) [7,9,17]. We employ a continuous-parameter genetic algorithm to compress the input pulse to its transform-limited form. We then apply the adaptive pulse shaper to the Stokes pulse in a femtosecond coherent anti-Stokes Raman scattering (CARS) experiment on dipicolinic acid solution. The best detection sensitivity is achieved when a transform limited Stokes pulse is used.

2. Ultra-violet pulse shaper

The first AOM-based pulse shaper that directly shapes UV pulses was demonstrated by Roth, et. al. [9]. We use a similar UV pulse shaper, schematically shown on the left part in Fig. 1. A regeneratively amplified Ti:Sapphire laser system (Spectra-Physics, Spitfire) provides pulses at 808 nm with a duration of ~100 fs, a repetition rate of 1 kHz, and a power of 800 mW, of which 200 mW is used in the second harmonic generation. The power of the output second harmonic beam is 40 mW, which is subsequently routed into the pulse shaper. The details of the pulse shaper design and the AOM information can be found in Reference [9], and summarized here. The density of the holographic gratings is 2400 lines/mm, and the focal length of the spherical focusing mirrors is 50 cm. The AOM is at the focus of the spherical mirrors, and the beam spot size at the AOM is 150 µm. The aperture size of the AOM is 20 mm, leading to a shaping capability of 133 points. We achieve a shaper efficiency of ~10%, the same as that achieved in Reference [9]. The acoustic wave is synthesized by mixing the real and imaginary parts of the modulation functions (generated by an arbitrary waveform generator (AWG)) with a 200 MHz sinusoidal signal. The synthesized modulation signal is then amplified and fed into the piezo-electric transducer of the AOM. The acoustic wave is synchronized with the optical pulses. The details of the signal synthesis technique could be found in Reference [18].

 

Fig. 1. Schematic diagram of the experiment. AOM: acousto-optic modulator; AWG: arbitrary waveform generator; BK7: BK7 glass slide; BS: beamsplitter; CH: chopper; FM: flipping mirror; G: grating; L: lens; MS: moving stage; PH: pinhole; SM: spherical focusing mirror.

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3. Adaptive chirp compensation

We employ the genetic algorithm [11] to compensate for the pulse chirp, including the chirp introduced by the shaper. Adaptive chirp compensation usually involves nonlinear processes such as second harmonic generation (SHG) to get the feedback signal [8,19,20]. However, the SHG scheme cannot be employed to UV pulses due to the lack of SHG material. In this work, we employ a different method, i.e., we use the third-order phase-matched four wave mixing (FWM) signal generated by a transient-gating frequency-resolved optical gating (TG-FROG) setup [21,22] as the feedback to the algorithm. The FWM signal has the advantage of being at the same wavelength with the input pulse. The TG-FROG setup uses a folded BoxCARS geometry [23], and is also used to characterize the shaped pulse, as shown in Fig. 1. The input shaped pulse is split into three beams, which are collimated and parallel with one another and arranged at the three corners of a rectangle. The three beams are then focused onto a 150 µm thick BK7 glass with a convex lens of 10 cm focal length. When the three pulses are overlapped both spatially and temporally, a phase matched four wave mixing signal with the same wavelength is generated at the fourth corner of the rectangle. The power of this signal P_FWM is used as the feedback to the algorithm, as shown in Fig. 1. Based on the measured P_FWM for different pulse shapes, the genetic algorithm iteratively optimizes the pulse phase function to maximize P_FWM. Since ${\text{P}}_{\text{FWM}}\propto {\displaystyle {\int }_{-\infty }^{\infty }{\text{I}}^3(\text{t})\text{dt}}$, where I(t) is the instantaneous intensity of the shaped pulse, maximizing PFWM is equivalent to compensating the pulse chirp.

We use a continuous parameter genetic algorithm in the experiment. Each spectral phase function is represented by a vector with 40 phase values on different wavelengths, with a wavelength separation of 0.1 nm. We take 200 arbitrary phase functions as the initial trials, and order them according to their “fitness”, which are the magnitudes of their feedback signals. The 24 best pulses are kept onto the next generation, where they reproduce another 24 “children”, keeping the population 48 in each generation. A mutation process is then performed to prevent early convergence of the algorithm, where each phase is assigned a random value with a mutation probability of 0.04. The resultant 48 phase functions are then ordered by their fitness again, and the entire process runs iteratively until the largest feedback signals converge. We use a modified algorithm in our experiment. In each generation, we only measure the signal from the 24 reproduced “children” pulses, and assume that the 24 best-fit pulses from the last generation generate the same signals without measuring them in the experiment again (in fact the signals they generate fluctuate due to noise). Although this modified algorithm has less accuracy in the pulse shape control due to the neglect of noises such as laser fluctuation, it allows us to reduce the time needed for algorithm convergence by about a factor of two. For the particular purpose of chirp compensation demonstrated in this work, we found that this modified algorithm produced a satisfactory result, which will be shown later in this section. Thus, the modified algorithm is a good compromise between performance and speed. We refer the readers to Reference [24] for the details of the reproduction and the mutation algorithms.

 

Fig. 2. The maximum and the average feedback signals achieved in each generation.

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Figure 2 shows the maximum and the average four wave mixing signals achieved in each generation. The maximum signal converges after about 50 generations of iteration. The chirp-compensated pulse is characterized by TG-FROG. Figure 3 shows the intensity and the phase of the pulse in (a) temporal and (b) spectral domain respectively. The pulse before chirp compensation (by applying a flat phase function to the pulse shaper), which suffers from the chirp introduced by the shaper geometry, is also shown in Fig. 3 for comparison. The genetic algorithm successfully compresses the pulse to a full width at half maximum (FWHM) of 115 fs, identical to that of the transform limited pulse. The spectral phase is flat within 1.1 radians across the pulse spectrum.

 

Fig. 3. Comparison of pulses after and before chirp compensation. (a) Temporal intensities of the pulse after (solid line) and before (dashed line) chirp compensation. (b) Spectrum (solid line) and spectral phases of the pulse after (thick dashed line) and before (thin dashed line) chirp compensation.

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4. Adaptive optimization of the Stokes pulse in a femtosecond CARS experiment

We use this adaptively controlled UV pulse shaper in a femtosecond CARS experiment. Femtosecond CARS has been investigated extensively as an optical tool to study molecular vibrational and rotational dynamics [25 and references therein], and was further proposed for chemical identification [26]. In a femtosecond CARS experiment, the temporally overlapped pump and Stokes pulses resonantly excite the molecule, and create coherence between the ground state vibrational levels via Raman transitions. The probe pulse interacts with the coherence at a certain delayed time, and generates a CARS signal. The dynamics of the CARS signal as a function of probe pulse delay reveals the decay times and frequency differences between the vibrational levels, thus providing chemical information about the molecule. The details of our femtosecond CARS experiments can be found in Reference [27].

Here we employ the adaptive pulse shaper to optimize the Stokes pulse to get the largest CARS signal. The schematic diagram of the experiment is shown in Fig. 4(a). The amplified pulses from the experiment shown in Fig. 1 are used to pump an optical parametric amplifier (OPA), a noncollinear OPA (NOPA), and a second harmonic generator (SHG), with the output wavelengths of 382 nm, 660 nm, and 404 nm, which are used as the pump, the probe, and the Stokes pulses respectively. The sample is a quartz cuvette with a path length of 1 mm, filled with dipicolinic acid (DPA) in a potassium-hydroxide-buffered water solution (H₂O/KOH) at the concentration of 300 mM. We are interested in DPA because it is one of the marker molecules in anthrax spores, and we are interested in the development of a fast detection technique for anthrax spores [26]. Ultraviolet pulses are needed for the pump and the Stokes beam to achieve resonant enhancement of the coherence. These two pulses excite the ground state vibrational modes near 1400 cm^-1, where two strong Raman modes of DPA (1395 cm^-1 and 1446 cm^-1) give a characteristic coherence beat signal at the frequency of 51 cm^-1 [27,28]. The first peak of the beat signal is observed at a probe delay of 650 fs (corresponding to the 51 cm^-1 frequency difference). Here we use the CARS signal at the probe pulse delay of 650 fs as the feedback signal, and optimize the phase of the Stokes pulse to maximize this signal for the best detection sensitivity. We characterize the Stokes pulse after algorithm convergence, and the measurement shows that the Stokes pulse converges to its transform limited form. We then employ the optimally shaped Stokes pulse in a CARS versus probe delay scan, as shown in Fig. 4(b). A similar scan employing a transform-limited Stokes pulse without the pulse shaper is shown in the same figure for comparison. The two traces show the same vibrational dynamics of the DPA molecules. The fact that the transform-limited Stokes pulse is optimal for CARS experiment is because the pump and the Stokes pulses are still far from the molecule’s absorption resonance (in our case, the absorption of the electronic states of DPA molecules occurs near 270 nm). Our result successfully demonstrates the applicability of the adaptive feedback algorithm on a UV pulse shaper.

 

Fig. 4. (a) Schematic diagram of the femtosecond CARS experiment employing the adaptive pulse shaper. (b) CARS experiment on 300 mM dipicolinic acid solution using a Stokes pulse with the optimized spectral phase (solid line), as compared to the same experiment using a transform limited Stokes pulse (dashed line). DPA: dipicolinic acid solution; NOPA: noncollinear OPA; OPA: optical parametric amplifier; PMT: photomultiplier tube; SHG: second harmonic generation.

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5. Conclusion

In summary, we demonstrate the control of a femtosecond UV pulse shaper with an adaptive genetic algorithm. We show that the genetic algorithm successfully drives the pulse shaper to compensate for the chirp within the input pulse. The pulse is compressed to its transformlimited form with a temporal width of 115 fs. The application of the adaptive pulse shaper to the Stokes pulse in a femtosecond CARS experiment verifies that a transform-limited Stokes pulse is optimal for the best detection sensitivity.