Adaptively shaped, sub-picosecond pulses at 3.4μm are obtained from a synchronously pumped optical parametric oscillator based on periodically poled lithium niobate. A simulated annealing algorithm is used in a learning loop to gain adaptive control of the mid-infrared idler pulse shape via shaping of a chirped near-infrared pump pulse. Both indirect control, via optimization of the signal average power, and direct control, via optimization of the two-photon absorption of the idler in an InGaAs detector, has been demonstrated. Both these optimization parameters lead to compressed idler pulses, with slightly differing pulse shapes. By optimization of the cross correlation signal in an interferometer with unequal arm lengths we are also able to deliver compressed double pulses with a variable time delay.
© 2005 Optical Society of America
Ultrashort mid-infrared (MIR) pulses with controllable phase and amplitude properties have a variety of potential applications in the field of coherent control, including the vibrational excitations of biological molecules. Ultrashort pulses in this wavelength regime (approximately 2 – 20μm) are mainly generated via nonlinear processes such as difference frequency mixing [1–3], parametric amplification [4,5] and optical parametric oscillation [6,7], although direct generation in free electron lasers has also been demonstrated . While direct pulse shaping is possible in the MIR , programmable techniques, which in turn allow adaptive pulse shaping based on learning loops , are presently only available at shorter wavelengths. This is due to the limited IR transparency range of liquid-crystal spatial light modulators (LC-SLM) and the low diffraction efficiency of acousto-optic modulators at MIR wavelengths. Even deformable mirror membranes are limited in the MIR as very large deformations are required for phase modulation in this regime. However, several groups have demonstrated indirect programmable pulse shaping of MIR pulses by pulse shaping in the visible or near-infrared (NIR) followed by parametric frequency conversion [1–5]. In these difference frequency mixing or parametric amplification experiments the resulting output electric field is the result of a convolution of the two input fields. Hence, control over at least one of the input fields allows control over the output field. If the aim is not simply to control the MIR pulse shape but rather to achieve high fidelity transfer of the visible or NIR pulse amplitude and phase profile then it is necessary to narrow the spectrum of the unshaped input field to be quasi-monochromatic [3,4].
In this work, we believe for the first time, we apply these techniques to an optical parametric oscillator (OPO) by shaping 1.047μm pump pulses, resonating the signal pulses, and obtaining shaped idler output pulses at 3.4μm. We demonstrate both programmable and adaptive pulse shaping, the latter employing a learning loop with a simulated annealing (SA) algorithm. Applying these techniques to an OPO rather than single pass parametric processes allows access to a new regime of operation where efficient frequency conversion can be obtained at much lower pulse energies and higher repetition rates. In this way, an efficient and tunable, adaptive MIR pulse generator becomes possible.
2. Experiments and results
Figure 1 shows a schematic diagram of the experimental apparatus used in our initial demonstrations. The pump source consisted of a continuous-wave mode-locked 1.047μm Nd:YLF oscillator/amplifier described elsewhere , producing bandwidth-limited 4ps pulses with 120MHz repetition rate. In order to allow pulse shaping into the sub-picosecond regime the pump light was launched into a 20cm-long, polarization-maintaining, single-mode fiber such that self-phase modulation (SPM) caused a broadening of the spectrum without significantly effecting the pulse duration. The spectrum and second harmonic intensity autocorrelation (full-width half maximum (FWHM) of 6.5ps) of the resultant pulse are shown in fig. 2. Assuming a sech2 pulse shape (the pump oscillator uses the additive pulse modelocking technique) this corresponds to a pulse intensity FWHM of 4.2ps.
The output of the fiber was then expanded in one axis in order to nearly fill the aperture of the input grating of a 4-f pulse-shaper , in which a 128-pixel LC-SLM (CRI SLM-128-MIR) applied a programmable spectral phase profile. In order to avoid damaging the LC-SLM the average power incident upon it was limited to ~2W. The spectral phase developed through SPM was calculated and by applying a phase profile which cancels out the 2nd and 4th order phase dispersion, a pulse of approximately 800fs FWHM duration should be achievable. The autocorrelation of the experimentally compressed pulse using such compensation, shown in fig. 3, is consistent with the expected pulse shape and duration. Similar calculations for a fully compensated phase profile suggest pulses of less than 700fs are possible, but with strong side lobes. With no phase applied to the SLM the autocorrelation of the output of the pulse shaper was identical to that of the input (shown in fig. 2), although it should be noted that a pulse tilt of 0.1mm/ps is expected for our experimental parameters . The output of the pulse shaper was reshaped to a circular spot with further cylindrical optics and delivered to the OPO via relay optics. It was then focused to a waist in the centre of a 10.7mm-long periodically poled lithium niobate (PPLN) crystal with a spot size (1/e2 radius of intensity) of 44μm, which corresponds to confocal focusing when the measured pump M2 values of 1.6 (horizontal) by 1.5 (vertical) are taken into account. The PPLN crystal was held in an oven at 120°C and a poling period of 29.2μm was selected, leading to a signal wavelength of 1.509μm and an idler wavelength of 3.4μm. It should be noted that this choice of wavelengths was not critical to these experiments and that the normal broad tuning of the OPO was available. The standing wave OPO cavity was singly resonant and consisted of 4 mirrors with high transmission at the idler wavelength. Two 150mm radius curvature mirrors with high reflectivity at the signal wavelength ensured approximate confocal focusing of the signal through the PPLN crystal. Two plane mirrors completed the cavity; one of high reflectivity and the other was either a 65% or an 85% reflectivity output coupler for the signal. The PPLN length was selected bearing in mind the temporal walk off expected between the pump and signal of approximately 100fs/mm and to ensure that its acceptance bandwidth was greater than the pump bandwidth. In order to avoid inadvertent pulse shaping effects we took care throughout these experiments to operate at a cavity length significantly shorter than that which can lead to pulse compression effects due to the signal walking through the pump pulse .
With no phase applied to the LC-SLM the OPO was found to oscillate at an average threshold power incident upon the pump input mirror of 100mW. The calculated phase profile for pump pulse compression was then applied, resulting in a reduction of threshold to 48mW. Under these conditions the signal and idler autocorrelations also showed compressed pulses of similar duration to the 800fs pump pulse shown in fig. 3, thus demonstrating programmable control over the idler pulse shape.
We then attempted to gain adaptive control over the behavior of the OPO through the learning loop shown in fig. 1, except that in these first experiments we chose to adaptively optimize the signal output power measured when pumping with a power fixed at twice the threshold observed for the unshaped pump pulse. The phase profile across the SLM can be described by the function ϕ(ω) where the frequency ω is spread linearly across the SLM aperture. This function can be expanded by a Taylor Series expansion to give:
The first and second terms do not affect the pulse shape and could be ignored in this context . We therefore constructed the phase profile from the quadratic, cubic and quartic terms. We used an SA that was a simplified version of the very fast simulated re-annealing code developed by Ingeber [14,15]. The code made use of the optimal annealing schedule and generating function scheme, but did not implement re-annealing. The SA was used to control the phase profile coefficients and after 500 iterations, which took 125 seconds (due to the 4Hz refresh rate of the LC-SLM), the output power was fully optimized with a correspondingly lowered threshold for oscillation of 42mW, slightly lower than that found through applying the calculated phase profile. The coefficients found through this iterative process were similar to those calculated for compression of the pump pulse and consequent autocorrelation measurements of the pump, signal and idler yield nearly identical results to that shown in fig. 3, corresponding to compressed pulses of 800fs duration.
We then attempted to gain a more direct adaptive control over the idler output by changing the fitness parameter to the two-photon absorption signal generated by the idler in an InGaAs photodiode, as shown schematically in fig. 1. The effect of this adaptive optimization on the idler autocorrelation is shown in fig. 4(a) and is compared to the idler autocorrelations with no applied phase (b) and with the programmed phase for pump pulse compression (c). The interferometric autocorrelation traces were taken using two-photon absorption in the same InGaAs detector as was used for the optimization procedure. As yet, we have not developed MIR FROG (frequency resolved optical gating) techniques to enable full pulse amplitude and phase information to be retrieved, but future plans involve using two-photon absorption and the sonogram method . It can be seen from fig. 4 that direct adaptive optimization of the idler two-photon absorption signal has also led to a compressed idler pulse of similar full-width half-maximum duration but without the small side-lobes present in the autocorrelations for the programmed pulse compression. The optimized phase profile applied by the LC-SLM was found to be very similar to those used for pulse compression over the central part of the spectrum, but had much higher phase delays at the edges of the spectrum. It can also be seen that with no phase applied, corresponding to a chirped pump pulse, the idler output pulse is also chirped, as evidenced by the lack of interference in the wings of the interferometric autocorrelation.
In order to demonstrate shaping beyond simple pulse compression, we changed the optimization parameter to the idler two-photon absorption signal obtained from the autocorrelator when it had been set up with a deliberate offset in the lengths of the two arms. Thus we were attempting to optimize the cross-correlation signal of the leading and trailing pulses of an induced double-pulse train. Figure 5 shows the interferometric autocorrelations of the idler obtained for two different offsets. Although unique retrieval of the exact pulse shape for an autocorrelation trace is not possible, it is clear that the traces are consistent with the formation of a double pulse with a controllable peak separation.
It should be noted that in the experiments conducted here we have demonstrated the adaptive control of the idler output but not, as yet, the high fidelity transfer of the amplitude and spectral phase profile of an arbitrarily shaped pump pulse. Previous work based on parametric amplification and difference frequency mixing [3,4] has suggested that this could be achieved if the signal could be kept as a relatively narrow-band transform-limited pulse (constant spectral phase), with good temporal overlap with the complex shaped pump pulse. Future work is aimed at demonstrating this by employing a frequency selective component within the signal-resonant OPO cavity, such as a birefringent filter  or a diffraction grating . This would have the added benefit of automatically guarding against inadvertent pulse compression due to cavity length detuning . Further work should also examine the robustness of the adaptive system against various forms of laser noise. No obvious problems of this nature were observed either in the autocorrelation measurements, which were however an average over many pulses, or in the convergence of the SA. Finally, future work will also use a compact fiber-based femtosecond laser pump source  for a more user-friendly system and to access pulse widths nearer to 100fs. In addition, we aim to use the fiber source in a master oscillator power amplifier configuration with the pulse shaper placed after the low-power master oscillator, thus overcoming its current average-power damage limitations.
In summary, we have demonstrated adaptive control over the output of a synchronously pumped optical parametric oscillator. In this way, we have achieved pulse shaping of the MIR idler output both directly, via adaptive optimization of the two-photon absorption of the idler in an InGaAs photodiode, and indirectly, via optimization of the OPO signal output power. Both compressed single pulses and compressed double pulses, with a variable time delay, have been demonstrated. Immediate future work will concentrate on obtaining high fidelity transfer of the NIR pump pulse amplitude and spectral phase profile to the MIR idler output. Tuning to beyond 5μm is possible in PPLN based OPOs  and, with the use of alternative nonlinear gain media, much further wavelength coverage is clearly possible . In this way we aim to develop a compact and efficient, adaptive MIR pulse generator for application to coherent control of biological molecules.
This work has been supported by the UK Engineering and Physical Sciences Research Council (EPSRC grant GR/T25590/01). Naveed Naz and Hazel Hung both acknowledge the support of EPSRC studentships. We also acknowledge Fibrecore Ltd. for supplying the polarization-maintaining optical fiber and INES Test and Measurement GmbH for supplying the GPIB card used in this work.
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