1. Introduction

The spatial light modulator (SLM) is a powerful tool for pulse shaping of femtosecond lasers [1–4], dispersion compensation in chirped pulse amplification [5–8], and feedback control of various physical and chemical phenomena [9–11]. However, in conventional SLM’s made of liquid crystal there is a possibility of optical damage induced by intense laser pulses, which restricts their application to relatively low intensities. In order to use an SLM after chirped pulse amplification of the Ti:sapphire laser and for pulse compression after spectral broadening by self-phase modulation in a gas-filled hollow fiber [12] a novel SLM which can withstand high-intensity laser pulses is required. For the purpose of controlling high-field physical phenomena such as high-order harmonic generation [13,14], we have developed an SLM made of a one-dimensional array of fused-silica glass plates. The fused silica has an optical damage threshold in excess of 1 J/cm² [15]. Another application covers the transparency range from vacuum ultraviolet to mid infrared, which enables us to use the fused-silica SLM not only for the fundamental pulses of the Ti:sapphire laser but also for the third harmonic pulses and their amplified pulses in the KrF laser. It is reported that deformable-mirror-based modulators can also solve the above problems [7].

In this paper, we show the design and construction of a novel SLM made of fused-silica plates, and we demonstrate feedback control of dispersion compensation for femtosecond laser pulses from Ti:sapphire lasers using the SLM with an adaptive feedback control system.

2. Setup of Fused-Silica Spatial Light Modulator

The principle of the fused-silica SLM is quite simple. Figure 1 shows a schematic view of the SLM. For a beam passing through a fused-silica plate with thickness d, the phase delay introduced by the plate is 2πd(n-1)/λ, where n is the refractive index of fused silica at wavelength λ. When the plate is tilted at an angle θ, the optical path length inside the plate increases. Then, the phase shift ϕ(θ) is expressed as

For example, the phase changes by ±7.5 rad, when the angle of a fused-silica plate with a thickness of 1 mm is changed by ±1 deg at around 10 deg of tilt for a wavelength of 800 nm.

This can readily be accomplished by changing the angle using bimorphous piezo actuators, whose tip displacement is typically 1 mm for an applied voltage of 100 V.

 

Fig. 1. Schematic view of the fused-silica spatial light modulator.

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We constructed an SLM from an array of 48 fused-silica plates with broad-band (600–1000 nm) antireflection coatings. Each plate has dimensions of 2 mm in width, 1 mm in thickness, and 20 mm in length. Since the fused-silica plates were prepared by cutting them from a large piece of fused-silica plate after polishing, the surface figure was better than λ/10 over almost all area. The parallelism was less than 15 mrad, and difference in thickness from piece to piece was within 3 µm. Each plate was set in a holder made of steel, which also held a bearing cylinder inside. The tip of the holder contacts with the bimorphous piezo actuator, which has a width of 1.8 mm. A total of 48 pixels were connected and aligned by using a shaft passing through the center of the bearing cylinders. The size of the gap between neighboring pixels was 0.18 mm, which was set by putting a plain washer between each of them on the shaft. Therefore the total width of the SLM active area was 104 mm. Although the dead space between the pixels introduces pre- and post pulses, those intensities are two orders of magnitude lower than the main pulse intensity in the SLM, which allows to use the processed pulse as it is in many nonlinear applications such as high-order harmonics generation. The change in the beam path after passing through the tilted plate in upward or downward direction can be compensated by reflecting the beam using a folding mirror installed at a position on the Fourier plane, as shown in Fig. 2. Although the plates are positioned a few mm away from the Fourier plane, the SLM performance is not degraded because of the wide Fourier plane and of the long focal length of the 4f optical configuration, which is constructed by a grating with 1200 groove/mm installed just below the folding mirror and a concave mirror with a radius of curvature of 1 m. In this case the spectral resolution is 3.4 nm/pixel. The corresponding separation of pre- and post pulses from the main pulse is approximately 600 fs.

 

Fig. 2. Experimental setup.

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3. Experiments

In a preliminary experiment, we confirmed the amount of phase shift obtained by installing the SLM without the folding mirror in one of the arms of a Mach-Zehnder interferometer. Fringe patterns generated by an expanded HeNe laser beam after passing through the interferometer were observed with a CCD camera. The angle of each fused-silica plate was changed at around a reference point of 10 deg. This resulted in a maximum phase shift of ±5 rad at a wavelength of 633 nm for a maximum applied voltage of ±60 V. We were able to increment the voltage in 0.1 V steps, which corresponded to a phase shift of 5 mrad, though it was hard to confirm this value. However, within the resolution of the instruments, the minimum phase shift observed was 50 mrad. It should be noted that the maximum phase shift observed in the actual setup with the Ti:sapphire laser at 800 nm is ±12 rad because of the double-pass configuration using the folding mirror. The reproducibility of the phase shift was not complete because of hysteresis (~15%) inherent in the piezo actuators. However, this does not matter in a feedback control system, because we do not need to control the absolute position but rather the relative positions of the actuators, as is described later.

We tried to demonstrate feedback control of the dispersion compensation for the femtosecond laser pulses using this SLM system. The experimental setup is shown in Fig. 2. A Kerr-lens mode-locked Ti:sapphire oscillator provided near transform-limited 20-fs pulses. These pulses were sent to the SLM system, and subsequently to a second harmonic generation (SHG) autocorrelator for pulsewidth measurement. The pulses were chirped to approximately 120 fs by inserting a 3-cm long fused silica block into the optical path. In order to avoid a change in the beam pointing toward the SLM system, the pulses were precompensated by the SLM and then chirped by the block before they reached the autocorrelator. The autocorrelation traces were monitored with a digital oscilloscope, and the peak value was sent to a personal computer that was used to control the applied voltages for the piezo actuators. The algorithm used for feedback control loop to determine each set of optimum positions of for the piezo actuators was a well-known simulated annealing method [16]. In the optimization procedure, the control parameter was first set at π/2. Each one of 48 pixels was shifted by π/2, -π/2, and 0, and then one of these was selected in order to increase the objective parameter, i.e., the SHG intensity. After all 48 pixels were operated on one by one in the same way, the control parameter was reduced to half the previous value, and the operation was continued. The control parameter was then subsequently changed to π/8, π/16, and so on, in order to converge on the optimum value.

 

Fig. 3. Autocorrelation traces (a) before and (b) after the compensation of material dispersion. (c) SHG peak intensity as a function of the number of iterations.

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Since the initial positioning of the 48 actuators can not be completely aligned, the SLM system initially gives a random phase function. In order to compensate for this characteristics, we have carried out a couple of experiments. First, the random phase shift due to the initial condition of the fused-silica plates was compensated by the SLM system itself. Next, the pulse was stretched by inserting a block and the dispersion was compensated by the SLM system again. Figures 3(a) and (b) respectively are the autocorrelation traces before and after compensation for the material dispersion. The pulse was successfully compressed to nearly the Fourier transform limit, i.e., 20 fs assuming a sech² pulse shape. Figure 3(c) shows the SHG peak intensity as a function of the number of iterations. It took several minutes for convergence to take place. In another series, the random phase shift due to the SLM itself and dispersion caused by the block were compensated simultaneously. The result obtained by this process was also satisfactory. In both cases, the update time per pixel was about 0.9 s, with the limitation being the creeping of the bimorphous piezo actuators. This slow response can be improved by over a factor of more than 10 by means of an impact drive force method using piezo actuators [17], which is now under development. Another point to be addressed is that the transmittance of the beam was about 60%, including the grating efficiency (82%/reflection). The intrinsic transmission in a double pass through the fused-silica plates was estimated to be around 90%. The corresponding transmission loss of 10% is due to loss at the dead spaces between pixels. Is is noted that the dead spaces reduce the peak intensity of the main pulse by 18%, where the pre- and post pulses contain an additional 8%.

We also used the SLM to modulate the outputs from an amplifier which provided 1 mJ, 65 fs pulses at a repetition rate of 10 Hz. The beam diameter was 10 mm at the 1/e² point. The experimental setup was the same as shown in Fig. 2 with exception that the interferometric SHG autocorrelator was replaced by a noncollinear single-shot SHG autocorrelator. Since the shot-to-shot fluctuations of the amplifier outputs were large, the system could not provide good convergence. Therefore we made the feedback loop open and manually applied a phase shift based on the previous results for the oscillator outputs. As a result, the pulses that had been chirped to about 90 fs by the 3-cm long fused-silica block were well compressed to 65 fs by the SLM. It should be noted that the light intensity on the block is 2×10¹⁰ W/cm², which corresponds to a B-integral value of approximately 1 rad after passing through the block. Thus, in the present setup we are almost at the limit for high input energies without causing degradation of the temporal and spatial characteristics by nonlinear effects such as self-phase modulation and self-focussing. Of course, this does not matter for the SLM itself because the nonlinear effects caused by the fused-silica plates which are positioned near the Fourier plane are negligible.

4. Conclusion

In conclusion, we have shown a novel SLM made of fused-silica plates for feedback control of intense femtosecond laser pulses. We have demonstrated the dispersion compensation of femtosecond pulses both from a Ti:sapphire oscillator and from an amplifier using the SLM. We have a plan to improve the SLM by applying an impact drive force method [17] in order to shorten the update time and to enable calibrated single-step control. The application of the SLM to ultraviolet femtosecond pulses is another area of interest because of the potential to compensate material dispersion including high-order terms, which is 5–10 times stronger than at 800 nm.