Characterization of a liquid-crystal pulse shaper over 0.36-PHz bandwidth

Abstract

Summary form only given. Implementing programmable phase control using a liquid-crystal spatial light modulator (LC-SLM) over a bandwidth approaching a PHz presents specific challenges associated with calibrating the phase response of the device, which is characteristically nonlinear with both wavelength and applied voltage. Here we introduce a powerful new calibration protocol, which not only maps the phase response of the device as a function of wavelength and voltage across nearly an octave (400-770 nm), but also provides sufficient information to recover the thickness of the liquid-crystal cell and the Sellmeier equation of the liquid-crystal.A Ti:sapphire-pumped femtosecond OPO was used to generate broadband tunable pulses via multiple nonphasematched frequency-mixing processes [1]. The pulse shaper was a folded 4f system in which the incident and returning beams were coupled in and out of the system by a fused silica prism, with a small vertical offset to allow the shaped pulses to be analyzed. A 12,288 pixel reflective liquid-crystal-on-silicon LC-SLM was used to shape the pulses. The purpose of the calibration is to produce a function providing the optical phase written by the shaper as a function of both wavelength and applied voltage. This procedure necessitates the construction of separate functional maps of frequency-to-pixel number and voltage-to-phase. The spatial distribution of the frequencies across the surface of the SLM is determined by the material dispersion of the fused silica prism. Writing a phase step to each pixel leads to a discontinuity at the corresponding wavelength in the reflected spectrum. Fitting a quadratic curve to these data points provided the pixel-to-frequency relationship, which was in good agreement with the theoretical behavior calculated from the Sellmeier equation for fused silica. To calculate the phase change as a function of drive voltage we used an in-line spectral interferometry technique. The horizontally polarized light exiting the OPO was rotated to 45° and passed through a quartz plate whose optic axis was horizontal. The quartz plate splits the input pulse into two time delayed replicas with orthogonal polarizations. Only the phase of horizontally polarized light is affected by the LC-SLM, leaving the vertically polarized light as a reference. The drive voltage to the LC-SLM pixels was then increased from zero to its maximum value in 255 linear steps and the changing interference pattern recorded on a spectrometer (Fig. 1(b)). We simulated the interference spectrum in MATLAB and used a minimization function to determine the change in phase due to the LC-SLM voltage (Fig. 1(a)). We carried out the measurement procedure for pulses centered at a number of wavelengths between 400-770 nm. The extracted phase changes due to the SLM are shown in Fig. 1(c) (red lines). The phase change observed experimentally arises from the optical path difference between the test and reference pulses, a result of the voltage-dependent birefringence of the liquidcrystal cells.We fitted each phase curve both individually and simultaneously to determine the liquid-crystal cell thickness (L/2, 5.1±0.05μm) and the dispersion equation for the two refractive indices (Fig. 1(d)). The phase change modeled by a best-fit dispersion equation is shown in Fig. 1(c) (blue lines) and compared with the phase response obtained experimentally (red lines). The best agreement was obtained at higher voltages, with some deviation from Eq. (1) at lower voltages since it does not account for electrostatic forces not associated with the applied field but which also act on the liquid-crystals. Full details of the implementation of the technique will be presented.