A real-time spatial–temporal processor based on cascaded nonlinearities converts space-domain images to time-domain waveforms by the interaction of spectrally decomposed ultrashort pulses and spatially Fourier-transformed images carried by quasi-monochromatic light waves. We use four-wave mixing, achieved by cascaded second-order nonlinearities with type II noncollinear phase matching, for femtosecond-rate processing. We present a detailed analysis of the nonlinear mixing process with waves containing wide temporal and angular bandwidths. The wide bandwidths give rise to phase-mismatch terms in each process of the cascade. We define a complex spatial–temporal filter to characterize the effects of the phase-mismatch terms, modeling the deviations from the ideal system response. New experimental results that support our findings are presented.
© 2000 Optical Society of America
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(320.5540) Ultrafast optics : Pulse shaping
Dan Marom, Dmitriy Panasenko, Pang-Chen Sun, and Yeshaiahu Fainman, "Femtosecond-rate space-to-time conversion," J. Opt. Soc. Am. B 17, 1759-1773 (2000)