Real-time spatial-temporal signal processing with optical nonlinearities

The instantaneous response time of parametric optical nonlinearitics enable real-time processing of, and interaction between, spatial and temporal optical waveforms. We review the various signal-processing alternatives based on three- and four-wave-mixing arrangements among spatial and temporal information carrying waveforms. The fast response time of the interaction permits information exchange between the time and space domains, providing the ability to correlate and convolve signals from the two domains. We demonstrate the usefulness of real-time signal processing with optical nonlinearities with the following experiments: converting waveforms from the time to space domain as well as from the space to time domain, spectral phase conjugation and spectral inversion of ultrafast waveforms, transmission of the spatial correlation function on an ultrafast waveform, and a suggestion for a single-shot triple autocorrelation measurement.