We simulate an optical time-domain mixer that can be used to make a photonic analog-to-digital converter
(ADC) or a digital demodulator for high-speed optical communications signals. In the basic mixer, a high
frequency RF signal modulates a repetitively chirped optical carrier; this RF/optical waveform then is dispersed
in one transverse dimension, and imaged onto a 2-dimensional transparency or spatial light modulator whose
pixels are modulated with randomly chosen transmission or reflection coefficients (the optical mixing matrix).
Following transmission through or reflection from the mixing matrix, the optical waveform from each row of the
matrix is recombined and directed to a photodiode and electronics that integrate over the repetition period of the
chirped source. Finally, each of these signals is digitized by an independent ADC sampling at a rate equal to the
pulse repetition rate of the chirp source. A digital replica of the input RF signal can be recovered by digital
signal processing from the digital output of the ADCs and the values of the transmission or reflection
coefficients of the mixing matrix. The effective sampling rate is given by the number of pixels per row of the
mixing matrix times the repetition rate of the chirp source while the effective resolution is controlled by the
resolution of the electronic ADCs and the distortions introduced by the optical mixing process.