Non-linear Signal Retrieval in Wide-Band Photonic Time-Stretch Systems Using the Gerchberg-Saxton Algorithm

The Gerchberg-Saxton algorithm, which is often used for phase retrieval in free space diffractive optics, is here applied to the problem of signal retrieval in dual-output (phase-diverse) photonic time-stretch systems. Using wide band noise covering the first two fading frequencies as an input signal we numerically analyze the proposed algorithm for different numbers of iterations, measurement noise levels, mis-estimation of system parameters and optical modulation depths. We show that the algorithm can successfully compensate for non-linear distortion of the signal due to chromatic dispersion, that it is robust to noise and mis-estimated system parameters, and that it converges very rapidly (within ten iterations). For lower signal-to-noise ratios and/or smaller modulation depths it also provides a non-iterative method of retrieving the input signal