Use of optical speckle patterns for compressive sensing of RF signals in the GHz band

Abstract

We demonstrate that speckle patterns at the output of multimode optical waveguides can be used for a compressive sensing (CS) measurement matrix (MM) to measure sparse RF signals in the GHz band (1-100 GHz). In our system mode-locked femtosecond laser pulses are stretched to a width on the order of the interpulse time, modulated by the RF, and injected into a multimode waveguide. The speckle pattern out of the guide is imaged onto an array of photodiodes whose output is digitized by a bank of ADCs. We have measured the CS MM for multimode fibers and used these MMs to demonstrate that sparse RF signals (sparsity K) modulated on a chirped optical carrier can be recovered from M measurements (the number of photodiodes) consistent with the CS relation M ~ K log(N/K) (N is the number of samples needed for Nyquist rate sampling). We demonstrate experimentally that speckle sampling gives comparable results to the photonic WDM sampling system used previously for periodic undersampling (multi-coset sampling) of RF chirp pulses. We have also calculated MMs for both multimode fibers and planar waveguides using their respective mode solutions to determine optimal waveguide parameters for a CS system. Our results suggest a path to a CS system for GHz band RF signals that can be completely constructed using photonic integrated circuit (PIC) technology.