Laser Speckle in Multimode Waveguides for Random Projections in Compressive Sensing and Reservoir Computing

Detection of wideband RF signals has applications in sensing and communications. When the signals of interest are sparse, compressive sensing (CS) provides a sub-Nyquist sampling strategy with potential size, weight, and power savings. The critical element in a CS receiver is the device that produces the wideband CS measurement matrix (MM), a MxN matrix with M <; <; N satisfying certain properties [1]. We have shown that passive optical speckle in multimode waveguides provides excellent MMs for CS. The M rows of the MM are obtained from M photodetectors placed at different locations within the output speckle pattern. A range of algorithms can be used to recover the sparse input signal from the resulting measurement vector. We have experimentally demonstrated two speckle-based CS systems: (1) a real-time system with M = 16 implemented using multimode fiber (MMF) that recovers RF frequency, amplitude, and phase, and (2) a simplified spectrometer system implemented using a multimode planar waveguide on a silicon photonic chip that detects only RF frequency and amplitude.