Recent results using laser speckle in multimode waveguides for random projections

Random projections are used in applications such as compressive sensing, speckle spectroscopy, and recurrent neural networks. Most prior work has used speckle in free-space systems. Here we report results using laser speckle in planar and cylindrical waveguides with the goal of integrating the whole system in a photonic integrated circuit. We demonstrate a compressive sensing RF receiver over the 2-19 GHz band that recovers the amplitude, phase and frequency of one or two RF sinusoids in a 4.5-ns time window. The RF signal is modulated on a wavelength-chirped optical field, derived from a dispersed mode-locked laser pulse, that propagates through a 5-m, 105-micron fiber. The output of the fiber is imaged onto a fiber bundle such that 32 independent measurements of the speckle pattern are made, and differential outputs of pairs of photodiodes are then digitized to give 16 compressive measurements. The frequency resolution in a single pulse is about 100 MHz, but the resolution can be improved to about 20 KHz by using 100 pulses at a 35 MHz rate. A simpler system uses a stable single-frequency laser diode and speckle in a planar waveguide to determine RF frequency to about 100 MHz. Finally, speckle in a multimode waveguide is used as the reservoir in a recurrent neural network to predict an RF time series.