Photonic reservoir computer using speckle in multimode waveguide ring resonators

Photonic reservoir computers (RC) come in single mode ring and multimode array geometries. We propose and simulate a photonic RC architecture using speckle in a multimode waveguide ring resonator that requires neither the ultra-high-speed analog-digital conversion nor the spatial light modulator used in other designs. We show that the equations for propagation around a multimode (MM) ring resonator along with an optical nonlinearity, and optical feedback can be cast exactly in the standard RC form with speckle mixing performing the pseudo-random matrix multiplications. The hyperparameters are the outcoupling efficiency, the nonlinearity saturation intensity, the input bias, and the waveguide properties. In particular, the number of waveguide modes is a measure of the number of effective neurons in the RC. Simulations show a ring using a strongly guiding 50-µm planar waveguide gives 206 effective neurons and excellent predictions of Mackey-Glass waveforms for a broad range of the hyperparameters, while a weakly guiding MM 200-µm diameter fiber gives 4,238 effective neurons and excellent predictions of chaotic solutions of the Kuramoto-Sivashinsky equation. We discuss physical realizations for implementing the system with a chip-scale device or with discrete components and a MM optical fiber.