Abstract: One or more optical resonators are coupled to an optical waveguide in sequence. Each of the resonators includes a corresponding modulator. A signal controller is configured to electrically drive each modulator with a corresponding composite electrical signal. Each composite electrical signal includes two or more frequency components of a frequency comb defined by the one or more resonators. The result of this configuration is that an input-output relation between an input of the waveguide and an output of the waveguide is a linear transformation defined by the composite electrical signals using frequencies of the frequency comb as a basis. Such linear transformations can be reciprocal or non-reciprocal, unitary or non-unitary.

Abstract: Systems and methods for activation in an optical circuit in accordance with embodiments of the invention are illustrated. One embodiment includes an optical activation circuit, wherein the circuit comprises a directional coupler, an optical-to-electrical conversion circuit, a time delay element, a nonlinear signal conditioner, and a phase shifter. The directional coupler receives an optical input and provides a first portion to the optical-to-electrical conversion circuit and a second portion to the time delay element, the time delay element provides a delayed signal to the phase shifter, and the optical-to-electrical conversion circuit converts an optical signal from the directional coupler to an electrical signal used to activate the phase shifter to shift the phase of the delayed signal.

Abstract: A method is disclosed for designing an analog computer that implements a trained recurrent neural network. A computer simulates a wave-based physical system including a wave propagation domain, a boundary layer that approximates a boundary condition, a source of waves, probes for measuring properties of propagated waves, a material within a central region of the wave propagation domain. The simulation also includes a discretized numerical model of a differential equation describing dynamics of wave propagation in the physical system.

Abstract: An isotropic imaging filter is provided that includes a photonic crystal slab, where the photonic crystal slab includes a square lattice of air through holes, a dielectric constant, a thickness (d), a through hole radius (r), and a lattice constant (a), where the square lattice of air holes are separated according to a value of the lattice constant, where the thickness is configured according to d=M(a), where the through hole radii is configured according to r=N(a), where the thickness and the hole radii are configured to generate isotropic bands of guided resonances of an incident image.

Abstract: Systems and methods for training photonic neural networks in accordance with embodiments of the invention are illustrated. One embodiment includes a method for training a set of one or more optical interference units (OIUs) of a photonic artificial neural network (ANN), wherein the method includes calculating a loss for an original input to the photonic ANN, computing an adjoint input based on the calculated loss, measuring intensities for a set of one or more phase shifters in the set of OIUs when the computed adjoint input and the original input are interfered with each other within the set of OIUs, computing a gradient from the measured intensities, and tuning phase shifters of the OIU based on the computed gradient.

Abstract: Systems and methods for activation in an optical circuit in accordance with embodiments of the invention are illustrated. One embodiment includes an optical activation circuit, wherein the circuit comprises a directional coupler, an optical-to-electrical conversion circuit, a time delay element, a nonlinear signal conditioner, and a phase shifter. The directional coupler receives an optical input and provides a first portion to the optical-to-electrical conversion circuit and a second portion to the time delay element, the time delay element provides a delayed signal to the phase shifter, and the optical-to-electrical conversion circuit converts an optical signal from the directional coupler to an electrical signal used to activate the phase shifter to shift the phase of the delayed signal.

Abstract: An isotropic imaging filter is provided that includes a photonic crystal slab, where the photonic crystal slab includes a square lattice of air through holes, a dielectric constant, a thickness (d), a through hole radius (r), and a lattice constant (a), where the square lattice of air holes are separated according to a value of the lattice constant, where the thickness is configured according to d=M(a), where the through hole radii is configured according to r=N(a), where the thickness and the hole radii are configured to generate isotropic bands of guided resonances of an incident image.

Abstract: An isotropic imaging filter is provided that includes a photonic crystal slab, where the photonic crystal slab includes a square lattice of air through holes, a dielectric constant, a thickness (d), a through hole radius (r), and a lattice constant (a), where the square lattice of air holes are separated according to a value of the lattice constant, where the thickness is configured according to d=M(a), where the through hole radii is configured according to r=N(a), where the thickness and the hole radii are configured to generate isotropic bands of guided resonances of an incident image.