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: Improved training of optical neural networks is provided. In one example: 1) we choose input and target vectors, we program those into an input vector generator and a measurement unit, respectively, we turn on the optical input source power, and we monitor the electrical signal representing the cost function. 2) we can then modulate two or more controllable elements inside the optical network at different frequencies and look for the size and sign of the corresponding distinct AC variations in the measured cost function, simultaneously giving us the gradients with respect to each element.

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 optical design for delivering or receiving light from a fluid being measured is disclosed. The optical design is capable of immersion in the fluid being measured, and is capable of operating with fluids that have a different index of refraction. The optical design includes a solid prism of optical material to which a fiber optic attaches by a suitable adhesive. In an optical delivery system, light from the fiber enters the prism and reflects off an internal mirror to a second internal reflective surface. The second internal reflective surface focuses the light to a fixed point through an exit surface of the prism. The second internal reflective surface may in the shape of an ellipse, or may comprise a diffractive surface. The exit surface has a spherical concave shape that is centered on the fixed point where the light is focused, so that light passes through the exit surface at substantially ninety degrees.

Abstract: An optical design for delivering or receiving light from a fluid being measured is disclosed. The optical design is capable of immersion in the fluid being measured, and is capable of operating with fluids that have a different index of refraction. The optical design includes a solid prism of optical material to which a fiber optic attaches by a suitable adhesive. In an optical delivery system, light from the fiber enters the prism and reflects off an internal mirror to a second internal reflective surface. The second internal reflective surface focuses the light to a fixed point through an exit surface of the prism. The second internal reflective surface may in the shape of an ellipse, or may comprise a diffractive surface. The exit surface has a spherical concave shape that is centered on the fixed point where the light is focused, so that light passes through the exit surface at substantially ninety degrees.