Abstract: Systems and methods for performing matrix operations using a path-number balanced optical network are provided. The optical network is formed as an array including active optical components and passive optical components arranged at a substantially central location of the array. The optical network includes at least NM active optical components which are used to implement a first matrix of any size N×M by embedding the first matrix in a second matrix of a larger size. The optical network performs matrix-vector and matrix-matrix operations by propagating one or more pluralities of optical signals corresponding to an input vector through the optical network.

Abstract: Methods and apparatus for training a matrix-based differentiable program using a photonics-based processor. The matrix-based differentiable program includes at least one matrix-valued variable associated with a matrix of values in a Euclidean vector space. The method comprises configuring components of the photonics-based processor to represent the matrix of values as an angular representation, processing, using the components of the photonics-based processor, training data to compute an error vector, determining in parallel, at least some gradients of parameters of the angular representation, wherein the determining is based on the error vector and a current input training vector, and updating the matrix of values by updating the angular representation based on the determined gradients.

Abstract: A nano-opto-electro-mechanical System (NOEMS) phase shifter is described. The NOEMS may include a multi-slot waveguide structure suspended in air. The multi-slot waveguide structure may include three or more waveguides separated from each other by slots. The width of the slots may be sufficiently small to support slot modes, where a substantial portion of the mode energy is within the slots. For example, the slots may have widths less than 200 nm or less than 100 nm. The multi-slot waveguide structure may be disposed in a trench formed though the upper cladding of a substrate. An undercut may be formed under the multi-slot waveguide structure to enable free motion of the structure. NOEMS phase modulators of the types described herein may be used in connection with photonic processing systems, telecom/datacom systems, analog systems, etc.

Abstract: Low-noise optical differential receivers are described. Such differential receivers may include a differential amplifier having first and second inputs and first and second outputs, and four photodetectors. A first and a second of such photodetectors are coupled to the first input of the differential amplifier, and a third and a fourth of such photodetectors are coupled to the second input of the differential amplifier. The anode of the first photodetector and the cathode of the second photodetector are coupled to the first input of the differential amplifier. The cathode of the third photodetector and the anode of the fourth photodetector are coupled to the second input of the differential amplifier. The optical receiver may involve two stages of signal subtraction, which may significantly increase noise immunity.

Abstract: Systems and methods for performing matrix operations using a photonic processor are provided. The photonic processor includes encoders configured to encode a numerical value into an optical signal and optical multiplication devices configured to output an electrical signal proportional to a product of one or more encoded values. The optical multiplication devices include a first input waveguide, a second input waveguide, a coupler circuit coupled to the first input waveguide and the second input waveguide, a first detector and a second detector coupled to the coupler circuit, and a circuit coupled to the first detector and second detector and configured to output a current that is proportional to a product of a first input value and a second input value.

Abstract: Photonic packages are described. One such photonic package includes a photonic chip, an application specific integrated circuit, and optionally, an interposer. The photonic chip includes photonic microelectromechanical system (MEMS) devices. A photonic package may include a material layer patterned to include recesses. The recesses are aligned with the photonic MEMS devices so as to form enclosed cavities around the photonic MEMS devices. This arrangement preserves the integrity of the photonic MEMS devices.

Abstract: Optical encoders for encoding signed, real numbers using optical fields are described. The optical fields may be detected using coherent detection, without the need for independent phase and amplitude control. This encoding technique enables the use of simple and non-ideal modulators (e.g., modulators that provide neither pure phase nor pure amplitude modulation) for high-precision encoding. A photonic system implementing optical encoding techniques may include a modulator configured to be driven by a single electrical modulating signal and a coherent receiver. An optical transformation unit optically coupled between the modulator and the coherent receiver may transform the phase and/or the intensity of the modulated optical field. The optical encoding techniques described herein may be used in a variety of contexts, including high-speed telecommunications, on chip-phase sensitive measurements for sensing, communications and computing, and optical machine learning.

Abstract: Aspects of the present application relate to techniques for computing convolutions and cross-correlations of input matrices. A first technique is based on the transformation of convolution operations into a matrix-vector product. A second technique is based on two-dimensional matrix multiplication. A third technique is based on the convolution theorem, which states that convolutions correspond to multiplications in a transform space. Embodiments include methods for computing convolutions of a filter matrix and an input data matrix; apparatuses for computing convolutions of a filter matrix and an input data matrix; and a non-transitory computer readable medium programmed with instructions that, when executed by a processor perform a method for computing convolutions of a filter matrix and an input data matrix.

Abstract: Methods and apparatus for training a matrix-based differentiable program using a photonics-based processor. The matrix-based differentiable program includes at least one matrix-valued variable associated with a matrix of values in a Euclidean vector space. The method comprises configuring components of the photonics-based processor to represent the matrix of values as an angular representation, processing, using the components of the photonics-based processor, training data to compute an error vector, determining in parallel, at least some gradients of parameters of the angular representation, wherein the determining is based on the error vector and a current input training vector, and updating the matrix of values by updating the angular representation based on the determined gradients.