Mr. Dmitri S. Pavlichin Profile

Dmitri S. Pavlichin

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Proceedings Article | 4 June 2014 Paper

Optical modular arithmetic

Dmitri Pavlichin, Hideo Mabuchi

Proceedings Volume 9083, 908315 (2014) https://doi.org/10.1117/12.2051108

KEYWORDS: Beam splitters, Binary data, Phase shifts, Control systems, Scattering, Optical circuits, Waveguides, Switches, Laser scattering, Feedback loops

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Nanoscale integrated photonic devices and circuits offer a path to ultra-low power computation at the few-photon level. Here we propose an optical circuit that performs a ubiquitous operation: the controlled, random-access readout of a collection of stored memory phases or, equivalently, the computation of the inner product of a vector of phases with a binary selector" vector, where the arithmetic is done modulo 2pi and the result is encoded in the phase of a coherent field. This circuit, a collection of cascaded interferometers driven by a coherent input field, demonstrates the use of coherence as a computational resource, and of the use of recently-developed mathematical tools for modeling optical circuits with many coupled parts. The construction extends in a straightforward way to the computation of matrix-vector and matrix-matrix products, and, with the inclusion of an optical feedback loop, to the computation of a weighted" readout of stored memory phases. We note some applications of these circuits for error correction and for computing tasks requiring fast vector inner products, e.g. statistical classification and some machine learning algorithms.

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