Multiplication with Fourier Optics Simulating 16-Bit Modular Multiplication

Abstract

This paper will describe a simulator developed by the authors to explore the design of Fourier transform based multiplication using optics. Then it will demonstrate an application to the problem of constructing an all-optical modular multiplication circuit. That circuit implements a novel approximate version of the Montgomery multiplication algorithm that enables the calculation to be performed entirely in the analog domain. The results will be used to corroborate the feasibility of scaling the design up to 16-bits without the need for analog to digital conversions at intermediate steps.

Michelson interferometric methods for full optical complex convolution

“…[35][36][37][38][39][40] Laws of quantum mechanics limit the Speed of classical electronic semiconductor hardware-based complicated calculations. [41][42][43][44][45][46][47][48][49] At the same time, in optics, the Optical Fourier Transform (FT) and dot-product multiplication performed passively by a single lens or metalens have reduced computational complexity compared to logarithmic scaling in electronic processing units, [50][51][52][53][54][55][56] both free-space [57][58][59][60][61][62][63][64][65] and integrated photonic integrated circuits versions. [66][67][68][69][70][71][72][73][74][75][76][77][78][79][80] The only drawback of Spatial Light Modulators (SLMs) based optical computing systems would be the refresh rate of the device itself, but with recent resea...…”