Generalized all-optical complex exponential operator

TL;DR

This paper introduces a generalized complex exponential operator using a diffractive optical neural network, enabling high-speed optical computation of complex exponentials with broad applicability and demonstrating promising results for optoelectronic integration.

Contribution

The study presents a novel GCEO that leverages DONN for arbitrary complex exponential calculations, advancing optical computing capabilities beyond previous limitations.

Findings

Successfully computed complex exponentials with high accuracy

Demonstrated generalizability to inputs of varying precision

Highlighted potential for optical computing in optoelectronic systems

Abstract

Euler's formula, an extraordinary mathematical formula, establishes a vital link between complex-valued operations and trigonometric functions, finding widespread application in various fields. With the end of Moore's Law, electronic computing methods are encountering developmental bottlenecks. With its enviable potential, optical computing has successfully achieved high-speed operation of designed complex numbers. However, the challenge of processing and manipulating arbitrary complex numbers persists. This study introduces a generalized complex exponential operator (GCEO), utilizing a diffractive optical neural network (DONN) for the computation of the complex exponential through Euler's formula. Experiments validate a series of complex exponential calculations using the GCEO. The GCEO has demonstrated generalizability and can compute inputs of any precision within an appropriate error margin. The proposed operator highlights the immense potential of DONN in optical computation and is poised to significantly contribute to the development of computational methods for optoelectronic integration.