Generalized all-optical complex exponential operator

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.