Optical Algorithm for Derivative of Real-Valued Functions

TL;DR

This paper presents an innovative optical algorithm and experimental setup that perform derivatives of real-valued functions using laser beams, advancing optical computing for calculus operations.

Contribution

It introduces a novel optical differentiation algorithm and demonstrates the implementation of higher-order derivatives through phase encoding in light beams.

Findings

Successful experimental implementation of the first derivative of functions.

Extension to n-th derivatives using phase encoding.

Potential for optical computing in calculus applications.

Abstract

The derivation of a function is a fundamental tool for solving problems in calculus. Consequently, the motivations for investigating physical systems capable of performing this task are numerous. Furthermore, the potential to develop an optical computer to replace conventional computers has led us to create an optical algorithm and propose an experimental setup for implementing the derivative of one-dimensional real-valued functions using a paraxial and monochromatic laser beam. To complement the differentiation algorithm, we have experimentally implemented a novel optical algorithm that can transfer a two-dimensional phase-encoded function to the intensity profile of a light beam. Additionally, we demonstrate how to implement the n-th derivative of functions encoded in the phase of the transverse profile of photons.