Optical algorithm for derivative of real-valued functions

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 extend the optical algorithm to implement high-order derivatives of two-dimensional real-valued functions encoded in the phase of the transverse profile of photons. •New optical algorithm for implementing the derivative of real valued functions.•New optical algorithm to transfer a two-dimensional phase-encoded function to the intensity profile of a light beam.•Algorithms compatible with existing platforms for optical computing.•Optical computing with transverse profile of the light beam.