MATLAB Implementation of GS Algorithm for Beam Shaping

This document introduces the GS (Gerchberg-Saxton) algorithm - an innovative computational method for transforming Gaussian beam pulses into annular beams with uniform intensity distribution. The GS algorithm employs iterative Fourier transform operations to alternately apply constraints in both spatial and frequency domains. In MATLAB implementation, key functions include fft2/ifft2 for Fourier transforms, phase retrieval techniques, and intensity normalization procedures. Notably, the GS algorithm serves as a fundamental computational tool with broad applications across optical communications, energy conversion systems, and advanced imaging technologies. The underlying principle involves precisely modulating both phase and amplitude profiles of optical waves to achieve desired electromagnetic field characteristics. The algorithm typically requires 50-200 iterations with convergence monitoring through error metric calculations. Future developments anticipate enhanced GS variants incorporating adaptive step sizes and GPU acceleration, promising expanded applications in photonic computing and laser material processing.