The analysis of the laser beam shape of the fundamental Gaussian mode by testing the numerical angular spectrum technique

Abstract

Laser beams are described through the diffraction eigenfunctions or the so-called modes. The principal fundamental Gaussian mode TEM00 is well described analytically in the paraxial approximation of the diffraction integral, and is applied here as the reference for checking the accuracy of the numerical angular spectrum technique. It has been shown that the beam angle divergence larger or smaller influences the Gaussian beam diffraction properties and affects the beam near-field and the far-field. The angular spectrum technique, has been used, with two fast Fourier transformations applied, which turns out to be accurate and fast. The results were simulated with the help of a dedicated computational program written in Borland C++Builder and Matlab software. Some numerical simulation examples of diffraction patterns are also given to illustrate the propagation characteristics of Gaussian beams, where the shape and the intensity distributions of Gaussian beams in the near-field and in the far-field can change.