Complex beam parameter and ABCD law for non-Gaussian and nonspherical light beams

Abstract

We define the width, divergence, and curvature radius for non-Gaussian and nonspherical light beams. A complex beam parameter is also defined as a function of the three previous ones. We then prove that the ABCD law remains valid for transforming the new complex beam parameter when a non-Gaussian and nonspherical, orthogonal, or cylindrical symmetric laser beam passes through a real ABCD optical system. The product of the minimum width multiplied by the divergence of the beam is invariant under ABCD transformations. Some examples are given.