Propagation of a General Gaussian Beam by Paraxial Ray Tracing in an Arbitrary Optical System

Abstract

The propagation of a partially coherent Gaussian beam in a homogeneous medium can be explained with various methods. One of them is Gaussian shell model beams [1–8]. It uses the Gaussian Schell-model source whose irradiance distribution and degree of coherence are both Gaussian. We will describe Gaussian beams as the ray distribution L as functions of linear and angular coordinates. Of course, since the Gaussian Shell model beam can be produced by a superposition of independent coherent Gaussian beams, our concept is similar to the Gaussian Shell model concept. However, the goal of the present paper is to describe the propagation of general Gaussian beams through an arbitrary optical system by using the geometrical paraxial ray tracing method. In other words, many rays propagate through a reference plane, these rays distribute with the Gaussian profile in linear and angular direction cosine coordinates, and every ray propagates according to the laws of geometrical optics. At first, we introduce the ray distribution density of a circular symmetric Gaussian beam and investigate how that Gaussian beam propagates through an arbitrary axially symmetric optical system or in a homogeneous medium under the paraxial approximation, and we determine the physical meanings of the parameters. Also, we introduce the complex parameter q and the Lagrange invariant L for this general Gaussian beam and discover that this Gaussian beam also follows the Kogelnik ABCD law, just as a classical coherent Gaussian beam does.