The goal is to optimize the system, so the beam size is the smallest at 100 mm away from the laser output. We will focus the beam using a singlet lens. Knowing the wavelength and the far field divergence angle, using equations (1) through (3), the beam waist is calculated to be 0.0125 mm, with a Rayleigh range of 1.383 mm. Suppose we have the following specifications of the laser from measured data: In this example, we will set up a laser beam focusing system using a singlet lens and demonstrate how to optimize for the best focus using ray-based approach. For a paraxial Gaussian beam, within the Rayleigh range, z > z R, beam size changes linearly with propagation distance, so beam can be modeled as a point source. Rays are imaginary lines which represent normals to the surfaces of constant phase, or the wavefront (see "What is a ray?" for more details). Geometrical optics is the modeling of optical systems by tracing rays. Ray-based approach to model Gaussian beam This means that the radius is infinite at waist location z = 0, reaches its minimum of 2 z R at z = z R, and asymptotically approaches infinity as z approaches infinity. The phase radius of curvature of the beam is a function of the distance from the beam waist, z: Here, z R is the Rayleigh range of the beam given by The divergence angle θ of the beam is given by The beam size is a function of the distance from the waist. Please note that OpticStudio uses the half width or radius to describe beam width.įor large distances the beam size expands linearly. As shown in the schematic below This Gaussian beam can be described using any two of the three parameters: Gaussian beam theoryĬonsider an ideal Gaussian beam with waist w 0. In this article we’ll introduce method 1 - how to model laser beam propagation using ray-based approach. This series of three Knowledgebase articles discuss how to model Gaussian beam using these three methods. It models laser beam by propagating a coherent wavefront, which allows very detailed study of arbitrary coherent optical beams. It models Gaussian beam and reports various beam data, including beam size and waist location as it propagates through a paraxial optical system. It models beam propagation using geometrical ray trace. OpticStudio sequential mode provides three tools to model Gaussian beam propagation: This article is the first of the three-article series describing the ray-based approach to model laser beam propagation. We’ll also discuss when is appropriate to use which methods. In this series of three articles, we’ll discuss how to set up a Gaussian laser source, how to analyze the beam as it propagates through the optical system, and how to optimize for the smallest spot size using these three methods. Three tools can be used in OpticStudio sequential mode to model Gaussian beam propagation. They are: This article is part of the Modeling Laser Beam Propagation in OpticStudio free tutorial.
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