This article answers the frequently asked question: What are the definitions of the terms used by OpticStudio to describe a Gaussian beam? In Sequential mode, these terms are used by the Paraxial Gaussian Beam analysis and Physical Optics Propagation analysis.

**Authored By Hui Chen**

## Introduction

OpticStudio Sequential Mode provides two analysis features that enable you to launch a Gaussian beam and analyze its characteristics as the beam propagates in the optical system. They are

- the Paraxial Gaussian Beam analysis
- the Physical Optics Propagation analysis

OpticStudio uses terms such as Waist and Angle to describe a Gaussian beam. Beam Size, Divergence and Rayleigh Range are used to report the beam characteristics as it propagates from surface to surface. This article discusses how these terms are defined in OpticStudio.

## Gaussian beam parameters

Consider an ideal Gaussian beam with waist `w _{0}`. This Gaussian beam can be described using any two of the three parameters, wavelength

`λ`, beam waist

`w`, and divergence angle

_{0}*θ*, as shown in the schematic below.

OpticStudio uses the half width or radius to describe the beam size. The beam waist is where the beam size reaches its minimum. Beam waist w0 is the half width or radius of the Gaussian beam at its thinnest. OpticStudio uses the half divergence angle represented by *θ* to describe the beam divergence.

The beam size is a function of the distance from the waist, `z`:

For large distances the beam size expands linearly. The half divergence angle of the beam is given by:

Here, `z`_{R }is the Rayleigh range of the beam given by:

The phase radius of curvature of the beam is a function of the distance from the beam waist, `z`:

This means that the radius is infinite at waist location ` z` = 0, reaches its minimum of

`2`at

*z*_{R}`, and asymptotically approaches infinity as`

*z*=*z*_{R}`z`approaches infinity.

If you open the Paraxial Gaussian Beam analysis, under **Settings**, you’ll see an entry called “**Waist Size:** “. This is for you to enter the Gaussian beam waist `w0` in Lens Units.

If you open the Physical Optics Propagation analysis, under **Settings…Beam Definition…Beam Type**:, you have the option to define a Gaussian beam using either its Waist `w _{0}`, or its far-field divergence half-angle

`θ`in degrees, or a combination of beam size (not waist) and the far-field divergence half-angle

`θ`in degrees.

KA-01886

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