#### Apr 14, 2022

## How to model laser beam propagation in OpticStudio Part 2 - Using Paraxial Gaussian Beam analysis to model Gaussian beam

In a blog post, you will learn the key steps in modeling laser beam propagation in **OpticStudio**. Discover what tools are available, how to set up, analyze laser beam propagation, and optimize for the smallest beam size in a simple singlet lens system in OpticStudio sequential mode.

OpticStudio Sequential Mode provides three tools to model Gaussian beam propagation:

- Ray-based approach. It models beam propagation using geometrical ray tracing.
- Paraxial Gaussian Beam. It models Gaussian beam and reports various beam data, including beam size and waist location as it propagates through a paraxial optical system.
- Physical Optics Propagation (POP) models laser beam by propagating a coherent wavefront, which allows very detailed study of arbitrary coherent optical beams.

This blog post introduces the Paraxial Gaussian Beam analysis tool. It shows how to set up the analysis to optimize for the smallest laser beam size.** Paraxial Gaussian Beam analysis**

You can find the tool at Analyze...Lasers and Fibers...Gaussian Beams…Paraxial Gaussian Beam. The Paraxial Gaussian Beam analysis is an interactive feature that works as a “calculator” that quickly computes Gaussian beam characteristics. This feature computes ideal and mixed-mode Gaussian beam data as a given input beam propagates through the lens system. It requires the definition of the initial input embedded beam properties and its M2 value. The advantage is it allows you to enter both ideal and mixed-mode (M2>1) Gaussian beam and displays beam data as it propagates surface by surface in your optical system. The limit is that the calculation of Gaussian beam parameters is based upon paraxial ray data, therefore the results may not be accurate for systems that have large aberrations, or those cannot be described by paraxial optics, such as non-rotationally symmetric systems. This feature also ignores all apertures and assumes the Gaussian beam propagates well within the apertures of all the lenses in the system.

- The input embedded beam is defined by its Wavelength, Waist Size (radius), and waist locations which are specified using the distance between the beam waist location and surface 1 in the system.
- M2 Factor. The ideal M2 value is unity, but real lasers will always have an M2 value greater than unity.

OpticStudio then propagates this embedded beam through the lens system, and at each surface, the beam data, including beam size, beam divergence, and waist locations, is computed and displayed in the output window. OpticStudio computes the Gaussian beam parameters for both X and Y orientations.

**Example**

We’ll tackle the same problem as described in in the previous post, designing a laser beam focusing system using a single lens.

The specifications are the same:

- Nominal Wavelength = 355 nm
- Measured 5 mm from laser output:
- Beam diameter = 2 mm
- Measured divergence = 9 mrad

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. We will model this system using the Paraxial Gaussian beam analysis tool so that the beam spot is the smallest at 100 mm away from the laser output.

The starting system is very similar to that of the ray-based approach. The only difference is that the Paraxial Gaussian Beam analysis does not allow the beam to be launched at Object surface 0. Therefore, a dummy surface needs to be inserted after the Object. The Object thickness is set to 0 so the dummy surface is co-located with the object and the beam will be launched from this dummy surface instead. To start we will enter 100 mm as the thickness on the dummy surface and set it as a variable for optimization. Instead of looking at the beam divergence angle, we’ll look at the beam size.

The operand GBPS returns paraxial Gaussian beam size, computed by the Paraxial Gaussian Beam analysis tool. In the Merit Function Editor, we’ll enter one line using GBPS as shown below. The current beam size (radius) at the Stop surface is 0.949 mm.

Our target beam radius at surface 3 should be 1 mm based on the measurement data. This suggests the first guess of 100 mm separation between the beam launch (surface 1) and the laser output (surface 2) is off. Through optimization, OpticStudio can find the proper beam launch location, so the beam diameter is 2 mm as measured on Stop surface 3.

After a quick optimization, OpticStudio finds a new beam launch position that’s 105.611 mm to the left of surface 2 laser output. This will be our new beam launch location. If you recall in the previous post where we used the ray approach to find the beam waist location, the value returned was 106.108 mm in front of the laser output. This small discrepancy is expected because these two analysis tools use different computational methods.

Next, we will optimize the singlet lens to focus the beam to the smallest beam size at 100 mm from the laser output.

- The radii of curvature of the lens surface are made variable.
- In the Merit function editor, the GBPS operand parameters are changed to minimize the paraxial Gaussian beam size at the image plane by setting the Surf to 6, the image plane, the Target to 0, and the Weight to 1.0.
- The current beam size at the image plane is calculated to be 1.849 mm.

After optimization, the smallest paraxial Gaussian beam size is calculated to be 9.369 µm (this is a more accurate value for the focused beam size at the waist than the geometric ray trace values calculated in the Spot Diagram in part 1 of this series).

The Paraxial Gaussian Beam analysis is an interactive feature that works as a “calculator” to quickly computes Gaussian beam characteristics, allowing you to enter both ideal and mixed-mode (M2>1) Gaussian beam and displays beam data as it propagates surface by surface in your optical system. The limit is that calculation of Gaussian beam parameters is based upon paraxial ray data, so the results may not be accurate for systems with large aberrations, or those cannot be described by paraxial optics, such as non-rotationally symmetric systems. This feature also ignores all apertures and assumes the Gaussian beam propagates well within the apertures of all the lenses in the system. The full version of this article, with downloadable sample files, is available **here**.

If you missed part one of this blog series, you could find it **here**. To learn how to model a laser beam using physic optics propagation check our **blog homepage** next week.

Try Zemax optical design software capabilities for yourself, request a **free trial** today!

**Author: **Hui Chen

Senior Optical Engineer

Zemax an Ansys Company