## How to model laser beam propagation in OpticStudio Part 3 - Using Physical Optics Propagation to model Gaussian beams

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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. Itmodels 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 Physical Optics Propagation (POP) tool. It discusses how to set up POP and use it to find the best focus of the laser beam.

Physical Optics Propagation

Physical Optics Propagation models optical systems by propagating wavefronts. The beam is represented by an array of discretely sampled points, analogous to the discrete sampling using rays for geometric optics analysis. The entire array is then propagated through the free space between optical surfaces. At each optical surface, a transfer function is computed which transfers the beam from one side of the optical surface to the other. Because the beam is described by its full complex-valued electric field in the array, Physical Optics Propagation allows very detailed study of arbitrary coherent optical beams, including Gaussian or higher order multi-mode laser beams of any form (beams are user definable), or diffraction effects far from focus, or effects of finite lens apertures, such as spatial filtering. This post will not get into the details of how to use Physical Optics Propagation tool. Users are recommended to read the series of three Knowledgebase articles that discuss the tool in detail at, Using Physical Optics Propagation (POP), Part 1: Inspecting the beams.

Example

We’ll tackle the same problem as described in previous blog posts, design a laser beam focusing system using a singlet lens at 100 mm away from the laser output.

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 of a Gaussian beam, the beam waist is calculated to be 0.0125 mm, with a Rayleigh range of 1.383 mm.

For this analysis, we will start with the same sample file we used previously. We insert a new surface after the object surface and change object surface thickness to zero and move its thickness 106.108 mm to surface 1 thickness.

We then setup the POP tools:

• In the Physical Optics Propagation…Settings…General tab, enter Start Surface as surface 1 and End Surface as surface 6.

• In the Physical Optics Propagation…Settings…Beam Definition tab, set the Beam Type as Gaussian Waist, enter X/Y Sampling of 256x256, Waist X/Y as 0.0125 mm, and use the Automatic button to let OpticStudio compute the appropriate array size to sample the beam.

When Save is clicked in the settings  OpticStudio will save all current settings into a configuration file, and these same settings will be used for computing the POPD operand placed in the Merit Function Editor.

Existing operands are cleared from the merit fuction a POPD operand is added which will return the beam X half-width or beam size at surface 3. This is where the beam size should match the measured size of 1 mm. After updating the Merit Function Editor the POPD operand returns beam size at the surface 3 to be 1.0037 mm, not exactly 1 mm as the measured beam size.

This means the Gaussian beam waist location is slightly off. To make the beam radius 1 mm on surface 3, we target a value of 1 mm for the POPD operand on line 2, vary the thickness on surface 1 and reoptimize. After optimization, the new thickness on surface 1 is 105.689 mm and the beam size on surface 3 is now exactly 1 mm. Two more operands GBPS and POPD on line 4 and 6 in the Merit function editor return the Paraxial Gaussian beam size and the POP beam size at the image plane. The Paraxial Gaussian Beam returns beams size of 9.97 um and the POP returns beam size of 9.811 um.

We can further run an optimization to see if this is in fact the smallest beam size we can achieve using a singlet lens at 100 mm away from laser output. We fix the thickness on surface 1 and add variables to the front and back radii of the singlet lens. Next, we assign a Target of 0 and Weight of 1 on the POPD operand on line 6 of the merit function. This is to optimize for the smallest POP beam size on the image plane.

After optimization, POPD returns a slightly smaller beam radius of 9.48 um. Note the POP computed spot size 9.48 um agrees quite well with the Paraxial Gaussian Beam computed spot size 9.45 um.

To read a comparison for when to use the different methods of Gaussian beam propagation in OpticStudio, and to downloads sample files, please view the full version of this article How to model laser beam propagation in OpticStudio: Part 3 - Using Physical Optics Propagation to model Gaussian beams – Knowledgebase (zemax.com).

Click here for previous blog posts on how to model laser beam propagation on OpticStudio.

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Author:
Hui Chen
Senior Optical Engineer
Zemax an Ansys Company