# Exploring Physical Optics Propagation (POP) in OpticStudio

The Physical Optics Propagation analysis is a powerful Sequential Mode tool for analyzing beam propagation and fiber coupling. This article is intended to serve as an introduction to the capabilities of this analysis tool, and takes the reader through several use case examples. It also demonstrates use of a key supplementary feature, the Beam File Viewer.

Authored By Andrew Locke, edited by Sandrine Auriol

## Introduction

Geometrical ray tracing is an incomplete description of light propagation. Strictly speaking, the propagation of light is a coherent process. As a wavefront travels through free space or optical medium, the wavefront coherently interferes with itself. Modeling this coherent propagation comprises the domain of physical optics. Physical Optics Propagation (POP) is the capability of OpticStudio which uses diffraction calculations to propagate a wavefront through an optical system surface by surface. The coherent nature of light is fully accounted for by this capability.

## What is Physical Optics Propagation?

When using POP, the wavefront is modeled using an array of points. Each point in the array stores complex amplitude information about the beam. The array is user-definable in terms of its dimension, sampling and aspect ratio.

To propagate the beam from one surface to another, either a Fresnel diffraction propagation or an angular spectrum propagation algorithm is used. OpticStudio automatically chooses the algorithm that yields the highest numerical accuracy. The diffraction propagation algorithms yield correct results for any propagation distance, for any arbitrary beam and can account for any surface aperture, including user defined apertures (UDAs).

POP applications include fiber coupling (single and multimode), diffraction propagation through any type of optical space, computing shifts in best waist focus position due to aberrations, and computing beam flux and irradiance on optical surfaces. Physical Optics Propagation can also be used for detailed analysis of arbitrary laser beam propagation through complex optics including M-squared calculations.

## Anamorphic beams

Open the file {Zemax}\Samples\Physical Optics\Anamorphic Beams.zmx via File..Open or the Open button on the toolbar. This file demonstrates beam propagation through anamorphic prisms.

If the Use Session Files option is enabled under Setup...Project Preferences...General when the file is opened, the Lens Data Editor, a Spot Diagram, Shaded Model layout and a Physical Optics Propagation window will open. The POP window shows the beam irradiance at the Image surface (Surface 14).

To see the initial beam settings, click on Settings from the menu bar of the Physical Optics Propagation window and then click on the Beam Definition tab. The beam type is Gaussian and the (radial) waist size in both X and Y is 0.004 mm (4 microns). Now, click on the General tab. The beam is set to start at Surface 1 and is propagated to the image surface. Check the Separate X, Y option. This option allows for greater accuracy when propagating astigmatic/anamorphic beams. Turning this option on results in OpticStudio using separate phase references in the X and Y directions.

Now, click on OK to re-run the analysis.

Note, that while the input beam is a rotationally symmetric Gaussian beam (with a waist of 4 microns), the output beam is anamorphic as a result of the propagation through the anamorphic prisms (represented by surfaces 5 through 13). The pilot beam data (at the bottom of the window) illustrates this numerically. The pilot beam is a best-fit Gaussian beam. The fit is generated based on the actual wavefront parameters.

To perform a more detailed analysis of the anamorphic beam, you can use Physical Optics Propagation cross-section plots. To make a POP cross-section plot, click on Settings from the menu bar of the POP window. Now, click on the Display tab and set Show to Cross X. Click OK.

TIP: You can click on Text in the POP window in the tab at the bottom to generate a text summary of the data that is displayed. The data can then be copied to the clipboard and pasted into other applications by highlighting a range of data and using the standard Windows shortcuts (Control-C and Control-V). You can also copy the entire text by clicking the Copy icon in the menu bar or save the data to a text file by clicking the Save As button in the menu bar. This can be useful when more comprehensive data analysis is required.

## Axicon with ring focus

Open the file {Zemax}\Samples\Physical Optics\Axicon with ring focus.zmx. This file demonstrates the use of the Physical Optics Propagation capabilities of OpticStudio to compute the transformation of a laser beam into a ring shaped distribution. These ring shaped beams are often used in medical applications such as laser corneal surgery or laser materials processing.

The sag of the axicon can confuse the automatic choice of the propagation algorithm in POP.

For that reason, POP settings are often manually set with axicons:

## Fiber coupling

Open the file {Zemax}\Samples\Physical Optics\Fiber Coupling.zmx. This file demonstrates the use of the Physical Optics Propagation capabilities of OpticStudio to compute fiber coupling. Observe that fiber coupling information is listed at the bottom of the POP window that opens with this file (make sure Use Session Files are checked). Presently, the coupling is excellent with an efficiency that exceeds 99%!

The beam being coupled, as shown in the Beam Definition tab of the POP window settings, is a Gaussian beam with a waist size of 2 mm. To see how the receiving fiber is defined, take a look at the Fiber Data tab of the POP window settings. Observe that the receiving fiber mode is Gaussian and has a waist of 8 microns. Notice also that the Compute Fiber Coupling Integral is checked. OpticStudio will only display fiber coupling information if this box is checked. Otherwise, pilot beam data will be displayed at the bottom of the POP window.

To simulate coupling into a narrower fiber, try changing the receiving fiber mode. In the Fiber Data tab, change Waist X and Waist Y to 0.004 and then click OK. The coupling will be recomputed.

As expected, coupling into a narrow fiber has reduced the efficiency.

TIP: Users of the full, licensed version of OpticStudio can optimize fiber coupling based on Physical Optics Propagation calculations using the FICP merit function operand

Licensed users can also explore single-mode fiber coupling in further detail in the Knowledgebase article, "Single-mode fiber coupling in OpticStudio".

## Gibbs phenomenon

We will now look at using Physical Optics Propagation to model near field diffraction effects that occur when a uniform beam is truncated by an aperture. Open the file {Zemax}\Samples\Physical Optics\Gibbs Phenomenon.zmx.

Notice the "U" next to the Semi-Diameter of the stop surface in this example. This indicates that a fixed, hard aperture has been placed on this surface. The radial size of the aperture is equal to the Semi-Diameter of the surface. Thus, in this case, the aperture is a circular aperture with a radius of 0.1 mm.

The file will open with two cross-section POP windows. One window shows the POP output at surface 1 while the other window shows the results at the image surface (surface 2). Both windows have the same beam defined. The only difference is the End Surface defined in the General tab of the Settings dialog. The Beam Definition tab shows that a uniform beam with a waist size of 0.1 mm has been defined using the Top Hat beam type.

The left cross-section plot shows the uniform beam amplitude prior to the aperture. The right plot shows the characteristic ringing from diffraction that is seen at the edges of the beam a short distance after the aperture.

This ringing will not be predicted by geometrical ray tracing. Physical Optics Propagation is required to model such effects.

TIP: Since Physical Optics Propagation propagates arrays of complex amplitude, the phase of the beam can be displayed as well. To view the phase output using POP, simply change the Data setting in the Display tab of the POP settings dialog to Phase.

## Spatial filters

Open the file {Zemax}\Samples\Physical Optics\Pinhole Aperture.zmx. This example demonstrates modeling a spatial filter using POP. The lens represented by surfaces 2 and 3 bring light to a focus at the location of surface 4. An aperture is placed on surface 5, which is co-located with surface 4. To see how this aperture is defined, first double-click where it says Standard for surface 5 in the Lens Data Editor to open the Surface Properties. Next, click on the Aperture tab. A "pinhole" sized circular aperture with a radius of 6 microns has been set on this surface.

The two Physical Optics Propagation windows that open with this file show the beam output before the pinhole (surface 4) and after it (surface 5).

The beam has been significantly altered by the pinhole. If the input beam was aberrated, the pinhole would only allow the fundamental mode to transmit, cleaning up the beam. The total power of the beam after the pinhole has been reduced significantly (from the original input of 1 Watt). While the pinhole allowed for beam cleanup, it has also reduced the beam power to 0.18 Watts, less than 20% of the original power!

TIP: The comment listed in the Comment column of the Lens Data Editor will be displayed in the POP window for whichever surface is the End Surface defined for the propagation. This can help you to differentiate one POP window from another when generating beam output at different surfaces.

## Complex optics

Physical Optics Propagation is not limited to propagation through simple lenses. The calculation can also be performed for propagation through complex optics like lens arrays.

Open the file {Zemax}\Samples\Physical Optics\Lenslet Array.zmx. This file demonstrates the propagation of a top hat beam through a rectangular array of spherical lenses. The array is modeled on surface 2 which is defined using a User-Defined type surface. This type of surface is entirely arbitrary and is defined via an external DLL. For more information about these types of surfaces, take a look at the Knowledgebase article, "How to compile a User-Defined surface".

The User-Defined Surface used in this example is one of the many sample DLLs that come with OpticStudio, a rectangular array of spherical lenslets. The parameters of the array are defined by the parameter columns in the Lens Data Editor. To see these parameters, click anywhere on the row corresponding to surface 2 in the LDE. Next, scroll to the right using the right arrow key on your keyboard. Scroll past the Conic constant column. You will see columns defining the number of elements in the array as well as the width of each individual element in X and Y. The radius of curvature of each element in the array is defined using the standard Radius parameter.

The Surface Sag window that opens with this file shows the curvature and aperture of each lenslet element in the array.

The POP window that opens with this file shows the results of a uniform beam (top hat) propagated through the array.

Observe the individual images formed by each of the array elements. The rectangular apertures of the lenslets also cause diffraction. To see this more clearly in the Physical Optics Propagation window, open the settings for the window and click on the Display tab. Change the Scale setting to Log -5 and click OK.

TIP: Users of the full, licensed version of OpticStudio can optimize the results of POP calculations using the POPD merit function operand.

## Beam File Viewer

Physical Optics Propagation also gives you the capability to save the beam output for later review. You can then view the saved files using the Beam File Viewer.

To demonstrate these capabilities, open the file {Zemax}\Samples\Physical Optics\Tangential and Sagittal Focus.zmx. This file shows the propagation of a rotationally symmetric Gaussian beam through a toroidal lens (surfaces 2 and 3). The toroidal lens imparts astigmatism on the beam.

Open the settings for the Physical Optics Propagation window which computes the beam output at surface 6 (the image surface) and click on the Display tab. Check the box Save Output Beam To and specify Toroidal Lens for the filename next to the box. Then, check the box Save Beam At All Surfaces and click OK.

OpticStudio will recompute the analysis but this time it will save the beam output at each surface. To view the saved output, go to the Analyze Ribbon and select Beam File Viewer from the Laser and Fibers group of analyses. Open the settings for the Beam File Viewer and click on the arrow to the right of the File drop-down box. This will show the available beam files that can be viewed. The name of the file that you saved (Toroidal Lens) will be listed along with a number appended at the end of it. The number corresponds to the surface number at which the beam in the file was saved. Since you checked Save Beam At All Surfaces in the POP window, a file will be listed for each surface. Choose the Toroidal Lens_0001 file and click OK.

The output of the Beam File Viewer is essentially the same as a POP window. The settings of the Beam File Viewer include many of the same options available in the Display tab of a POP window. To look at the POP output at other surfaces, choose the appropriate file in the File drop-down in the Beam File Viewer settings.

TIP: Pressing the left or right arrows on the keyboard will scroll through the beam outputs, one surface at a time.

## References

Video Tutorial: Simulating lasers