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 ZEMAX 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.

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. ZEMAX 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.

Open the file "Samples > Physical Optics > Anamorphic Beams.zmx" using the menu option, "File > Open" or the "Ope" button on the button bar.

This file demonstrates beam propagation through anamorphic prisms.

If the "Use Session Files" option is checked under the File menu 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 ZEMAX 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 anamoprhic 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 menu bar 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 using the standard Windows shortcuts (Control-C and Control-V). This can be useful when more comprehensive data analysis is required.

Open the file "Samples > Physical Optics > Fiber Coupling.zmx". This file demonstrates the use of the Physical Optics Propagation capabilities of ZEMAX 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" is 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. ZEMAX 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 ZEMAX 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 Knowledge Base article, "How to Model Coupling Between Single-Mode Fibers".

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 "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.

Open the file "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. 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.

Feel free to continue to explore Physical Optics Propagation in ZEMAX by opening the other sample files available in the Physical Optics folder. Experiment with other beam definitions available in the "Beam Definition" and "Fiber Data" tabs of the POP window settings in these files.

The ZEMAX manual and Help system are excellent sources of information that you can use while you continue to explore the capabilities of ZEMAX. Both can be accessed from the Help menu in the main menu.



To continue your guided tour of ZEMAX, you are encouraged to take a look at the following Knowledge Base article:

Exploring Non-Sequential Mode in ZEMAX