Home/Analysis Technologies/Optical analysis/Physical Optics Propagation (POP)
Analysis Technologies | Optical Analysis
A method that represents a beam as an array of complex amplitudes and propagates it from surface to surface including diffraction, carrying the phase information that ray tracing loses.
Coherent beam propagation
Propagated as an array of complex amplitudes
Ansys Zemax OpticStudio
What the method is
Ray tracing includes no interference between rays. A small beam diameter, heavy clipping at an aperture, or a need for the distribution at an intermediate surface itself: in these situations the light has to be propagated as a field with amplitude and phase.
This method carries a coherent optical field from surface to surface over the range from a specified start surface to an end surface, as an analysis within the mode that assumes surface order. The field is represented as an array of points, each holding a complex amplitude. The array size, the number of sampling points and the aspect ratio are the user’s to decide. Two algorithms are available for surface-to-surface propagation, one based on Fresnel diffraction and one on the angular spectrum, and whichever is numerically more accurate is selected automatically.
There are premises. Propagation is assumed paraxial, and as a guide a beam diverging beyond about 20 degrees half-angle falls outside that premise. The field component normal to the surface is taken as zero, so the assumption also breaks down for strongly converging or diverging beams.
How it works
The treatment of propagation including diffraction is organized within the framework of Fourier optics: propagation as an angular spectrum of plane waves, the Fresnel approximation, and the Fraunhofer approximation, used according to the subject and the propagation distance. The two algorithms this method holds correspond to the first two of those.
Numerically, angular spectrum propagation based on the fast Fourier transform requires the angular spectrum to be sampled on a uniform grid. Where that condition breaks, interpolation becomes necessary, and the interpolation error grows the more oblique the geometry. That is why the design of the sampling decides how far the result can be trusted.
In practice the cautions come down to sampling and the extent of the computation region. The number of sampling points is the user’s to decide, and up to 16,384 by 16,384 points can be specified from the user interface. The width of the computation region has to be taken well wider than the beam; if the region is narrow relative to the beam, the tail of the field does not fit inside it and causes wrap-around. Clipping by the system’s apertures can be handled on the field, but only on the premise that the computation region is sufficient. That is why the documented procedure is to follow the beam surface by surface and confirm there is no aliasing or other anomaly, rather than looking only at the final surface after propagating.
Strengths of this method
Because amplitude and phase propagate together, the field itself can be extracted at any intermediate surface. That is different information from a calculation that only gives the diffraction image at the image plane.
Because clipping by an aperture can be handled on the field, propagation including the diffraction that follows can be traced directly.
Because it is represented as a complex amplitude on a computation grid, a field obtained from another analysis can be taken as input and passed through the optical system.
Where it fits
→ when handling a coherent beam where diffraction decides the result
→ when you need the amplitude and phase distribution at an intermediate surface itself
→ when you want to follow the effect of clipping at an aperture
→ when you want to pass a field obtained from wavelength-scale structure analysis through a macroscopic optical system
Systems containing elements that assume no path: in systems containing elements where no path is assumed, the accuracy of this method is generally not guaranteed. Replace them with an equivalent model that assumes surface order.
Systems dominated by geometric aberration: where aberrations matter more than diffraction, geometric metrics such as a spot diagram are enough.
When only the diffraction image at the image plane is needed: if only the diffraction image at the image plane of an imaging system is needed, lighter diffraction calculations are provided.
Strongly diverging beams: as a guide, a beam diverging beyond 20 degrees half-angle falls outside the paraxial assumption, so rigorous electromagnetic analysis or far-field projection is more suitable.
Applications
Evaluate how a Gaussian beam behaves as it passes through a real optical system.
Pass a field obtained from metalens or grating analysis through the optical system.
Pass fields between chip-side analysis and optical system analysis.
Check the state of the beam in systems handling coherent light, such as interferometers.
Inputs and outputs
INPUT
| Propagation range | Start and end surfaces, wavelength and field, and polarization settings |
|---|---|
| Incident beam | Gaussian, top-hat, or a field read from an external file |
| Sampling | The number of sampling points in each direction and the width of the computation region. Take it much wider than the beam |
| Optical system | Surface data and apertures. User-defined apertures are supported |
OUTPUT
| Intensity distribution | The intensity distribution of the propagated beam |
|---|---|
| Phase distribution | The phase distribution at the same surface |
| Beam files | A ZBF file that writes out the complex amplitude at any surface |
| Progress by surface | The state of the beam, which can be checked surface by surface |
How it works
Prepare a model that assumes surface order and specify the start and end surfaces, wavelength and field.
Give the beam type and width, take the computation region much wider than the beam, then settle the number of sampling points.
Propagate the beam over the specified range and obtain intensity and phase.
Rather than looking only at the final surface, follow the state surface by surface and confirm there is no aliasing or other anomaly.
Do not judge from the final surface alone. If the sampling is insufficient, an anomaly arising at an intermediate surface carries straight through to the final one. Step 02 is where most of your time should go.
Comparison with related methods
| Method | Relationship | Main targets | When to use which |
|---|---|---|---|
| Physical optics propagation (this method) | This method | Propagation of coherent fields | Within the mode that assumes surface order, propagates a complex amplitude field from surface to surface, giving amplitude and phase at intermediate surfaces too. |
| Sequential Ray Tracing | Complementary | Imaging systems with a defined surface order | On the same surface-order model, evaluates without interference between rays. It is the efficient choice while aberrations dominate. |
| Non-Sequential Ray Tracing | Alternative | Systems where the ray path is set by geometry | Accumulates flux along many rays. In systems containing elements where no path is assumed, the accuracy of complex amplitude propagation is not guaranteed, so it is not a substitute. |
| FDTD | Upstream | Wavelength-scale structures | The response of the structure itself is obtained by electromagnetic analysis, and that field is handed across as a beam file. |
| Lumerical MODE | Upstream | Waveguide cross-sectional modes | A method for obtaining the cross-sectional modes of a structure uniform along the propagation direction. The mode profile can be handed across as a beam file. |
Supporting products
Physical optics propagation is one of the analysis capabilities in this product’s surface-order mode. The propagated field can be written out as a beam file and exchanged with other analyses. See here for licensing, system requirements and deployment.
FAQ
Related technical information
Tell us the beam conditions and the metrics you want to evaluate, and we will propose the method and the way forward.