| Propagation of light is a coherent process. As the wavefront travels through free space or glass, each part of the wavefront coherently interferes with all the other parts. Modeling this coherent propagation is the realm of physical optics. |
Physical Optics Propagation (POP) is the ability of ZEMAX to use diffraction calculations to propagate any beam through an optical system surface by surface, including transfer of the beam through almost any ZEMAX surface type. |
POP is a very extensive and powerful feature. The initial beam is completely arbitrary. Any complex electric field distribution may be modeled. The initial beam may be inserted at any surface in the ZEMAX lens model. The beam is then propagated through any range of surfaces. For every space between optical surfaces, a full diffraction propagation may be computed. At every surface, a transfer function is applied to the beam which accounts for the effects of propagation through the surface. Vignetting, apertures, polarization, thin films, transmission, aberrations, distortion, magnification, and diffraction are all considered. |
POP may be used to predict aberration correction and transmission from pinhole apertures, Talbot imaging, edge diffraction effects, laser beam propagation, arbitrary fiber mode coupling, Fresnel zone plates, and many others. |
Beam modeling |
| Optical beams are modeled using numerical arrays. At each point in the array, the complex amplitude electric field is stored. Any amplitude and phase distribution is supported, the feature is not limited to Gaussian beams. |
The phase of the complex values of the electric field determines the phase of the wavefront relative to a reference surface. The amplitude of the values determines the power of the beam in user selectable power per area units, for example, in watts/centimeter squared. |
POP supports user selectable array sizes, and the X and Y direction sampling and point to point spacing may be different. Both dimensions and sampling change dynamically to best fit the beam during propagation. |
The initial beam may be defined in any of these ways: |
- Gaussian, may be anamorphic or diverging
- Uniform amplitude "top hat"
- Defined by external user written function
- Defined by user defined data file
- Defined by prior POP analysis
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Once the beam is defined, the propagation direction is determined by aligning the beam to any chief ray. POP supports propagation in any skew direction; the feature is not limited to axial or symmetric beams or systems. |
Propagation method |
| 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. |
As the beam propagates, ZEMAX automatically scales the dimensions of the array to properly fit the beam size. To minimize phase errors, ZEMAX finds the best surface to use for reference of the phase. |
Propagating through surfaces |
| When the beam reaches an optical surface between two media, ZEMAX computes a transfer function between the object and image space sides of the surface. The transfer function accounts for all the effects a surface may have on the beam, including: |
- Phase imparted to the wavefront
- Aberrations
- Amplitude transmittance of the surface
- Polarization
- Thin film effects
- Phase due to gratings, binary, or diffractive surfaces
- Change in beam size, magnification
- Changes in aspect ratio, due to obliquity or diffraction
- Vignetting by arbitrary apertures on surfaces
- Optical power
- Resampling to preserve accuracy
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The transfer function is computed using an exact ray trace of the local surface properties. The rays used are called the "probing rays". These probing rays are chosen to mimic the local beam properties. The method used is not sensitive to amplitude and phase fluctuations of the actual physical beam for numerical stability. |
The transfer function accounts for polarization using a polarization ray trace. The orthogonal complex amplitude and phase transfer function is used to model losses and phase rotations caused by thin films on the optical surfaces. |
Once the surface transfer function is applied, the beam may then propagate to the next optical surface. The surface by surface propagation proceeds through the entire optical system. The transfer function may also optionally be applied to multiple surfaces. This speeds the analysis when diffraction effects are negligible. |
The coordinate system of the beam travels along the chief ray, and rotates as required at coordinate breaks or tilts. The transfer function may be calculated for all ZEMAX surface types, even user-defined and diffractive surfaces. |
Support for polarization |
| Unpolarized beams are modeled using a single complex amplitude array. |
Polarized beams require the propagation of two orthogonally polarized arrays. Each array is propagated independently. At an optical surface, a polarization transfer function is computed and applied to the pair of polarized beams. This comprehensive method accounts for polarization dependent amplitude and phase transmission through coated or uncoated surfaces. |
POP output |
| ZEMAX can display beam irradiance or phase in correct dimensions and units at any surface in the optical system, using surface, contour, grey scale, false color, or cross section plots, or text listings. |
Complete beam information at any or all surfaces may be stored as data files for later use. Saved beam files may be used to start propagation analysis in another lens. |
POP fiber coupling |
| ZEMAX can determine the coupling efficiency by computing the complex overlap integral between the beam and any arbitrary fiber mode. |
The fiber mode is defined in the same way the initial beam is; using either a formula, a user supplied arbitrary function, or as a data file. The fiber coupling may be computed at, near, or away from beam focus, in any optical space where the fiber mode may be defined. |
Comparison of POP with ray tracing |
| Ray tracing is a widely applicable technique for modeling the propagation of light through an optical system, however ray tracing is not appropriate for all modeling tasks. Rays are incoherent in the sense that the path a ray takes during propagation is not affected by the presence or absence of other rays. The modeling of beam propagation via ray tracing is commonly called geometrical optics. |
The geometric optics features in ZEMAX do support what are traditionally called diffraction calculations, such as the Diffraction PSF and MTF. However, these calculations are based upon geometric ray tracing. Rays are used to propagate through the entire optical system, and the path length of the rays is used to reconstruct the wavefront in image space. A single Fraunhofer diffraction step from exit pupil to image surface is then used to compute the PSF or MTF. |
When using the geometric optics model, all of the diffraction is assumed to occur in just the last propagation, from the exit pupil to the image. Diffraction that occurs at the lens apertures, and as the beam propagates between the lenses, is ignored. For many optical systems, including most imaging lenses, this simplified model is adequate. For other systems, it is not. |
POP is based upon diffraction propagation at every surface, not just at the exit pupil. This allows proper consideration of diffraction from lens apertures, and at small apertures such as a pinhole near the focus of an aberrated beam. Geometrical optics cannot predict the aberration removal and energy transfer from a pinhole placed near focus, while POP can. Another example is Gibb’s Phenomenon, the intensity and phase ripples present in a beam after passing an aperture. |
Support for special surfaces |
| Nearly all surfaces ZEMAX supports, including aspheric, diffractive, and user-defined, may be used with the diffraction propagation and transfer algorithms in the POP feature. |
Surfaces such as gradient index, birefringent, and non-sequential are handled by ray tracing. Rays are traced through the surface to the next surface. The resulting amplitude and phase transfer function is then applied to the beam in place of a full diffraction propagation. |
For these surfaces, the surface transfer function concept is extended to span multiple surfaces at once, so a range of surfaces is described by a single transfer function. |
Groups of surfaces to be handled by ray tracing rather than diffraction propagation are user selected. |
Integration with ZEMAX |
| POP is fully integrated with ZEMAX. Just use an existing ZEMAX lens file, define the initial beam parameters, and the propagation proceeds. There is virtually no learning curve for POP. In spite of being one of the most technically advanced features in ZEMAX, POP is very easy to use. |
Beam data may be viewed as an irradiance (power per area, sometimes called intensity in the laser industry) plot, showing either the unpolarized irradiance or just the X- or Y- polarization component of the beam. Phase plots are also available. |
Both irradiance and phase may be displayed as cross sections, surfaces, grey scale, false color, or contour maps. Data may be viewed for any surface in the optical system, in linear or logarithmic displays. |
Beam data from a prior propagation may be displayed in a window. This allows a lengthy propagation calculation to be performed once, then the data reviewed at different surfaces or in a different format rapidly. |
The beam irradiance at any selected surfaces may also be displayed on a layout plot of the lens. ZEMAX optionally draws the saved beam file for selected surfaces on the layout plot, along with any other optical elements. This tool helps visualization of the beam scale relative to the optics used to control the beam propagation. |
POP reports the best-fit Gaussian beam parameters to any desired beam. These parameters include size, waist, divergence, Rayleigh range, and beam position relative to the waist. |
Skew Gaussian beam |
| For quick analysis of Gaussian beams, a subset of POP is available. This feature models a possibly astigmatic Gaussian beam propagating through the lens aligned with any ray, even a skew (non-axial, non-meridional) ray. The feature reports beam size, waist, divergence, Rayleigh range, and beam postion in both X and Y direction orientations. |
The advantages of the skew Gaussian beam feature are very rapid calculations and the ability to optimize properties of skew Gaussian beams at any surface in the optical system. |
Applications for POP |
| POP is very general, allowing any arbitrary beam to be quickly propagated through almost any optical system ZEMAX can model. Common applications include: |
- Modeling spatial filtering of aberrations
- Accounting for diffraction from lens/aperture edges
- Fiber coupling for coherent physical optics beams
- Arbitrary laser beam propagation through complex optics
- Analysis of beam shaping devices
- Diffraction propagation of beams through lenslet arrays
- Coherent interaction between propagating beams
- Correct modeling of diffraction propagation in optical spaces
- Computing shifts in waist focus position due to aberrations
- Computing flux and irradiance on optical surfaces
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