Coatings - General Sampled Coating

The General Sampled Coating type is specified by its reflected and transmitted power and phase for S and P polarization states at multiple angles and wavelengths. The General Sampled Coating type is similar to the Sampled Coating type but also allows for angular and polarization dependence.

The following rules apply to the General Sampled Coating type:

•The reflected and transmitted power coefficients cannot sum to more than one.

•It is not necessary to use the system wavelengths.

•FRED performs a linear interpolation to calculate the coefficients between sampled wavelengths.

•If the system wavelength is outside the range specified in the coating dialog, then the coefficients are equal to those of the closest wavelength in the range.

In the spreadsheet area of the coating definition, each row specifies an angle and each column specifies a wavelength.

Navigation

The General Sampled Coating type can be specified in the following way

1.Create a new coating

2.Select General Sampled Coating from the "Type" drop down menu in the Create a New Coating dialog box

NOTE: You cannot change the type specification for an existing coating.

Controls

Control	Inputs / Description	Defaults
Name	Enter the name of the coating	Coating n
Description	Enter a description of the coating. This is displayed in the object tree menu.	Blank
General Sampled Coating Parameters
Type	Drop down menu allowing selection of the coating type. Select General Sampled Coating type.	Sampled Coating
Wav	Enter coating wavelength(s) in microns	Default wavelength
Rs	Column 1: Relative reflected power coefficient for S-polarization Column 2: Phase change in degrees on reflection	0, 0
Rp	Column 1: Relative reflected power coefficient for P-polarization Column 2: Phase change in degrees on reflection	0, 0
Ts	Column 1: Relative transmitted power coefficient for S-polarization Column 2: Phase change in degrees on transmission	0, 0
Tp	Column 1: Relative transmitted power coefficient for P-polarization Column 2: Phase change in degrees on transmission	0, 0

OK	Accept settings and to close the dialog
Cancel	Discard settings and close the dialog.
Help	Access the Help.

Editing the angle and wavelength

The wavelength value can be modified by either typing the new wavelength (in microns) into the "Wav" cell directly or by selecting a new wavelength from the drop down list of predefined values. The predefined wavelengths include a large number of emission lines in addition to a number of common laser wavelengths. Use the scroll bar on the right side of the list to scan through the entire range.

The angle value can be changed by highlighting the existing angle specification and typing in the desired value.

Adding / Deleting angles and wavelengths

Additional angles and wavelengths can be added / deleted in the coating definition by right mouse clicking in the spreadsheet area and selecting "Add Angle (row)", "Add Wavelength (column)", "Delete Angle (row)" or "Delete Wavelength (column)" from the list menu.

There is no limit on the maximum number of angles and wavelengths that can be specified.

Auto-filling data

Transmission and reflection coefficient values can be automatically filled in using the commands "Set T = 1 - R (one cell)", "Set R = 1 - T (one cell)", "Set T = 1 - R (entire table)", "Set R = 1 - T (entire table)" from the list menu made available by right mouse clicking in the spreadsheet area.

For this discussion, a single "cell" refers to the group of Rs, Rp, Ts and Tp values given at a single wavelength and incident angle. When using the options "Set T = 1 - R (one cell)" and "Set R = 1 - T (one cell)", FRED uses the following calculations to fill in cell values:

Rs + Ts = 1 Rp + Tp = 1

The commands "Set T = 1 - R (entire table)" and "Set R = 1 - T (entire table)"

Check for un-physical entries

When this command is enabled by right mouse clicking in the spreadsheet area and selecting "Check for un-physical entities" from the list menu, FRED will check each cell in the spreadsheet to verify that conservation of energy is obeyed. This amounts to verifying Rs + Ts = 1 and Rp + Tp = 1 for each cell. FRED returns the results of this check in a dialog box but no values are altered.

Show / Hide phase

Checking this option by right mouse clicking in the spreadsheet area and selecting "Show/Hide phase" from the list menu toggles the visibility of the phase entries in the spreadsheet.

Specifying the interpolation angle component

When a ray is incident onto a surface with a general sampled coating FRED will linearly interpolate the reflection and transmission coefficients out of the sampled data. However, there are multiple options for specifying the angle that should be used for interpolation. Designation of a specific angle option depends on the coating definition relative to the application. The following interpolation angle options are available by right mouse clicking in the coating spreadsheet:

Setting	Meaning
Incident angle always	The ray incident angle coming into the surface will be used as the interpolation angle for the coating evaluation.
Transmitted angle always	The transmission angle for the ray is computed using Snell's Law and then used as the interpolation angle for the coating. If the ray is incident in a TIR condition, the interpolation angle is set to 90 degrees.
Angle on side of low refractive index	Whichever angle (incident or transmitted) lies on the low refractive index side of the interface is used as the interpolation angle of the coating. If the ray is incident in a TIR condition, then the interpolation angle is set to 90 degrees.
Angle on side of high refractive index	Whichever angle (incident or transmitted) lies on the high refractive index side of the interface is used as the interpolation angle of the coating. If the ray is incident in a TIR condition, then the interpolation angle is the incident angle.

Application Notes

Data interpolation

FRED performs a linear interpolation to calculate the coefficients between sampled wavelengths. If the system wavelength is outside the range specified in the coating dialog, then the coefficients are equal to those of the closest wavelength in the range. Consider the following table of General Sampled Coating specifications:

Suppose that a unit power linearly polarized ray at a wavelength of 0.55 microns with equal S and P components is incident on a surface with this coating at an angle of 45 degrees (S = P = 0.5). The incident ray will be split into a reflected and transmitted component. Linearly interpolating between the values of the coefficients, we can determine that the reflected component should have a relative power of 0.93*S + 0.85*P = 0.89, and the transmitted component should have a relative power equal to 0.07*S + 0.15*P = 0.11. After tracing a ray under these conditions and printing the Ray Summary, these calculations are verified as shown in the following image.

General Sampled Coating with polarized or unpolarized rays

Polarized Rays

Every polarized ray is decomposed into orthogonal (S and P) polarization states in the local coordinate system of the surface. The coefficients Rs and Ts apply to the S-polarized component, while the coefficients Rp and Tp apply to the P-polarized component.

Unpolarized Rays

FRED uses the average of the S and P reflection and transmission coefficients to determine the power of the reflected and transmitted rays. Therefore, the averaging process may result in the sum of the transmitted and reflected power being less than the incident power in the ray. The General Sampled Coating will not polarize a ray from an unpolarized source.

General SampledCoating data from file

General Sampled Coating data can be read directly from a text file as long as the text file is properly formatted. Two header lines are followed by coating data, with the first header line reading "type sampled_general_coating" and the second header line reading "format power_phase". Data is grouped by angle of incidence, with the first in the group reading "ANGL val" (val is the angle of incidence in degrees). The remaining lines in the text file have the format, "WAVE l Rs φRs Rp φRp Ts φTs Tp φTp", where l is the wavelength in microns and φij are the respective phases of the four components. An example file format is shown below.

General Sampled Coating from Zemax

FRED can also read General Sampled Coating data from Zemax. The standard Zemax file format is shown below. Note this file has only one header line and that the data format includes only WAVE l Rs Rp Ts Tp, where l is the wavelength in microns.