fresnelCoefficients

Compute Fresnel coefficients for optical coating

Since R2026a

Syntax

coeffs = fresnelCoefficients(oc)

coeffs = fresnelCoefficients(oc,Name=Value)

Description

Add-On Required: This feature requires the Optical Design and Simulation Library for Image Processing Toolbox add-on.

coeffs = fresnelCoefficients(oc) computes the Fresnel coefficients for an optical coating oc.

coeffs = fresnelCoefficients(oc,Name=Value) specifies options for computing Fresnel coefficients using one or more name-value arguments. For example, Wavelengths=300:10:800 specifies to compute the Fresnel coefficients for wavelengths between 300 to 800 nanometers, sampled 10 nanometers apart.

Examples

Compute Fresnel Coefficients for Optical Coating

Create a broadband anti-reflective optical coating that contains two alternating TiO2/SiO2 layer stacks.

ocBBAR = opticalCoating(Name="BBAR_4l", ...
CoatingMaterial = ["TiO2", "SiO2"], ...
LayerMaterialIndex = [1 2 1 2], ...
ThicknessUnit = "nm", ...
LayerThickness = [14.6 36.5 129.1 95.5]);

Compute the Fresnel coefficients for the optical coating.

coeffs = fresnelCoefficients(ocBBAR);

Define the wavelength range.

lambda = ocBBAR.WavelengthRange(1):ocBBAR.WavelengthRange(2);

Plot the mean amplitude reflection coefficients for s- and p-polarization, rs and rp, respectively, as a function of the wavelength.

mean_rs = mean(abs(coeffs.rs),1);
mean_rp = mean(abs(coeffs.rp),1);

figure;
plot(lambda,mean_rs,"b-",DisplayName="Mean |r_s|");
hold on;
plot(lambda,mean_rp,"r-",DisplayName="Mean |r_p|");
xlabel("Wavelength (nm)");
ylabel("Mean Amplitude Reflection Coefficient");
legend show;
title("Mean Fresnel Amplitude Reflection Coefficients vs. Wavelength");
hold off;

Plot the average reflectance as a function of the wavelength for all sampled incidence angles. By default, the sampled incident angle range is between 0 and 15 degrees.

plot(lambda,coeffs.Ra)
xlabel("Wavelength (nm)")
ylabel("R_a")
title("Average Reflectance of Optical Coating vs. Wavelength")

Input Arguments

oc — Optical coating

opticalCoating object

Optical coating, specified as an opticalCoating object.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: fresnelCoefficients(Wavelengths=300:10:800) specifies to compute the Fresnel coefficients for wavelengths between 300 to 800 nanometers, sampled 10 nanometers apart.

Wavelengths — Wavelengths

M-element numeric vector

Wavelengths for which to compute Fresnel coefficients, specified as an M-element numeric vector. M is the number of wavelengths, and each element of the vector represents a wavelength, in nanometers. By default, the Wavelengths value is the wavelength range specified by oc.WavelengthRange(1):oc.WavelengthRange(2).

IncidentAngles — Incident light angles

oc.IncidentAngleRange (default) | N-element row vector

Incident light angles for which to compute Fresnel coefficients, specified as an N-element row vector. N is the number of incident angles. The angles must be in the range [0, 90]. Units are in degrees. If you do not specify the IncidentAngles name-value argument, the function computes Fresnel coefficients at the incident angles specified by the IncidentAngleRange property of the opticalCoating object oc.

LightDirection — Incident light direction

"medium2substrate" (default) | "substrate2medium"

Incident light direction with respect to the coating, specified as one of these options:

• "medium2substrate" – Incoming incident light rays travel from the direction of the medium through the substrate.

• "substrate2medium" – Incoming incident light rays travel from the direction of the substrate through the medium.

Output Arguments

coeffs — Fresnel coefficients

structure

Fresnel coefficients, returned as a structure containing these fields:

• rs – Reflection amplitude coefficient, or complex ratio, for s-polarized incident light, stored as a N-by-M complex-valued matrix.

• rp – Reflection amplitude coefficient, or complex ratio, for p-polarized incident light, stored as a N-by-M complex-valued matrix.

• ts – Transmission amplitude coefficient, or complex ratio, for s-polarized incident light, stored as a N-by-M complex-valued matrix.

• tp – Transmission amplitude coefficient, or complex ratio, for p-polarized incident light, stored as a N-by-M complex-valued matrix.

• Rs – Reflection power coefficient, which signifies the reflectance, for s-polarized incident light, stored as a N-by-M matrix.

• Rp – Reflection power coefficient, which signifies the reflectance, for p-polarized incident light, stored as a N-by-M matrix.

• Ra – Average reflection power coefficient, stored as a N-by-M matrix. It is the average of the s-polarized and p-polarized power coefficients, Rs and Rp.

• Ts – Transmission power coefficient, which signifies the transmittance, for s-polarized incident light, stored as a N-by-M matrix.

• Tp – Transmission power coefficient, which signifies the transmittance, for p-polarized incident light, stored as a N-by-M matrix.

• Ta – Average transmission power coefficient, stored as a N-by-M matrix. It is the average of the s-polarized and p-polarized power coefficients, Ts and Tp.

• As - Absorbance coefficient for s-polarized incident light, stored as a N-by-M matrix.

• Ap - Absorbance coefficient for p-polarized incident light, stored as a N-by-M matrix.

N is the number of incident angles, and M is the number of wavelengths.

For s-polarized incident light, the electromagnetic field is in the plane perpendicular to the incident coating surface. For p-polarized incident light, the electromagnetic field is in the plane parallel to the incident coating surface.

Version History

Introduced in R2026a