diffraction gratings and does - Breault Research Organization, Inc.

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DIFFRACTION GRATINGS AND DOESSimulating Diffractive Optical Elements in ASAPHere,k is the starting coating number,r r' r" ... are the real energy (or complex amplitude) reflectance efficiencies, andt t' t" ... are the real energy (or complex amplitude) transmittance efficiencies.Starting with coating number k, coatings are entered with real energy (or complexamplitude) reflectance r and transmittance t diffraction efficiencies for the zerothorder. The default value for k is one more than the largest coating number defined,and is set to one at the start of program execution.In the first syntax, separate angular properties of the coating are specified by usingpreviously defined scatter MODELS wherei is the model for reflected S polarization,j is the model for reflected P polarization,m is the model for transmitted S polarization, andn is the model for transmitted P polarization.We can specify different reflection and transmission diffraction efficiencies for thezeroth order for different wavelengths, as specified on the last WAVELENGTHcommand. ASAP uses the normalized scatter model data and the reflection andtransmission diffraction efficiencies for the zeroth order to account for theangularly dependent nature of the diffraction grating. If you are not using afunctional scatter model such as USERBSDF, but rather data from BSDFDATA,ASAP linearly interpolates in logarithmic amplitude space to determine reflectionand transmission diffraction efficiencies at other orders than those specified in thedata set. However, with this syntax the same angularly dependent polarizationmodels are used for all sources at different wavelengths. Therefore, this form ofCOATING MODELS should be used for diffraction gratings that are nondispersive.Alternatively, in the second syntax, groups of six numbers can be entered toaccount for grating dispersion and volume holograms. Each group corresponds to awavelength entered on the last multiple WAVELENGTH(S) command. The firstnumber is the reflection diffraction efficiency of the zeroth order corresponding tothe first wavelength on the last multiple WAVELENGTH command. The next twonumbers are the angularly dependent S and P reflection diffraction efficiencymodels, as discussed previously, at that wavelength. The fourth number is the42 ASAP Technical Guide
DIFFRACTION GRATINGS AND DOESSimulating Diffractive Optical Elements in ASAP. . . . .transmission diffraction efficiency followed by its angularly dependent S and Ptransmission diffraction efficiency models, and so on for different wavelengths.Again, angular data is linearly interpolated in logarithmic amplitude space when afunction is unavailable.The reflection and transmission diffraction efficiencies for sources withwavelengths between those defined in COATING MODELS are interpolated, forexample, as in Equation 26. The actual diffraction efficiencies at an incidenceangle a and a wavelength b between the first two WAVELENGTH(S) w w' wouldbe,Equation 26(EQ 26)In these equations, r, r’, t, t’ are the complex amplitudes or square roots of the realenergy coefficients of the diffraction efficiencies. f(i,a) is the normalized angularamplitude,Equation 27where BSDF is the bi-directional scattering distribution function.(EQ 27)ASAP Technical Guide 43
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diffraction gratings and does - Breault Research Organization, Inc.

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