Calculates the reflection and transmission of a plane wave through a multi-layer stack using the analytic transfer matrix method. This function returns the fraction of transmitted and reflected power (Ts, Tp, Rs, Rp), and the complex reflection and transmission coefficients (ts, tp, rs, rp), for both S and P polarizations. All results are returned in a single dataset as a function of frequency and incidence angle (optional).
NOTE: From 2022 R1.2, stackrt script command supports fully anisotropic and dispersive materials by specifying the nine values of the second-order refractive index tensor. For anisotropic materials, the polarization of reflected light could vary from its incident polarization. The suffix sp and ps denote how polarization is changed in the returned power and coefficients. sp stands for s incident and p reflected/transmitted.
To calculate the fields within the stack, please see stackfield.
RT = stackrt(n,d,f);
n: Refractive index of each layer. Size can be
d: Thickness of each layer. Size is Nlayers.
f: Frequency vector with a length of Nfreq.
RT = stackrt(n,d,f,theta);
theta: Angle vector, in degrees. Optional.
For more information on the complex coefficients see Stack optical solver overview.
Example 1: Five-layer stack with isotropic materials
Calculate the reflection, transmission, and field distribution from a 5 layer stack.
f = linspace(c/400e-9, c/1000e-9,100); # frequency vector
theta = 0:1:45; # angle vector
d = [0; 200e-9; 300e-9; 400e-9; 0]; # air/SiO2/Si/SiO2/air
nf = length(f);
nd = length(d);
# refractive index of each layer (non-dispersive)
n1 = [1; 1.5; 2.5; 1.5; 1];
# refractive index of each layer (dispersive)
n2 = matrix(nd,nf);
n2(1,1:nf) = 1; # air
n2(2,1:nf) = getfdtdindex("SiO2 (Glass) - Palik",f,min(f),max(f));
n2(3,1:nf) = getfdtdindex("Si (Silicon) - Palik",f,min(f),max(f));
n2(4,1:nf) = getfdtdindex("SiO2 (Glass) - Palik",f,min(f),max(f));
n2(5,1:nf) = 1; # air
RT1 = stackrt(n1,d,f); # non-dispersive index data, and theta=0
RT2 = stackrt(n2,d,f,theta); # dispersive data index data, and theta from 0 to 45 deg
plot(RT1.lambda*1e6,RT1.Rp,RT1.Rs,RT1.Tp,RT1.Ts,"wavelength (um)","Power","non-disperisive, theta=0");
image(RT2.lambda*1e6,RT2.theta,RT2.Rp,"wavelength (um)","theta (deg)","Rp, dispersive example");
Example 2: Birefringent slab in air
N_layers = 3;
Nfreqs = 100;
n = matrix(N_layers, Nfreqs, 3);
n(1, :, :) = 1; # air
n(2, :, 1) = 2.1; # nx
n(2, :, 2) = 2.1; # ny
n(2, :, 3) = 2.5; # nz
n(3, :, :) = 1; # air
d = [0; 1e-6; 0]; # air/ birefringent slab / air
f = linspace(c/1e-6, c/1.5e-6, Nfreqs);
theta = 0:1:45;
RT = stackrt(n,d,f,theta);
Example 3: A fully anisotropic and dispersive slab in air
Download and run the attached script stackrt_anisotropic.lsf.
Please note that we use the Euler angle definition shown in lines 32-46 in the script file to rotate a diagonalized permittivity matrix and then derive the refractive index matrix.