Reflectance for total internal reflection

[wschmail]

I stumbled over surprising results when I use the package for structures where total internal reflectance can occur.
A simple example is the reflectance for a model with silicon as superstrate, silicon dioxide as layer and air as substrate.

using RigorousCoupledWaveAnalysis
using CairoMakie
using Interpolations

N = 0
λs = 300:0.2:950
Rtms = zeros(length(λs))
Rtes = zeros(length(λs))
Ttms = zeros(length(λs))
Ttes = zeros(length(λs))

θ = 1E-5
θ = 13

α = 0
px = py = 1.0

# -----------------------------------------------------------------
Si = InterpolPerm(RigorousCoupledWaveAnalysis.si_schinke)

# ---- Silicon with extinction coefficient set to zero behaves different
# Si = InterpolPerm(
#     interpolate(
#         (λs,),
#         real(RigorousCoupledWaveAnalysis.si_schinke.(λs)),
#         Gridded(Linear()),
#     ),
# )
# -----------------------------------------------------------------

Air = ConstantPerm(1)
SiO2 = ModelPerm(RigorousCoupledWaveAnalysis.sio2_malitson)

superstrate = Si
substrate = Air

sio2 = SimpleLayer(200, SiO2)
Mdl = RCWAModel([sio2], superstrate, substrate)

# ---------------------------------------------- #
for (i, λ) in enumerate(λs)
    Grd = rcwagrid(N, N, px, py, θ, α, λ, superstrate)
    ste, stm = rcwasource(Grd)
    # Rte, Tte = srcwa_reftra(ste, Mdl, Grd, λ)
    Rte, Tte = etm_reftra(ste, Mdl, Grd, λ)
    # Rtm, Ttm = srcwa_reftra(stm, Mdl, Grd, λ)
    Rtm, Ttm = etm_reftra(stm, Mdl, Grd, λ)
    Rtes[i] = Rte
    Ttes[i] = Tte
    Rtms[i] = Rtm
    Ttms[i] = Ttm
end

fig = Figure(; size=(900, 600))
ax = Axis(
    fig[1, 1];
    title="θ = $(θ) | TE",
    xticks=0:50:1000,
    yticks=-0.1:0.1:2,
    limits=(λs[1], λs[end], -0.1, 1.5),
    xlabel="Wavelength (nm)",
    ylabel="Reflectance & Transmittance",
)
lines!(ax, λs, Rtes; label="R")
lines!(ax, λs, Ttes; label="T")
axislegend(ax)
ax = Axis(
    fig[1, 2];
    title="θ = $(θ) | TM",
    xticks=0:50:1000,
    yticks=-0.1:0.1:2,
    limits=(λs[1], λs[end], -0.1, 1.5),
    xlabel="Wavelength (nm)",
    ylabel="Reflectance & Transmittance",
)
lines!(ax, λs, Rtms; label="R")
lines!(ax, λs, Ttms; label="T")
axislegend(ax)
fig

The code above gives:

When I set the extinction coefficient of silicon to zero I get:

Which is much closer to the result that I get with Filmetrics.

[jonschlipf]

Hi,
I never tried injecting a source in a lossy material, this is the first time I see this. I was not able to resolve this quickly, but will get back to it when I have more time.

I suspect the source vector might become complex, but am currently not too much into the code to know where this makes a problem.

The math is done in great detail in the supplemental document of our paper:
https://doi.org/10.1364/oe.438585
In case you want to check for yourself.