Does these Total Internal Reflection, Critical Angle simmulation results make sense?

My goal is to use this tool to study the light extraction from a LED or dielectric slab. First I’m checking if the Total Internal Reflection effect, Critical Angle, and Snell’s Law are satisfied by this simulation tool.

My model consisted of creating a layered structure in the following order: Superstrate, Layer1, and Substrate. The layer consisted of only one segment, and had a thickness and width of 1000 nm.

The first thing I simulated was a ray of light inside a dielectric slab of index of refraction n=3, going out to air n=1. To do this I set my

For a 3 to 1 transition the critical angle is arcsin(1/3)=19.47
The simulations yield straight horizontal lines for the reflectance and transmittance in the selected frequency range. I varied the angle of the TE polarization from 0 to 30, and got the following results:

angle 00, T = 0.74, R = 0.24
angle 10, T = 0.69, R = 0.3
angle 20, T = disappeared (not shown at 0), R = 1.0
angle 30, T = disappeared (not shown at 0), R = 1.0
angle 40, T = disappeared (not shown at 0), R = 1.0

So this seems to be working, exceeding an angle of 19.47 deg gives me total reflection.

Next I changed the layer index to n=2. The index of refraction of the layers were the following way: Superstrate(n=3), Layer1(n=2), and Substrate(n=1). I run the simulation and now got parabolic shapes on the curves of a reflectance of transmittance.

angle 00, T = 0.75, R = 0.25
angle 10, T = 0.96, R = 0.05
angle 20, T = disappeared (not shown at 0), R = 1.0
angle 30, T = disappeared (not shown at 0), R = 1.0
angle 40, T = disappeared (not shown at 0), R = 1.0

I would expect that for a transition from 2 to 1 the critical angle to be arcsin(1/2) = 30.00. But the simulations shows a 1.0 reflectance beyond 20 deg. I would expect some of the wave to be transmitted at 20 deg, not to be totally reflected.

I used only TE Incident polarization light. The wavelength range is from 300 nm to 310 nm, just because I am interested in ultraviolet emitting diodes. I set the widths, thickness, and period lengths to 1000 nm, to be able to use those geometrical optics formulas. (# of modes=50, Num of stacks=1, Num of Steps=11)

Does these results make sense? Do I need to use more complex models (like Fresnels Eq) to get the correct correspondence? Am I ignoring some simulation capabilities? Please, correct me.

I have the output of files if needed.

### 1 Responses

1. Dear Joel,

I am glad that you are using our tool, and thank you for giving us feedback.

Regarding to the problem you described, I tried the same scenario as you have given:

Superstrate, n=2;
Layer1, n=2, thickness=1000nm;
Substrate, n=1;
Wavelength range: 300 nm to 310 nm, with 11 steps;
Polarization: TE.

With a incident angle of 20 deg, I got the transmittance about 0.81; With a incident angle of 25 deg, I got the transmittance about 0.70, which I think are correct. I do not know why you got a different result. I may suggest you double check your inputs. If your have further questions, please let us know.

P.S. Thank you for pointing out that T disappeared in the total internal reflection case. This is because when calculating T from complex transmission coefficients, the solver handles the angle at the transmission side incorrectly if it is a complex number. We will fix it in our next release. For the time being you can just treat T as zero when it disappears.

Best wishes,
Xingjie Ni

Here are the exported results:

incident angle: 20 deg

wavelength nm, real(t), imag(t), real®, imag®, T, R
300, -0.132142, 1.43472, -0.433373, -0.0805132, 0.805706, 0.194294
301, 0.0560695, 1.4397, -0.439453, 0.0342813, 0.805706, 0.194294
302, 0.242094, 1.4203, -0.415898, 0.146024, 0.805706, 0.194294
303, 0.422858, 1.37734, -0.364852, 0.24734, 0.805706, 0.194294
304, 0.595476, 1.31198, -0.290201, 0.331779, 0.805706, 0.194294
305, 0.757291, 1.22572, -0.19724, 0.394196, 0.805706, 0.194294
306, 0.905907, 1.12036, -0.0922689, 0.431023, 0.805706, 0.194294
307, 1.03922, 0.997946, 0.017853, 0.440426, 0.805706, 0.194294
308, 1.15543, 0.86073, 0.126163, 0.422347, 0.805706, 0.194294
309, 1.25307, 0.71112, 0.226032, 0.378423, 0.805706, 0.194294
310, 1.331, 0.551642, 0.311555, 0.311814, 0.805706, 0.194294

incident angle: 25 deg

wavelength nm, real(t), imag(t), real®, imag®, T, R
300, 1.49101, 0.403387, 0.470329, 0.274589, 0.703391, 0.296609
301, 1.52991, 0.212628, 0.523978, 0.148514, 0.703391, 0.296609
302, 1.54449, 0.0197817, 0.54444, 0.0139485, 0.703391, 0.296609
303, 1.535, -0.172106, 0.531095, -0.12061, 0.703391, 0.296609
304, 1.50206, -0.3601, 0.485417, -0.246939, 0.703391, 0.296609
305, 1.44662, -0.541425, 0.410787, -0.357579, 0.703391, 0.296609
306, 1.36995, -0.71349, 0.312207, -0.446246, 0.703391, 0.296609
307, 1.27361, -0.873933, 0.195931, -0.508153, 0.703391, 0.296609
308, 1.15938, -1.02063, 0.0690429, -0.540224, 0.703391, 0.296609
309, 1.02924, -1.15174, -0.0609888, -0.541192, 0.703391, 0.296609
310, 0.885359, -1.2657, -0.186754, -0.511597, 0.703391, 0.296609