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# IR germanium mirror with non-perpendicular incidence.

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#### Hawaslsh

##### Full Member level 3
Hello All,

I was wondering what is the best way to set up a HFSS simulation in order to model the transmission and reflection of a germanium mirror at some arbitrary angle. Below is a simple drawing of that I am trying to accomplish

I had a though of how to solve it mathematically, but I want to run a simulation to confirm my thoughts. I treated the problem as a loaded transmission line. The slab of Ge is the transmission line whose length is determined by the angle and thickness. Since this is for an optical setup, the source and load impedance are 377Ω. That could be completely wrong which is why I wanted to run a simulation and ask you all.

My question to the crowd is, what would be the best way to set up such a simulation, in my case for HFSS. My initial thought was to model a small section of the problem as small TEM waveguides with a wave port to excite a linearly polarized plane wave. I attached a picture, not from HFSS, to give an idea.

I envision a 4 port simulation. The left picture shows the square TEM waveguides with the slab of dielectric at a 45 degree angle loading parts the waveguides. The right picture shows the ports and boundary conditions. I represented yellow as e-walls and blue as h-walls. I am not 100% sure those bounty conditions are correct in representing the real problem, but I think so?? The size of the waveguide will be determined by the frequency, λ/2. The white line just shows the polarization to make sure i have TE-mode incidence along the dielectric boundary. I will create the simulation later today but I wanted to get you'll opinion on the matter.

Sam

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#### Hawaslsh

##### Full Member level 3
I suppose I am asking what the best way to approach the problem would be. I treated the problem as a dielectric waveguide in this case, but I wouldn't mind an easier approach. In short I would like to calculate the transmission and reflection of a Ge slab as a function of incident angle and thickness. Can a Ge slab/mirror be used as a beam splitter at MIR or LWIR?

Would the Ge slab simply act as a mirror? If so, do I need to account for the reflection off the front and back face interfering with the transmitted and reflected power? For some reason I believe the input impedance of the Ge, which would determine the reflection, would be affected by the angle of incidence, mode of incidence, and thickness. It would be nice, and much easier, if all those assumptions turned out to be false.

Thanks for the help!

#### FvM

##### Super Moderator
Staff member
You find the reflection by plane parallel dielectric plates problem discussed in any good physics and more detailed in optics text books. No need to refer to wave guides.

Yes, it's about permittivity respectively refraction index, reflection coefficients, interference, also about polarization. You get different reflection coefficients for wave components polarized parallel and perpendicular to plane of incidence, which can be derived from simple geometrical relations.

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