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!