Complex Snell Law + Prism

ohadohad2

Hello all,

I'm trying to calculate the effects of losses on the behavior of refraction through a prism.

Now in the regular lossless case everything is easy and known, in the case where the prism is lossy my refraction angle at the first boundary is complex and this makes it much harder to calculate the tangential and normal components of k-vector at the second boundary.

The problem is that due to this I'm not sure how to use the geometrical properties that I could use when it was lossless since now the k-vector direction is complex.

I was thinking of using the real of the angle/ k-vector or using a rotation matrix to get the prism boundaries to align with my new axis and than it should be a straightforward continuity + dispersion relation calculation.

Any recommendations ?

Thanks,
Ohad.