Calculate the effects of losses on the behavior of refraction through a 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.

 

[eljose79]

Hi Ohad,

Thank you for bringing up this interesting topic. Losses can definitely affect the behavior of refraction through a prism and it's important to consider them in your calculations. One approach you could take is to use a complex refractive index, which takes into account both the real and imaginary components of the refractive index. This can be used to calculate the complex refraction angle at the first boundary, which can then be used to calculate the tangential and normal components of the k-vector at the second boundary.

Another approach you could consider is using a transfer matrix method, which takes into account the losses in the prism. This method allows for the calculation of the complex refractive index at each boundary, taking into account the losses, and can be used to determine the behavior of refraction through the prism.

I would also recommend looking into numerical methods, such as finite difference or finite element methods, which can handle complex refractive indices and take into account losses in your calculations. These methods can provide more accurate results compared to analytical methods and can handle more complex geometries.

I hope this helps and good luck with your calculations!