Interpretation of a complex angle of refraction

[elad]

TL;DR Summary

what is the meaning of complex angle of refraction?

Hi,

Refractive index can be complex.
When Snell's law is taken into account refraction angle can also be complex.
What is the meaning of the imaginary part and the real part of the refraction angle?
Which angle should I take into account when I want to follow the direction of a thermal radiation wave which is refracted (in the case of interphase between a dielectric material and an absorbing material)?

 

[Andy Resnick]

Born and Wolf has a good discussion of this subject in section 14.2 (7th edition). Without reproducing the lengthy expressions involved, the basic result is that waves in absorptive media are inhomogeneous: the surfaces of constant phase and surfaces of constant amplitude are no longer coincident.

Another aspect is that the phase of the reflected light is different than the phase of incident light; linearly polarized incident light becomes elliptically polarized. This can be used to determine the optical constants (real and imaginary components of the refractive index) of absorptive materials.