Why Is a Complex Index of Refraction Necessary?

[dimensionless]

Why would one need to use a complex index of refraction? Are there circumstances in which the ordinary index of refraction breaks down? What are they?

 

[Physics Monkey]

Complex indices of refraction are used to describe absorbing materials where the electric field is diminished in amplitude as it propagates. For example, an imperfect conductor has a complex index of refraction which leads to the well known result that the field only penetrates to certain depth called the skin depth. More generally, there are a whole class of lossy dielectrics that have complex indices of refraction. A system like a dilute atomic vapor can also have a complex index of refraction where again it describes the attenuation of light that passes through the gas.

 

[Cybertib]

But it is rather hard to understand if we might use complex or real optical index sometimes... Examples:
1/ Snell-Descartes law in complex gives different results than with real indexes. So, which one is true ?
2/ Link between optical index and dielectric function. Usually, n=sqrt(epsilon). But epsilon is complex. Then index is complex. What about critical angle = arcsin(n2/n1), then ? arcsin(Re(sqrt(epsilon_2)/sqrt(epsilon_1)) ? Or Re(arcsin(sqrt(epsion_2)/sqrt(epsilon_1))) ? Different results.
There many relations like this, in which complex formulation makes everything harder to feel.

 

[Andy Resnick]

The imaginary part of the index of refraction corresponds to absorption (or gain). Adapting Snell's law (or any other relationship using the refractive index) to a complex index of refraction is straightforward by using the relationship sin(i*q) = i sinh(q) and cos(i*q) = cosh(q).

http://link.aip.org/link/ajpias/v44/i8/p786/s1