Complex index of refraction

[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.