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

 

[sardar]

A complex index of refraction is a mathematical representation of the refractive properties of a material, which takes into account both the real and imaginary components of the refractive index. The real component represents the speed of light in the material, while the imaginary component accounts for the absorption of light by the material.

One would need to use a complex index of refraction in cases where the material being studied has a significant absorption of light. In these cases, the ordinary index of refraction, which only considers the real component, becomes inadequate in accurately describing the behavior of light in the material.

There are several circumstances in which the ordinary index of refraction breaks down and a complex index of refraction is needed. One example is when studying materials with high levels of opacity, such as metals, where a significant amount of light is absorbed and the real component of the refractive index alone is not sufficient to describe the behavior of light. Another example is in the study of materials with strong optical nonlinearities, where the ordinary index of refraction cannot fully capture the complex interactions between light and matter.

In summary, a complex index of refraction is necessary in situations where the ordinary index of refraction is not enough to accurately describe the behavior of light in a material. This is typically seen in materials with high absorption or strong optical nonlinearities.