# Optical Anistropic medium

1. Feb 13, 2009

### sanjibghosh

In case of anisotropic medium the energy is flowing in a different direction with respect to the direction of light propagation .How can it possible ? If so,then in what form the energy is flowing ?

How can I detect that energy is flowing in a different direction not the direction of light propagation?

2. Feb 13, 2009

### Andy Resnick

That's a very perceptive observation. All I know on this subject I learned from Born and Wolf.

For an anisotroptic medium, the electric and magnetic material fields D and H are not colinear with E and B. Typically we relax that a little and say only D and E are not colinear (dielectric tensor). The Poynting vector is E x H and may not be colinear with the direction of a wave normal- this is what is meant by the energy is not propogated in the direction of the wave normal. The phase velocity retains the same definition and is propogated in the direction of the wave normal, while the 'ray velocity' points in the direction of the Poynting vector.

In general terms, the two surfaces (one, an ellipsoid containing the wave normals and the other, an ellipsoid containing the ray vectors) are very complicated- the wave normal surface is 6th degree, while the ray surface is 4th degree. Picturing what happens to a single plane wave is not simple.

Fortunately, anisotropic crystals are either uniaxial or biaxial. Wave propogation in uniaxial crystals is straightforward- the complex surface simplifies to an ellipsoid, and there are two eigenstates- the extraordinary and ordinary ray.

For a biaxial crystal, the propogation is much more complicated and leads to conical refraction- the energy propagates in a cone.

Does that help? It's tough to picture.