# Bloch functions

For propagation in a periodic dielectric crystal i can by combining Maxwells equations under certain conditions get:

$$\bold{\nabla}\times{1\over\epsilon(\bold{x})}\bold{\nabla}\times\bold{H}=\left({\omega\over{c}}\right)^2\bold{H}$$

I can apply Bloch-Floquet theorem and then draw a lot of conclusion.
Where does Bloch-Floquet theorem come from, when can I apply it and how can it be explained?

Thanks!

/Daniel

Why not try google.For example the first search resualt I got is:

http://www.elettra.trieste.it/experiments/beamlines/lilit/htdocs/people/luca/tesihtml/node7.html [Broken]

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Claude Bile
The essence of the theorem is, that any solution to a periodic variation in the refractive index, must itself be periodic (To me, this is a fairly logical conclusion).

There is a wealth of information about this theorem, as it is not only used in photonic crystals, but also to study bandgaps in metals and semi-conductors.

As for the google, I thought the 3rd one down was pretty good (A little more layman for those that don't have a large mathematics background).

Claude.

Gokul43201
Staff Emeritus