Re: Nonlinear materials

On Tue, 3 Apr 2007, Julia Budde wrote:
> I've just started using the MIT PBG programme and I am wondering if there is
> any chance to include nonlinear materials in the calculations.
> Thank you very much!

There are three things you can do:

First, for weak nonlinearities, you can use perturbation theory as another 
poster mentioned.

Second, for strong nonlinearities, you can solve the eigenproblem 
self-consistently.  The simplest thing is to solve the eigenproblem for a 
mode of interest, then update the materials according to the nonlinearity, 
then solve the eigenproblem again, etc. until it converges.

However, you should carefully think about what you are doing, to know 
whether the self-consistent eigensolution is really what you want.  For 
strong nonlinear effects you get all sorts of dynamic phenomena, not 
usually just a set of boring eigenmodes placidly propagating without 
changing.  To look at the dynamics in a nonlinear system, you might want 
to:

Third, use instead our Meep time-domain code, which directly supports 
second- and third-order nonlinearities in Maxwell's equations.

Cordially,
Steven G. Johnson