Re: EM Fields and derivatives

On May 1, 2008, at 4:34 AM, Amnon Willinger wrote:
>
> Let's say that a field is given by an eigenvector A. is there an  
> algorithm that uses the eigenvector and the reciprocal lattice  
> vectors and can calculate a derivative of that field according to x  
> or y - i.e. give back an eigenvector B that represents the  
> derivative? (won't be a true eigenvector of the original problem of  
> course, but that is not the point)
>

No, MPB doesn't include routines to take arbitrary spatial derivatives  
of the fields.  Of course, you can do this yourself using a finite- 
difference approximation.

If your dielectric function is a smooth function, then in principle  
you could compute spatial derivatives with exponential accuracy by  
using MPB's internal planewave representation, but to do so you will  
have to hack MPB's code.  For dielectric functions with  
discontinuities, you'll get second-order accuracy at best by  
differentiating planewaves, so you might as well just use a center- 
difference approximation.

Regards,
Steven G. Johnson