Re: 2D and 3D structures periodic only in one direction

On May 6, 2009, at 1:13 PM, Paolo Bardella wrote:
> Is it possible to use MPB in order to study a 2D or 3D structure  
> whose refractive index n(x,y,z) is periodic only in one direction  
> n(x,y,z)=n(x,y,z+L) ?

MPB always imposes periodic boundary conditions.

However, in certain circumstances one can use it to study non-periodic  
structures, as long as the desired solutions are localized in the non- 
periodic directions, in which case one can use a supercell technique.

For example, to study a photonic-crystal slab, which is periodic in  
two directions (xy) but non-periodic in the third (z), you can still  
use MPB if the modes of interest are the guided modes in the slab.   
These modes are exponentially decaying in the z direction away from  
the slab, so as long as the computational cell is big enough in the z  
direction the boundary conditions in the z direction have an  
exponentially small effect on the solutions.

Steven