Re: how to plot off-axis propagation band str ucture?

On Tue, 6 Mar 2007, Young Soo Lee wrote:
> I want to plot the band structure of 1D photonic crystals which is 
> excited by off-axis propagation. One example is shown by Fig.7 on Page 
> 46 of Photonic Crystal: Molding the Flow of Light.
>
> In my opinion, we should treat the multilayer film as a 2D photonic 
> crystal in this case. One possible code is as follows,

> (set! geometry-lattice (make lattice (size 1 0.5 no-size))) ; 2d cell

No, the size should still be no-size in the y direction (parallel to the 
mirrors).  You can still put in a k vector in any direction you want.

By giving a finite periodicity (0.5) in the y direction, you will see a 
"folded" band structure, that results from the periodic relabeling of k in 
the finite Brillouin zone (as opposed to the infinite Brillouin zone for a 
uniform direction, for which all k are distinct).  This always results 
when you have a supercell, and is a result of you posing the wrong 
mathematical question, and is independent of the computational method.

(Besides the fact that you are wasting computational effort by specifying 
more than no-size---along uniform directions, MPB only needs one pixel.)

Cordially,
Steven G. Johnson