Re: projected band structure

On Wed, 14 Jun 2006, Kai Lin Woon wrote:
> I might have a suggestion that might sound stupid. I am looking at
> photonic crystal slab. I am trying to reproduce the light cone. The light
> cone is bounded by w=ck/n. In a TMKT band diagram, the n is the average
> refractive index at a given direction. However, in the paper

The light cone is *not* determined by the "average" refractive index in a 
given direction, at least not for any simple definition of "average". 
Rather, it is determined by the lowest-lying mode of the cladding as 
described in the PRB paper that you mention.

For a homogeneous cladding, of course, this is just w=ck/n.  But for a 
periodic cladding, say oxide pierced by a 2d array of holes, then to get 
the light line you must do a 2d calculation of the band structure in the 
oxide pattern...the lowest (TM *or* TE) band of this 2d pattern is then 
the boundary of the light cone.

Cordially,
Steven G. Johnson