Re: About the lightcone and projected slab mode

On Tue, 13 Mar 2007, Ryan Hao wrote:
> In the case of line defect waveguide in photonic crystal slab,I succeed 
> in caculating the waveguide mode with MPB.but there still something 
> left:I must find way to project the band strucure of the regular lattice 
> of the slab(slab mode) and the lightcone?You can see in the below 
> picture,the blue line represent for the lightcone,and the green line 
> represent for slab mode.

Projecting the light cone (for a uniform substrate/superstrate) is easy -- 
it is just the kmag output column divided by the substrate index.

For projecting the modes of the unperturbed slab, the easiest thing to do 
is to use the same computational cell as your line-defect waveguide, but 
without the defect.  (In fact, you can use a smaller supercell if you 
want, as long as you plot the slab bands for several values of ky from 0 
to 0.5, where y is the direction perpendicular to your waveguide, assuming 
a rectilinear supercell.)

Cordially,
Steven G. Johnson