Re: Propagation constant

Dear Steven,

>     My simulated structure is a 2D periodic photonic lattice (the contrast
> of refractive index is very small,  the order is only around exp(-4). Then
> kx and ky are meaningful for the bandstructure, but apparently there will be
> no bandgap with respect to frequency(w) along kx/ky. But it is supposed to
> have bandgaps of propagation constant(beta) to kx/ky. The solution form can
> be deduced to be &(wavefunction)=exp(-iqz)u(x,y), and following the Bloch's
> theorem, the eigenfunction u(x,y) can be written as
> u(x,y)=Uk(x,y)*exp(iK*r), where Uk(x,y) is periodic have the period of the
> lattice. From this solution form, it seems exp(-iqz) replaces exp(iwt) in
> the ordinary plane wave form. So do you think MPB can still solve it?
>
      I am not sure if I make myself understood. Really appreciate your help
and look forward to your reply. Thanks a lot!

Best wishes
Yiling


>
>
> Message: 2
> Date: Wed, 29 Oct 2008 01:01:21 -0400
> From: "Steven G. Johnson" <[email protected]>
> Subject: Re: [MPB-discuss] Propagation constant
> To: [email protected]
> Message-ID: <[email protected]>
> Content-Type: text/plain; charset=UTF-8; format=flowed; delsp=yes
>
> On Oct 28, 2008, at 10:19 PM, Yiling Qi wrote:
> >    Thanks for your kind response before, I have tried the find-k
> > function, it could work well but still not completely satisfy my
> > concern, since it can give out k(w), however what I would like to
> > get is a relationship between kx/ky and propagation constant beta(q)
> > which in my situation meet the solution form ?=exp(-iqz)u(x,y)  . If
> > I set kdir in find-k function to be along kz direction, then the
> > output is still no related with the other two directions. So do you
> > have any idea to help me solve this problem? Thanks a lot for your
> > attention.
>
> I don't understand your question.  If you have something like a
> waveguide, i.e. localized states in the xy directions, then kx and ky
> are not meaningful.  You should just use find-k along the z direction
> and you will get kz = -q, and the eigenmode is the u(x,y) function.
>
> Steven
>
>
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