Re: Resonant frequencies in PC slabs!

On Thu, 2 Nov 2006, Ngo Quang Minh wrote:
>    I would like to compute the defect modes (Resonant frequencies) in 
> photonic crystal slab. (According to the document of MPB User tutorial - 
> Finding a point defect state). I do not understand what my .ctl file is 
> wrong!

You have a fundamental problem: finding the resonant modes in a slab is a 
completely different problem from finding the defect mode in a 2d crystal 
with a complete 2d gap.  It looks like you think you can analyze this just 
like a 2d crystal, but that is not the case.

A photonic-crystal slab does *not* have a complete gap (there are 
extended, light-cone modes at every frequency), and so there is no 
exponentially localized point-defect mode.  This makes periodic boundary 
conditions problematic (in principle, if you look at all the modes of the 
periodic cell, including the supercell wavevector, you will see a resonant 
peak in the mode amplitude around the resonant frequency...but in practice 
this kind of computation is a bit painful).

Furthermore, the targeted solver has no chance of working because there 
are light-cone modes in addition to resonant modes inside the gap.

For point-defect resonant modes in slabs you are probably better off using 
our time-domain code, Meep, which can impose absorbing boundary conditions 
and compute the resonant frequency and lifetime.

Steven