Re: dispersion diagram slab waveguide; problems with symmetry

On Sep 17, 2010, at 7:19 AM, <[email protected]> <[email protected]> wrote:
> I am modeling a planar waveguide which has a finite thickness in the
> z-direction and is infinite in the xy-plane. To model this I use a
> one-dimensional computational cell along the z-direction and look  
> for the
> propagation in the x-direction.
>
> Now for the polarization/symmetry part:
> TE polarization has the electric field confined to the xy-plane.
[...]
> TM polarization has the magnetic field confined to the xy-plane.
> The magnetic field is given by

These solutions don't exist in the structure you describe, because it  
is not z-invariant.

Since your structure is y-invarant, you can look for solutions where  
either E or H is purely transverse to the xz plane, with run-yeven or  
run-yodd.

Or, because of the z=0 mirror plane, you can look for solutions that  
are even or odd in z; these solutions, to the extent that they are  
strongly localized in z, are TE-like or TM-like respectively but are  
not purely polarized.

See the discussions of symmetry and polarization in chapters 3, 6, and  
7 of our book: http://ab-initio.mit.edu/book

Steven