# Waveguide - Two Materials

1. Sep 4, 2009

### dalarev

1. The problem statement, all variables and given/known data

I'm attempting to find the General solution and boundary conditions for a TE$$_{m0}$$ waveguide split up into two different materials: a (any) dielectric on the bottom, and a metallic conductor on top. Image attached.

2. Relevant equations

General (homogenous) Helmholt's equation (not sure how to use latex),
E$$_{z}$$(x,y) = 0, because it's TE.
E$$_{x}$$(x,b) = 0, tangential to top surface.

3. The attempt at a solution

The problem here is the curved line, which I have called as
l = $$\stackrel{b}{a}$$*x. I'm thinking I can cancel out the partial derivatives with respect to y if I make the length, l, a function of x only.

Also, I can easily plug in n=0, but I have to derive the particular solutions before.

File size:
3.1 KB
Views:
60