Non uniform waveguide

Hello everyone,

I'm trying to solve a problem but I want to find a simpler way if possible. The basic idea is that I would have one waveguide, for simplicity I will just take a slab waveguide. However instead of being constant there is a point at which the distance between the slab suddenly changes. What is the best way to solve for this.

I was thinking of solving for the fields in each area and then trying to work out the coupling between the modes at either side of the discontinuity. But this seems like it would get very difficult very quickly when I go to stranger geometries.

Can anyone think of better way to solve for this? Any ideas are welcome :)

Thanks,
Mark