Rectangular Waveguides: Effective Index Method

[Phyisab****]

Homework Statement

Is anyone familiar with the effective index method for rectangular waveguides? I have a waveguide for which the width is much greater than the thickness. I think I need to start by treating it as a planar waveguide. But I am supposed to get an effective index which depends on the y coordinate. I know how to solve the planar waveguide, but what do I do differently that gives me a y dependent effective index for the planar waveguide solution?

 

[Phyisab****]

Is nobody familiar with this method? I only need a brief explanation of how it works.

The explanation I have in my text says "solve the planar problem in the x direction to obtain neff(y). Then solve the planar problem in the y direction"

I just don't understand how to get n effective as a function of y. Right now I'm thinking that it's only a function of y in the sense that it changes outside the core of the waveguide. So I'm leaning towards just solving the planar waveguide, and using the numerical value as the core index for the second planar waveguide problem. If I do this, it's pretty simple. But I have no idea if I'm on the right track at all.

 

[ehild]

Try this:

http://ece.uprm.edu/~pol/ppt/RectangularWaveGuides.ppt

ehild