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## 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?