Lecture -- Slab Waveguide Analysis Setup

This video describes guided modes in dielectric slab waveguides and then sets up the equations that must be solved to calculate the guided modes. It will be shown that Maxwell’s equations decouple dinto two independent modes for linear, homogeneous, and isotropic (LHI) materials. Analysis and discussion of the modes is not covered in this video.
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[@Terry_sama]

thanks for the video

[@halbarad7932]

A quick question. In anisotropic materials the equations do not separate in general as in 3:51 right? Does that mean, in some cases the eigenmode of the slab is not TM and/or TE polarized and can have all Ex Ey Ez components of the vector E (for instance) for it to be an eigenmode of the slab?

[@empossible1577]

You are exactly right. In general, all three field components are coupled and no simplifications can be made. If the anisotropy is oriented so the principle axes lie along x, y, and z, I do think you will still get your "purely" polarized modes.
I recently published a book on finite-difference frequency-domain (FDFD). Chapter 6 covers waveguide analysis, including slab waveguides. Chapter 10 covers anisotropy. Unfortunately, I do not analysis an anisotropic slab waveguide, but all the pieces to your puzzle are there. I have done this in the past for Dyakonov surface waves and it worked wonderfully. Here is a link to the book website:
empossible.net/fdfdbook/