Optical Mode solutions via wave equation

[Guest]

Hi,
I am a physicist and I have misplaced my undergrad math notes for the derivation of optical modes from Maxwell's wave equation. I have been studying "fundamentals of optoelectronics"-C.Pollack however, there are some missing math steps in his derivations. Can you please provide me with or direct me to any complete, line by line, derivation of the solutions of optical modes? Thank you very much.

Best,

Gemma