I have to make a program (using finite difference method) to determine the lowest normalized eigenvalue, ka, for the TM mode defined by Helmholtz differential equation. I have to do this using Matlab (I have just started studying it!!) but the main question is: what does actually represent the eigenvalue of the TM mode (I understand niether eigenvalue nor the modes). What's the phisical meaning of eigenvalue? what about TM, TE, TEM? (if there are some free resources about the last topic, i would like to know) Thanks a lot!