What do you mean by characteristic modes? Are you talking about modes in a waveguide? Are you talking about Bloch modes in a periodic structure?
I teach a semester long course in "Computational Electromagnetics" and cover both of these topics. You can access the course notes through my website.
**broken link removed**
Click on 'Resources' and you will see them.
For modes in a waveguide, work through Lectures 1, 2, 3, 9, 10, and 11.
For Bloch modes in periodic structures, work through Lectures 1, 2, 3, 6, 17, and 18.
Enjoy!