ECEN 5645 - Hints on Homework 9
Problem 13.6 - Orthogonality of te eigenmodes of a waveguide
Although you can attempt this problem by explicit integrations of the
field components given in 13.2-3, a more elegant approach is related
to the technique used for prooving conservation of power in a differential
equation.
Consider the differential equation for the field E^l(x) for the lth mode
and E^m(x) for the mth mode.
Multiply the eqation for E^l(x) by E^m(x) and subtract
the eqauation for E^m(x) multiplied by E^l(x).
Now consider infinite integrals over x of the resulting equation.