Excitation and coupling of normal modes in waveguides

Starting from the known structure of electromagnetic fields in homogeneous waveguides, ordinary linear differential equations of first order for the normal mode amplitudes are derived, which describe the excitation of normal modes by a harmonic source polarization of arbitrary spatial variation. These equations are easily modified to account for the coupling of normal modes in disturbed waveguides without employing the usual approximation of normal mode amplitudes with slow spatial variation. This procedure may be applied to arbitrary waveguides and resonators.