Transverse mode excitation and coupling in a waveguide free electron laser

An analysis of excitation, gain-coupling and evolution of transverse electromagnetic modes in a waveguide free electron laser is presented. We use a formalism of coupled-mode analysis to find the gain-dispersion equation of the coupled waveguide modes and diagonalize the system to find the eigenmodes ("supermodes") of the coupled system and their gain. We demonstrate the use of the method to find the mutual gain of the coupled TE₂₁ TM₂₁ modes which are degenerate. A noteworthy finding is that the gain of the supermode is higher than the gain of either of the separate waveguide modes when calculated in a model where coupling is neglected. The analytically calculated results are compared to the results of a numerical 3-D FEL code.