TRANSVERSE-MODE COUPLING AND SUPERMODE ESTABLISHMENT IN A FREE-ELECTRON LASER-OSCILLATOR

A three-dimensional study of transverse mode evolution in a f ree-elec tron laser (FEL) oscillator is presented. The total electromagnetic fi eld circulating in the resonator is represented as a superposition of transverse modes of the cavity. Coupled-mode theory is employed to der ive a generalized 3-D steady-state oscillation criterion, from which t he oscillator supermode can be found analytically in the linear gain a pproximation. The oscillator supermode, which is the eigenmode solutio n of the oscillator at steady-state, keeps its transverse profile and polarization after each round-trip. Relations between the oscillator s upermode and the amplifier supermode are discussed. It is shown that t hey are identical only when the feedback process is entirely non-dispe rsive and non-discriminating. We employ a 3-D nonlinear simulation cod e based on the same transverse mode expansion to demonstrate the evolv ement of transverse modes in the oscillator towards formation of a sup ermode in a simple example. The simulation shows that the steady-state result of the oscillation buildup simulation is identical to the supe rmode predicted by the analytical approach.