Theory of optical guiding in free electron lasers.

摘要

The spatial properties and hence overall performance of a free electron laser will depend on the fact that such a laser is generated by an electron beam which, as both a gain and refractive medium, is transversely nonuniform. Under certain circumstances, optical guiding may be realized, where the radiation field is stably confined near the electron beam and amplified along the beam indefinitely. In the small signal regime, the three dimensional evolution of the radiation field through the interaction region is determined by an expansion in the guided modes. The expansion is made possible by implementing the biorthogonality of the eigenmodes of the coupled system. The eigenmodes are found to be of vectorial form with three components, one specifies the guided radiation mode and the other two describe the density and energy modulations of the electron beam.;The numerical and analytical methods are developed for solutions of the guided modes. The former approach leads to a merit function with every minimum corresponding to a discrete guided mode. In the latter approach a variational approximation technique capable of giving all the characteristics of the guided modes is derived.;In the high gain regime, optical guiding may become dominant as the radiation field being amplified through the interaction region, resulting in a resonator with different patterns of propagation in forward and backward passes. The guided mode expansion is applied to the analysis of such novel resonator and design strategies are proposed. It is found that maximal gain and optimal transverse mode quality can be achieved simultaneously and the resonator be made optimal at high gain while stable at low gain, in addition, proper configurations of asymmetrical cavity can be used for the reduction of power loading on the cavity mirrors without affecting either gain or mode quality.