Abstract
Spontaneous and stimulated emission for various free-electron-laser configurations in the small-signal, single-electron regime is analyzed by using Madey’s theorem1 It is shown how the free-electron laser can be analyzed as a phased-array antenna. The radiation sources (i.e., the array elements) are generated by a single electron as it oscillates transversely in the various wiggler periods. The interference of the radiation from the various wiggler periods is considered to calculate the spontaneous emission. Madey’s theorem is then applied to obtain the stimulated emission. The calculations presented are classical and considerably simpler than those in the literature. Relations for the spontaneous emission and gain are derived for the free-electron laser, the optical klystron, higher harmonics in a planar wiggler free-electron laser, and the case of N wiggler sections connected through dispersive sections. Finally it is proved that the uniform wiggler free-electron laser has the maximum gain-energy acceptance product with respect to variations in phase shift and dispersion. For example, in the optical klystron the gain is increased by having a separate dispersive section.
© 1984 Optical Society of America
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