Spontaneous and stimulated emission for various free-electron laser configurations in the small signal single-electron regime is analyzed by using Madey’s theorem.1 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.

© 1984 Optical Society of America

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