The theory of free-electron lasers is extended to include the new coupling between an electron beam and optical wave propagating at an angle ϑ in an arbitrary harmonic. The coupling allows the laser to be tuned to a wider range of wavelengths and to include the effects of emittance in the electron beam. The formulation of the results in terms of coupling constants means that the existing knowledge of high gain, low gain, weak optical fields, strong optical fields, and short pulses in free-electron lasers can be immediately generalized to off-axis propagation in an arbitrary harmonic.

• Received 7 June 1984

DOI:https://doi.org/10.1103/PhysRevA.31.828