Quantum regime of harmonic generation in the free electron laser

An analysis of harmonic generation in a free electron laser (FEL) with a planar wiggler is presented in the regime where photon recoil cannot be neglected and the beam-wave interaction must be described quantum mechanically. This analysis shows that in contrast to the classical regime where photon recoil is negligible, in the quantum regime each harmonic can be excited independently using an appropriate value of detuning and the peak harmonic intensity increases linearly with harmonic number.