On the sideband structure of free electron laser emission spectra

Abstract

Assuming the magnetic field in a planar undulator of a typical infrared free electron laser, in the paper we address specific effects on the spontaneous emission and the small-signal gain imposed by the electron dynamics. It is analytically demonstrated that weak misalignment (order of 1 mrad) of the undulator axis with respect to the optical axis of the resonator leads to a spectrum being rich in side maxima (sidebands). These sidebands appear as a consequence of a phase modulation of the radiation of the electrons caused by the betatron oscillation, their spectral spacing roughly given by the Doppler up-shifted betatron frequency.