Measurement of stimulated transverse mode mixing in a free electron laser

We report the first measurement of the off-diagonal terms in the transverse gain matrix in a free electron laser. We show that the higher order transverse modes stimulated in the FEL interaction diminish in amplitude as the electron beam size is increased, that the far field and the near field effects of the excited modes are not equivalent, and that in this low divergence case, the mode mixing is insensitive to the resonance parameter. Remarkably close agreement is demonstrated with the theory [1]. The effects of a multiple mode input beam are also observed, and the theoretical expression is derived.