Čerenkov free-electron lasers have primarily operated on the fundamental guided mode of the dielectric waveguide. Higher-order generation would allow short wavelength emission in a relatively large scale resonator. In comparison to the fundamental mode, we find that gain on higher-order modes can be significant in a planar geometry. This analysis is presented with a discussion of practical limits.

• Received 5 December 2002

DOI:https://doi.org/10.1103/PhysRevE.67.036611