Optical Guiding in a Free-Electron Laser

By use of two-dimensional approximations for the equations that describe a high-gain free-electron laser (FEL) amplifier, and the properties of optical fibers, it is shown that the coherent interaction between the light and the electron beam in an FEL can optically guide the light. In the exponential-gain regime, the FEL performance in the presence of strong diffraction can be simply described by a cubic equation for the complex gain and the dispersion relation for an optical fiber. The phenomenon of optical guiding is illustrated with two-dimensional numerical simulations. The phenomenon has applications to short-wavelength FEL's, to directing of intense light, and to bending of x rays.