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Multimode coherent coupling and optical guiding in Raman free-electron lasers

Scharlemann and co-workers1 studied optical guiding in a short-wavelength free-electron laser (FEL) by using a weakly guiding optical fiber to model the bunched electron beam, and Bhattacharjee and co-workers2 presented a theoretical approach to the problem of optical guiding in a Raman FEL, in which the radiation wave is expanded as a complete set of vacuum waveguide modes. Generally speaking, different vacuum waveguide modes possess different wave number. In this sense, they are non-coherent. However, the dispersion relations of vacuum waveguide modes can be modified by introducing an electron beam so that some of them might have the same wave number and become coherent modes under proper conditions. Based on this, we have developed a multimode coherent coupling theory to investigate optical guiding in a Raman FEL amplifier. Under the assumption of a small-radius electron beam passing through an ideal linear wiggler magnetic field, the coherent coupling multimode dispersion equation in a rectangular waveguide is obtained. A special attention is paid to coherent coupling of TE10 mode with TE30 mode. Solving numerically the dispersion equation shows that the coherent coupling of TE10 mode with TE30 mode can result in optical guiding if proper operating parameters are chosen. However, the optical guiding is of strong frequency-dispersion.