OPTICAL MODES IN A PARTIALLY WAVE-GUIDED CAVITY

The behavior of the optical beam in an FEL cavity is well understood in both the long- and short-wavelength limits. At long wavelengths the optical mode interacts strongly with the walls, which act as a waveguide. At short wavelengths the optical beam in an FEL is undisturbed by the walls; it propagates as a simple Gaussian. We are interested in the intermediate regime, where, as the wavelength increases, the optical mode grows and begins to feel the influence of the walls, causing the mode shape to distort and losses to occur. Using a Fox-Li technique to propagate in free space and a decomposition of the Gaussian beam into waveguide modes inside the undulator, we calculate the changes in mode shape and cavity losses as the wavelength increases. The resulting theory and numerical calculations are an important consideration for the design of mid- to far-infrared FEL systems.