Hermite-Gaussian decomposition of free electron laser optical fields

Free electron lasers (FELs) are favored in many research applications due to their ability to operate primarily in the fundamental (Gaussian) mode. In oscillator FELs, the appropriate basis set for decomposition is uniquely determined by the cavity parameters. Since FEL amplifiers generate and amplify the optical field over the length of the undulator influenced only by the electron beam, the appropriate basis set is not uniquely determined. A methodology is presented to decompose the optical fields with a Hermite-Gaussian basis set chosen such that the number of higher-order modes is minimized. The methodology is used to study amplifier FEL optical beams for comparison with experiment