Higher-Order Modes in Free Electron Lasers

Free electron laser theory is developed from the Maxwell and Lorentz force equations; the properties and characteristics of the laser are reviewed. The wave equation is solved for the fundamental Gaussian mode, and higher-order modes in Cartesian and cylindrical coordinate spaces, yielding expressions for the complete and orthogonal basis sets of Hermite- and Laguerre- Gaussian beams. Motivated by the evident inclusion of higher-order modes in free electron laser simulations, a tool is developed for the higher-order (in particular Laguerre-Gaussian) modal analysis of simulated free electron laser beams.