Transformations of Gaussian light beams caused by reflection in FEL (Free Electron Lasers) resonators
Abstract
The transformation of Gaussian radiation beams caused by reflection off mirrors is an important issue for FELs operating as oscillators. The reflected radiation from a single incident Gaussian mode will contain other modes due to the finite mirror size, the deflection of the beam and mismatches in the curvature. A method for analytic computation of the reflection matrix is developed by taking the convolution of the source function at the surface of the mirror with the paraxial propagator. The mirror surface that reflects spherical incoming wavefronts into spherical outgoing is determined analytically. Integral expressions for the reflection coefficients R(mn) sub pq for any incoming mode u sub mn into the outgoing u sub pq are obtained as functions of the deflection angle phi, the reflected beam waist sub 0 and the mirror size. Analytic expansions of the reflection matrix in powers of the diffraction angle theta sub d much less than 1 are then obtained in both Hermite and Laguerre representations. The crosscoupling among vector components of the radiation field, caused by the curvature of the mirror surface, is included. It is shown that the lowest order contribution to the offdiagonal matrix elements is caused by the finite mirror size. The effects of the mirror curvature and the deflection of the light beam enter the reflection matrix as first order corrections in theta sub d.
 Publication:

Naval Research Lab. Report
 Pub Date:
 October 1988
 Bibcode:
 1988nrl..reptT....R
 Keywords:

 Cavity Resonators;
 Free Electron Lasers;
 Light Beams;
 Mirrors;
 Optical Reflection;
 Reflected Waves;
 Curvature;
 Deflection;
 Diffraction;
 Laguerre Functions;
 Oscillators;
 Lasers and Masers