Reflection Matrix for Optical Resonators in FEL (Free Electron Lasers) Oscillators

摘要

The transformations 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 found to be a paraboloid. Integral expressions for the reflection coefficients R sub pq superscript mn for any incoming mode u sub mn into the outgoing u sub pq are obtained as function of the reflection angle phi, the reflected beam spot size W sub 0 and the mirror size. The coefficient R sub 00 superscript 00 for the lowest-to-lowest mode reflection is determined analytically. The spot size W sub 0 can then be selected, depending on the mirror size, to maximize R sub 00 superscript 00. The ratio of the mirror size to the spot size is the dominant factor determining the reflection coefficient. The effects of deflecting the light beam enter as small corrections, of first order in the diffraction angle theta sub d < <1. Keywords: Laser oscillators; Free electron lasers; Resonators; Reflection matrix. (JHD)