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 <<1 are then obtained in both Hermite and Laguerre representations. The cross- coupling 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 off-diagonal 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. Keywords: Free electron lasers; Laser oscillators; Optical resonators; Reflection matrix.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 27, 1988
- Accession Number
- ADA202472
Entities
People
- Chai AMei Tang
- Phillip A. Sprangle
- S. Riyopoulos
Organizations
- United States Naval Research Laboratory