A canonical formulation for analyzing multielement unstable resonators
Abstract
A simple but general formulation for the unified analysis of many different varieties of unstable optical resonators is obtained by expressing the roundtrip Huygens' integral for the resonator in terms of the roundtrip paraxial ray matrix. Complicated multielement resonators are all reduced to a single equivalent collimatedbeam diffraction problem. Essential assumptions in the analysis are that all elements in the resonator obey paraxial ray theory and that there is only one significant output coupler or limiting aperture per round trip inside the resonator. The only parameters needed to describe an arbitrary unstable resonator in this formulation are the roundtrip magnification and either the equivalent Fresnel number or else an equivalent collimated Fresnel number, plus for variablereflectivity mirrors a specification of the mirror reflectivity profile.
 Publication:

IEEE Journal of Quantum Electronics
 Pub Date:
 January 1976
 DOI:
 10.1109/JQE.1976.1069033
 Bibcode:
 1976IJQE...12...35S
 Keywords:

 Canonical Forms;
 Frequency Stability;
 Optical Resonators;
 Ray Tracing;
 Wave Diffraction;
 Mathematical Models;
 Matrices (Mathematics);
 Mirrors;
 Ring Lasers;
 Systems Analysis;
 Systems Stability;
 Lasers and Masers