Analytic approaches to unstable resonators
Abstract
A method for obtaining asymptotic solutions of the unstable resonator integral equation which is valid for all values of the magnification was developed. Approximations were made on the Greens functions rather than the eigenmodes, leading to results which are easily generalized to different mirror geometries. 'Diffraction dominated eigenmodes' for resonators where each ray escapes after a few transits were differentiated from 'waveguide dominated eigenmodes' which are obtained for cavities with a large number of transits per ray. The solutions obtained were seen to agree in the appropriate limits with other asymptotic solutions, numerical results, and geometric optics predictions. To include the effects of gain, the unstable resonator equation was derived from Maxwell's equations in a polarizable medium. The resulting equations have the same structure as the empty resonator equation, and similar approximations can be used. Some features of the effects of saturation on the eigenmodes of an unstable resonator were considered.
 Publication:

Final Report
 Pub Date:
 1979
 Bibcode:
 1979sai..reptR....N
 Keywords:

 Asymptotes;
 Eigenvalues;
 Eigenvectors;
 Fresnel Integrals;
 Optical Resonators;
 Approximation;
 Cylindrical Bodies;
 Diffraction Patterns;
 Waveguides;
 Electronics and Electrical Engineering