Asymptotic Analysis of Off-Center Unstable Confocal Resonators.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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A polynomial equation for the eigenvalues of the modes of off-center unstable confocal resonators is developed. A constant gain for steady state modes in a bare cavity is assumed. The field is build-up from right and left-traveling diffraction components for a number of round trips through the resonator and geometrical components from the core region. Using an asymptotic expansion of the diffraction integral, the boundary conditions are developed. These, with the propagation equations across the resonator, are used to relate the diffraction and geometrical components to the diffraction amplitude after one round trip in the cavity. The polynomial equation for the eigenvalues is developed from the first round trip amplitude function, after approximating a slowly varying function of the field to be constant. A method is proposed for examining the behavior of the approximated function for the centered resonator case and including it in mode calculations if necessary. Author
- Electricity and Magnetism