An Analysis of Multireflector Optical Resonators

Citation

Clark, Peter Osgoode (1964) An Analysis of Multireflector Optical Resonators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/M4PW-BM47. https://resolver.caltech.edu/CaltechETD:etd-09112002-181405

Abstract

Geometrical optics and self-consistent field techniques are used to determine the properties of multireflector optical resonators in which the field distributions are multiply-reflected and travel in clockwise and counter-clockwise directions in the cavity. Two types of resonators are considered, a symmetric N-mirror resonator whose axis is a regular N-sided polygon and a nonsymmetric four-mirror resonator whose axis is a parallelogram. The geometrical optics approach leads to sets of coupled nonlinear difference equations which describe the paths of optical rays in the resonators. Approximate solutions to the equations are obtained and a calculation of the first correction term is carried out in the case of the symmetric cavity. It is shown that the approximate analysis may also be formulated in a chain matrix representation. Stability conditions are obtained which determine the mirror curvatures and spacings for high or low-loss multireflector resonators. The set of difference equations may be reduced to recurrence relations which enable the path of an optical ray in the cavity to be calculated exactly using a digital computer. Integral equations are obtained which determine the mode distributions in the symmetric N-mirror and nonsymmetric four-mirror cavities. The equations are not solved exactly except in the particular case of a "pseudo-confocal" symmetric resonator which has non-spherical mirrors. Solutions to the general integral equations are determined in the zero wavelength limit. Resonance conditions and detailed descriptions of the field distributions are obtained for both the symmetric and nonsymmetric resonators. For the particular cases of the symmetric three and four-mirror resonators the diffraction losses are obtained by transforming the integral equations to a form such that existing numerical solutions may be used. Two-mirror cavities are treated as simplifications of the multireflector theory. The results of other authors are obtained and extended. The expressions for the resonance condition and minimum mode volume for the symmetric nonconfocal resonator are found to differ slightly from those previously derived. Amplitude and phase distributions throughout the volume of a plane-parallel Fabry-Perot resonator are calculated numerically on an IBM 7090 computer.

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