Citation
Clark, Peter Osgoode (1964) An analysis of multireflector optical resonators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/M4PWBM47. https://resolver.caltech.edu/CaltechETD:etd09112002181405
Abstract
Geometrical optics and selfconsistent field techniques are used to determine the properties of multireflector optical resonators in which the field distributions are multiplyreflected and travel in clockwise and counterclockwise directions in the cavity. Two types of resonators are considered, a symmetric Nmirror resonator whose axis is a regular Nsided polygon and a nonsymmetric fourmirror 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 lowloss 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 Nmirror and nonsymmetric fourmirror cavities. The equations are not solved exactly except in the particular case of a "pseudoconfocal" symmetric resonator which has nonspherical 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 fourmirror resonators the diffraction losses are obtained by transforming the integral equations to a form such that existing numerical solutions may be used.
Twomirror 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 planeparallel FabryPerot resonator are calculated numerically on an IBM 7090 computer.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Electrical Engineering 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  10 March 1964 
Record Number:  CaltechETD:etd09112002181405 
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd09112002181405 
DOI:  10.7907/M4PWBM47 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  3455 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  13 Sep 2002 
Last Modified:  21 Dec 2019 02:06 
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