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https://hdl.handle.net/2142/23319
Description
Title
The beam modes of general optical cavities
Author(s)
Smith, Suzanne Dadgar
Issue Date
1991
Doctoral Committee Chair(s)
Verdeyen, Joseph T.
Department of Study
Electrical and Computer Engineering
Discipline
Electrical and Computer Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
This thesis describes the use of the eigenvalue method for computing the modes of cavity resonators. A matrix formulation of the integral equation describing the modes of a resonator is a powerful and flexible method of solution, in particular, when compared to iterative techniques. The matrix formulation includes improvements in speed and provides the higher-order field solutions, not readily available from the iterative method. A general formulation of the technique is presented and then verified by an application to two test cases, the parallel plate and Gaussian tapered mirror geometries. These two cases can be solved using methods other than the eigenvalue method. The parallel plate geometry is solved with the iterative solution to the integral equation and the Gaussian taper by analytic means. The results can then be compared with those from the eigenvalue method. Flexibility of the eigenvalue method is enhanced by the inclusion of a variable parameter set defining an optimal basis set for the expansion of the cavity fields. Computational limitations of the method due to the accuracy of the Hermite polynomial computation are also discussed. New results are presented for a hole-coupled tapered geometry, which can be used as a beginning model for the numerical study of semiconductor laser cavities.
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