The beam modes of general optical cavities

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical and Computer Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Smith, Suzanne Dadgar

Contributors dc:contributor

• Verdeyen, Joseph T.

• Engineering, Electronics and Electrical

Statement dc:rights

• Copyright 1991 Smith, Suzanne Dadgar

Language dc:language

eng

Identifier

AAI9210995
(UMI)AAI9210995

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23319