Published In

Journal of the Optical Society of America A: Optics, Image Science and Vision

Document Type

Article

Publication Date

3-1-1995

Subjects

Matrices, Optics -- Mathematical models, Gaussian beams -- Propagation

Abstract

Sylvester's theorem is often applied to problems involving light propagation through periodic optical systems represented by unimodular 2 × 2 transfer matrices. We extend this theorem to apply to broader classes of optics-related matrices. These matrices may be 2 × 2 or take on an important augmented 3 × 3 form. The results, which are summarized in tabular form, are useful for the analysis and the synthesis of a variety of optical systems, such as those that contain periodic distributed-feedback lasers, lossy birefringent filters, periodic pulse compressors, and misaligned lenses and mirrors. The results are also applicable to other types of system such as periodic electric circuits with intracavity independent sources, high-energy particle accelerators, and periodic computer graphics manipulations that may include object translation. As an example, we use the 3 × 3 form of Sylvester's theorem to examine Gaussian beam propagation in a misaligned resonator.

Description

This paper was published in Journal of the Optical Society of America A and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-12-3-578. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Persistent Identifier

http://archives.pdx.edu/ds/psu/8249

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