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Title: Reciprocity and orthogonality relations for ring resonators

Abstract

A general and rigorous derivation of the reciprocity and orthogonality relations for ring resonators is given without resorting to matrix representations. The general form of the integral equations appropriate to the study of ring resonators containing at least one hard aperture is discussed, and a reciprocity relation for a very general class of ring resonator is established using a theorem concerning so-called Hilbert-Schmidt kernels. It is shown that under very general conditions linear ring resonators are reciprocal and that the transverse eigenmodes for propagation in any direction around the resonator are biorthogonal to those for propagation in the opposite direction. 17 references.

Authors:
;
Publication Date:
Research Org.:
Max-Planck-Institut fuer Quantenoptik, Garching, West Germany
OSTI Identifier:
5811553
Resource Type:
Journal Article
Journal Name:
IEEE J. Quant. Electron.; (United States)
Additional Journal Information:
Journal Volume: QE-20
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; RING LASERS; RESONANCE; APERTURES; EIGENVALUES; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; EQUATIONS; LASERS; OPENINGS; 420300* - Engineering- Lasers- (-1989)

Citation Formats

Wright, E M, and Obrien, D P. Reciprocity and orthogonality relations for ring resonators. United States: N. p., 1984. Web. doi:10.1109/JQE.1984.1072319.
Wright, E M, & Obrien, D P. Reciprocity and orthogonality relations for ring resonators. United States. https://doi.org/10.1109/JQE.1984.1072319
Wright, E M, and Obrien, D P. 1984. "Reciprocity and orthogonality relations for ring resonators". United States. https://doi.org/10.1109/JQE.1984.1072319.
@article{osti_5811553,
title = {Reciprocity and orthogonality relations for ring resonators},
author = {Wright, E M and Obrien, D P},
abstractNote = {A general and rigorous derivation of the reciprocity and orthogonality relations for ring resonators is given without resorting to matrix representations. The general form of the integral equations appropriate to the study of ring resonators containing at least one hard aperture is discussed, and a reciprocity relation for a very general class of ring resonator is established using a theorem concerning so-called Hilbert-Schmidt kernels. It is shown that under very general conditions linear ring resonators are reciprocal and that the transverse eigenmodes for propagation in any direction around the resonator are biorthogonal to those for propagation in the opposite direction. 17 references.},
doi = {10.1109/JQE.1984.1072319},
url = {https://www.osti.gov/biblio/5811553}, journal = {IEEE J. Quant. Electron.; (United States)},
number = ,
volume = QE-20,
place = {United States},
year = {Sat Dec 01 00:00:00 EST 1984},
month = {Sat Dec 01 00:00:00 EST 1984}
}