Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Eigenmode expansions using biorthogonal functions: complex-valued Hermite–Gaussians

Not Accessible

Your library or personal account may give you access

Abstract

A number of important optical systems, including gain-guided semiconductor lasers and unstable optical resonators, have governing equations that are linear but not Hermitian or self-adjoint. As a consequence, the propagation eigenmodes of these systems are not orthogonal in the usual fashion but rather are biorthogonal to a set of adjoint functions. If one wishes to expand an arbitrary wave of such a system in terms of its eigenmodes, conventional wisdom says that the expansion coefficients are given by the quadrature integrals between the input wave and the adjoint functions. Using a parabolic gain-guided system with complex Hermite–Gaussian eigenfunctions as a test case, we find that under a wide range of circumstances finite expansions using the quadrature integrals fail to converge properly, even for simple and realistic input functions. We then demonstrate that the coefficients for a finite expansion with minimum least-squares error in a biorthogonal system must be obtained from a more complex procedure based on inverting the eigenmode orthogonality matrix. Further tests on the complex Hermite–Gaussian system show that series expansions using these minimum-error coefficients converge and give much smaller errors under all circumstances.

© 1997 Optical Society of America

Full Article  |  PDF Article
More Like This
Eigenmode expansions using biorthogonal functions: complex-valued Hermite-Gaussians: reply to comment

Adnah Kostenbauder, Yan Sun, and A. E. Siegman
J. Opt. Soc. Am. A 23(6) 1528-1529 (2006)

Hermite–gaussian functions of complex argument as optical-beam eigenfunctions

A. E. Siegman
J. Opt. Soc. Am. 63(9) 1093-1094 (1973)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (11)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (35)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved