An application of matrix theory to the evolution of coupled modes

David A. Edwards; Joseph D. Fehribach; Richard O. Moore; Colin J. McKinstrie

doi:10.1137/110860744

An application of matrix theory to the evolution of coupled modes

David A. Edwards, Joseph D. Fehribach, Richard O. Moore, Colin J. McKinstrie

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In order to overcome loss in optical fibers, experimentalists are interested in employing parametric amplifiers using four-wave mixing. Upon linearizing the nonlinear Schrödinger equation typically used as a model for such amplifiers, a system of ODEs results for the complex amplitude. The solution can also be expressed as the product of transfer matrices and the initial condition and its conjugate. Physical insight about the fiber-optic system can be gained by examining the theoretical properties of the matrices in the mathematical system. This module, suitable for inclusion in an advanced undergraduate or graduate linear algebra course, explores these properties and should provide a good physical motivation for the theoretical explorations in such a course.

Original language	English (US)
Pages (from-to)	764-787
Number of pages	24
Journal	SIAM Review
Volume	55
Issue number	4
DOIs	https://doi.org/10.1137/110860744
State	Published - 2013

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computational Mathematics
Applied Mathematics

Keywords

Education
Eigenvalues
Fiber optics
Matrix theory
Singular value decomposition

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10.1137/110860744

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abstract = "In order to overcome loss in optical fibers, experimentalists are interested in employing parametric amplifiers using four-wave mixing. Upon linearizing the nonlinear Schr{\"o}dinger equation typically used as a model for such amplifiers, a system of ODEs results for the complex amplitude. The solution can also be expressed as the product of transfer matrices and the initial condition and its conjugate. Physical insight about the fiber-optic system can be gained by examining the theoretical properties of the matrices in the mathematical system. This module, suitable for inclusion in an advanced undergraduate or graduate linear algebra course, explores these properties and should provide a good physical motivation for the theoretical explorations in such a course.",

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AU - Moore, Richard O.

AU - McKinstrie, Colin J.

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N2 - In order to overcome loss in optical fibers, experimentalists are interested in employing parametric amplifiers using four-wave mixing. Upon linearizing the nonlinear Schrödinger equation typically used as a model for such amplifiers, a system of ODEs results for the complex amplitude. The solution can also be expressed as the product of transfer matrices and the initial condition and its conjugate. Physical insight about the fiber-optic system can be gained by examining the theoretical properties of the matrices in the mathematical system. This module, suitable for inclusion in an advanced undergraduate or graduate linear algebra course, explores these properties and should provide a good physical motivation for the theoretical explorations in such a course.

AB - In order to overcome loss in optical fibers, experimentalists are interested in employing parametric amplifiers using four-wave mixing. Upon linearizing the nonlinear Schrödinger equation typically used as a model for such amplifiers, a system of ODEs results for the complex amplitude. The solution can also be expressed as the product of transfer matrices and the initial condition and its conjugate. Physical insight about the fiber-optic system can be gained by examining the theoretical properties of the matrices in the mathematical system. This module, suitable for inclusion in an advanced undergraduate or graduate linear algebra course, explores these properties and should provide a good physical motivation for the theoretical explorations in such a course.

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KW - Eigenvalues

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KW - Matrix theory

KW - Singular value decomposition

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An application of matrix theory to the evolution of coupled modes

Abstract

All Science Journal Classification (ASJC) codes

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