An Application of Matrix Theory to the Evolution of Coupled Modes

被引：0

作者：

Edwards, David A. ^{[1
]}

Fehribach, Joseph D. ^{[2
]}

Moore, Richard O. ^{[3
]}

McKinstrie, Colin J. ^{[4
]}

机构：

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[2] Worcester Polytech Inst, Dept Math Sci, Worcester, MA 01609 USA

[3] New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA

[4] Alcatel Lucent, Bell Labs, Holmdel, NJ 07733 USA

来源：

SIAM REVIEW | 2013年 / 55卷 / 04期

基金：

美国国家科学基金会;

关键词：

education; eigenvalues; fiber optics; matrix theory; singular value decomposition; OPTICAL PARAMETRIC-AMPLIFIERS; DISPERSIVE DIELECTRIC FIBERS; QUANTUM-NOISE PROPERTIES; WAVES; AMPLIFICATION; TRANSMISSION; REDUCTION; PULSES;

D O I：

10.1137/110860744

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In order to overcome loss in optical fibers, experimentalists are interested in employing parametric amplifiers using four-wave mixing. Upon linearizing the nonlinear Schrodinger 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.

引用

页码：764 / 787

页数：24

共 50 条

[41] An application of the infinite matrix theory to Mathieu equation
De Malafosse, Bruno
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2006, 52 (10-11) : 1439 - 1452
[42] Application of random matrix theory to biological networks
Luo, Feng
Zhong, Jianxin
Yang, Yunfeng
Scheuermann, Richard H.
Zhou, Jizhong
[J]. PHYSICS LETTERS A, 2006, 357 (06) : 420 - 423
[43] Application of random matrix theory to quasiperiodic systems
Schreiber, M
Grimm, U
Römer, RA
Zhong, JX
[J]. PHYSICA A, 1999, 266 (1-4): : 477 - 480
[44] Theory and application of the functional expansion fission matrix
He, Donghao
Zhang, Tengfei
Liu, Xiaojing
[J]. ANNALS OF NUCLEAR ENERGY, 2022, 179
[45] APPLICATION OF REACTION MATRIX THEORY TO MESON PROCESSES
COOK, JL
[J]. AUSTRALIAN JOURNAL OF PHYSICS, 1968, 21 (06): : 769 - +
[46] The BV formalism: Theory and application to a matrix model
Iseppi, Roberta A.
[J]. REVIEWS IN MATHEMATICAL PHYSICS, 2019, 31 (10)
[47] A generalization of the pascal matrix and an application to coding theory
Nikseresht, Ashkan
Khormaei, Marziyeh Beygi
Namazi, Shohreh
[J]. LINEAR & MULTILINEAR ALGEBRA, 2024, 72 (09): : 1523 - 1534
[48] EVOLUTION OF THE TRANSVERSE-MODES IN A FEL, AND APPLICATION TO THE ORSAY EXPERIMENT
ELLEAUME, P
DEACON, DAG
[J]. PROCEEDINGS OF THE SOCIETY OF PHOTO-OPTICAL INSTRUMENTATION ENGINEERS, 1984, 453 : 262 - 268
[49] Application of algebraic properties of matrix to the study of normal modes of vibration in molecules
Diana Bîclea
[J]. The European Physical Journal Plus, 137
[50] Relaxation schemes for normal modes of magnetic vortices: Application to the scattering matrix
Wysin, GM
[J]. PHYSICAL REVIEW B, 2001, 63 (09):

← 1 2 3 4 5 →