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
收藏
页码：764 / 787
页数：24
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