## Schmidt decompositions of parametric processes I: Basic theory and simple examples |

Optics Express, Vol. 21, Issue 2, pp. 1374-1394 (2013)

http://dx.doi.org/10.1364/OE.21.001374

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### Abstract

Parametric devices based on four-wave mixing in fibers perform many signal-processing functions required by optical communication systems. In these devices, strong pumps drive weak signal and idler sidebands, which can have one or two polarization components, and one or many frequency components. The evolution of these components (modes) is governed by a system of coupled-mode equations. Schmidt decompositions of the associated transfer matrices determine the natural input and output mode vectors of such systems, and facilitate the optimization of device performance. In this paper, the basic properties of Schmidt decompositions are derived from first principles and are illustrated by two simple examples (one- and two-mode parametric amplification). In a forthcoming paper, several nontrivial examples relevant to current research (including four-mode parametric amplification) will be discussed.

© 2013 OSA

**OCIS Codes**

(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(270.6570) Quantum optics : Squeezed states

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: September 11, 2012

Revised Manuscript: December 5, 2012

Manuscript Accepted: December 30, 2012

Published: January 14, 2013

**Citation**

C. J. McKinstrie and M. Karlsson, "Schmidt decompositions of parametric processes I: Basic theory and simple examples," Opt. Express **21**, 1374-1394 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-1374

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