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.
Highlights
Parametric devices based on four-wave mixing in fibers perform many signal-processing functions required by optical communication systems
The basic properties of Schmidt decompositions are derived from first principles and are illustrated by two simple examples
Parametric devices based on four-wave mixing (FWM) in fibers can amplify, frequency convert, phase conjugate, regenerate and sample optical signals in classical communication systems [1,2,3,4,5,6]
Summary
Parametric devices based on four-wave mixing (FWM) in fibers can amplify, frequency convert, phase conjugate, regenerate and sample optical signals in classical communication systems [1,2,3,4,5,6] They can generate photon pairs for quantum information experiments [7,8,9,10]. Previous derivations of these results were based on the laws of quantum optics [17, 18], in which context they are standard [21,22,23,24]. In a forthcoming paper, new solutions of the CMEs are obtained and used to discuss several nontrivial examples of current interest (including four-mode parametric amplification)
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