Abstract
Visualisation of complex nonlinear equation solutions is a useful analysis tool for various scientific and engineering applications. We have re-examined the geometrical interpretation of the classical nonlinear four-wave mixing equations for the specific scheme of a phase sensitive one-pump fiber optical parametric amplification, which has recently attracted revived interest in the optical communications due to potential low noise properties of such amplifiers. Analysis of the phase portraits of the corresponding dynamical systems provide valuable additional insight into field dynamics and properties of the amplifiers. Simple geometric approach has been proposed to describe evolution of the waves, involved in phase-sensitive fiber optical parametric amplification (PS-FOPA) process, using a Hamiltonian structure of the governing equations. We have demonstrated how the proposed approach can be applied to the optimization problems arising in the design of the specific PS-FOPA scheme. The method considered here is rather general and can be used in various applications.
Highlights
Optical parametric amplification (OPA) in fibers [1, 2] is a classical nonlinear phenomenon that manifests itself as a process of nonlinear energy transfer from powerful pumping wave(s) to signal wave(s), leading to effective amplification of the latter
Fiber OPA has attracted a great deal of renewed interest as a promising technology for low-noise parametric amplification in high-capacity optical communications [3,4,5,6,7,8,9,10,11,12]
This recent revival of rather classical field is strongly supported by advances in the technology of highlynonlinear fibers (HNLF) with a good figure of merit
Summary
Optical parametric amplification (OPA) in fibers [1, 2] is a classical nonlinear phenomenon that manifests itself as a process of nonlinear energy transfer from powerful pumping wave(s) (considered as energy sources) to signal wave(s), leading to effective amplification of the latter. Fiber OPA has attracted a great deal of renewed interest as a promising technology for low-noise parametric amplification in high-capacity optical communications [3,4,5,6,7,8,9,10,11,12] This recent revival of rather classical field is strongly supported by advances in the technology of highlynonlinear fibers (HNLF) with a good figure of merit (high nonlinear coefficient with a reasonably low losses). Low noise in-line amplifiers would offer significant link performance improvement Such phase-sensitive amplifiers may open up new opportunities for all-optical regeneration of coherent optical signal [9, 13,14,15]. We will study energy transfer between pump and signal using intuitive phase portraits (geometric interpretation) and find optimum parameters of phase-sensitive fibre optic parametric amplifiers (PS-FOPA) leading to the maximum gain
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