Simple geometric interpretation of signal evolution in phase-sensitive fibre optic parametric amplifier

Abstract

Visualisation of complex nonlinear equation solutions is a useful analysis tool for various scientific and engineering applications. We have re-examined 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.

The coupled 1:2 resonance in a symmetric case and parametric amplification model

“…Here we will try to find some boundary conditions for phase space and maximum transfer energy. In many papers of physics journals, the scientists considered the dynamics of this problem (for instance see [5,7,15,16,18,19,22]). For example in [16,18,19], some results on the analysis of phase portraits and the solution of the optimization problem are presented.…”

“…As we mentioned above, the major problem is the existence of trajectories under maximum transfer energy. Based on application, with these findings, we can use a proper example to phase-sensitive amplification (see [16,18,19]). Also we can improve the detuned parameters, initial conditions, and level energies.…”