Minimization of Optical Rogue Waves Formation based on Hamiltonian approach

Abstract

It is well known that Benjamin-Feir instability plays a crucial role in generating underseas rogue waves, for which its formation process can be carried out within a short period of time, but causing devastating threats to our natural habitats. One can attempt to control or stabilize such nonlinear plane waves via self-dissipation, provided that amplitude of such waves is sufficiently low. For rogue waves with higher amplitude, it suffices to observe the stable wave patterns underseas, and makes use of damping techniques to recover its original amplitude into normal amplitudes. Currently, there is a lack of specialized mathematical tools for analyzing underlying physics of these large magnitude nonlinear rogue waves. In this paper, we provide a framework of mathematical model for formation of rogue waves, and demonstrate statistical properties of optical rogue waves through Hamiltonian approach (that is widely used in statistical mechanics field). Next, we formulate new optimization criteria for minimizing its intensity by making use of first-order Riccati differential equation, and outline several important physical factors that we need to control in reality. This opens a new door for mitigating detrimental effects from fiber nonlinearity in optical communications.