Few-cycle solitons in supercontinuum generation dynamics

Abstract

Abstract. We review several propagation models that do not rely on the slowly-varying-envelope approximation (SVEA), and can thus be considered as fundamental models addressing the formation and propagation of few-cycle pulsed field structures and solitary waves arising in the course of intense ultrashort optical pulse evolution in nonlinear media and beyond octave-bandwidth optical spectrum broadening. These generic models are: the modified-Korteweg-de-Vries (mKdV), the sineGordon (sG), and the mixed mKdV-sG equations. To include wave polarization dynamics, the vector extensions of both mKdV and sG equations are introduced. Multi-octave-spanning supercontinuum generation and few-cycle soliton structures are highlighted from numerical simulations.

Construction of rational solutions of the real modified Korteweg-de Vries equation from its periodic solutions

“…Recently, a model based on two coupled mKdV equations was used to describe the soliton propagation in two parallel optical waveguide array, in the presence of linear nondispersing coupling and in the few-cycle regime [26]. The mKdV, sG, and mKdV-sG equations were also used in modeling the generation of supercontinuum like white light laser in optical fibers [27,28]. The mKdV equation also appears in many other fields of nonlinear science and is responsible for unearthing the underlying science of the nonlinear systems.…”

Smooth positon solutions of the focusing modified Korteweg–de Vries equation

“…Recently, a model based on two coupled mKdV equations was used to describe the soliton propagation in two parallel optical waveguides, in the presence of linear nondispersing coupling and in the few-cycle regime [22]. The mKdV, sG, and mKdV-sG equations were used in modelling the process of generation of supercontinuum light in optical fibers [23,24]. The mKdV equation also appears in other fields such as ion acoustic soliton experiments in plasmas [25,26], fluid mechanics [27], soliton propagation in lattices and acoustic waves in certain anharmonic lattices [28], nonlinear van Alfvén waves propagating in plasmas [29,30], meandering ocean currents [31], the dynamics of traffic flow [32,33], and the study of Schottky barrier transmission lines [34].…”