Wave-turbulence approach of supercontinuum generation: Influence of self-steepening and higher-order dispersion

Abstract

International audienceWe analyze the influence of self-steepening and higher-order dispersion on the process of optical wave thermalization. This study is aimed at developing a thermodynamic formulation of supercontinuum generation in photonic crystal fibers. In the highly nonlinear regime of supercontinuum generation, the optical field exhibits a turbulent dynamics that may be described by the kinetic wave theory. In this respect, the phenomenon of spectral broadening inherent to supercontinuum generation may be interpreted as a natural process of thermalization, which is characterized by an irreversible evolution of the optical field toward a thermodynamic equilibrium state. The numerical simulations show that, under certain conditions, the intensity of the field spontaneously concentrates around two specific frequencies. The theory reveals that these particular frequencies are selected in such a way that the corresponding wave packets propagate with the same group velocity, which is shown to also match the average group velocity of the optical field. This “velocity-locking” effect and the underlying process of spectral fission are interpreted in the light of a fundamental property of statistical equilibrium thermodynamics. It is shown that a velocity locking is required, in the sense that it prevents “a macroscopic internal motion in the wave system.” Furthermore, the kinetic wave theory sheds light on the role of self-steepening in the incoherent regime of supercontinuum generation. A family of equilibrium spectra is derived in the presence of self-steepening. They are found in quantitative agreement with the numerical simulations of the generalized nonlinear Schrödinger equation, without adjustable parameters

Femtosecond laser induced phenomena in transparent solid materials: Fundamentals and applications

“…Consequently, white light supercontinuum containing Stokes and anti-Stokes waves is generated. Other mechanisms, such as four-wave mixing [71], pulse splitting [ 135 ], self-steepening and generation of optical shocks [136,137], stimulated Raman scattering [138], are also proposed to be the possible reasons for supercontinuum generation [139]. It is also reported that the power threshold for supercontinuum generation is consistent with the calculated critical power for self-focusing, confirming that self-focusing is a dominant initiator of the sequence of processes generating supercontinuum.…”

Emergence of rogue waves from optical turbulence

“…However, we underline that, in general, the formation of a large scale coherent structure is only possible if the amount of incoherence in the system is not too large [31,32], a feature that was also observed in the highly incoherent regime of supercontinuum generation [33][34][35]. This aspect has been the subject of a detailed study in the context of wave condensation, where it was shown that the emergence of a large-scale coherent structure (a plane wave) only occurs below some critical 'energy' [36][37][38].…”

Rogue waves, rational solitons and wave turbulence theory

“…The WT theory describes the essential properties of this irreversible evolution towards the Rayleigh-Jeans equilibrium distribution [25]. This thermalization process has been studied in the framework of NLS-like equations in various different optical configurations [47], including supercontinuum generation [48,49], spontaneous repolarization [50], discrete systems [51], as well as in various optical media characterized by different nonlinearities [52][53][54].…”