Variational approach to study soliton dynamics in a passive fiber loop resonator with coherently driven phase-modulated external field.

Abstract

We report a detailed semianalytical treatment to investigate the dynamics of a single cavity soliton (CS) and two copropagating CSs separately in a Kerr mediated passive optical fiber resonator which is driven by a phase-modulated pump. The perturbation is dealt with by introducing Rayleigh's dissipation function in the framework of a variational principle that results in a set of coupled ordinary differential equations describing the evolution of individual soliton parameters. We further derive closed-form expressions for quick estimation of the temporal trajectory, drift velocity, and the phase shift accumulated by the CS due to the externally modulated pump. We also extend the variational approach to solve a two-soliton interaction problem in the absence as well as in the presence of the externally modulated field. In the absence of a phase-modulated field, the two copropagating solitons can attract, repulse, or propagate independently depending on their initial delay. The final state of interaction can be predicted through a second-order differential equation which is derived by the variational method. While in the presence of the phase-modulated field, the two-soliton interaction can result in annihilation, merging, breathing, or a two-soliton state depending on the detuning frequency and the pump power. Variational treatment analytically predicts these states and portrays the related dynamics that agrees with the full numerical simulation carried out by solving the normalized Lugiato-Lefever equation. The results obtained through this variational approach will enrich the understanding of complex pulse dynamics under a phase-modulated driving field in passive dissipative systems.