Non-Lagrangian approach for coupled complex Ginzburg-Landau systems with higher order-dispersion

Abstract

It is known that after a particular distance of evolution in fiber lasers, two (input) asymmetric soliton like pulses emerge as two (output) symmetric pulses having same and constant energy. We report such a compensation technique in dispersion managed fiber lasers by means of a semi-analytical method known as collective variable approach (CVA) with including third-order dispersion (TOD). The minimum length of fiber laser, at which the output symmetric pulses are obtained from the input asymmetric ones, is calculated for each and every pulse parameters numerically by employing Runge-Kutta fourth order method. The impacts of intercore linear coupling, asymmetric nature of initial parameters and TOD on the evolution of pulse parameters and on the minimum length are also investigated. It is found that strong intercore linear coupling and asymmetric nature of input pulse parameters result in the reduction of fiber laser length. Also, the role of TOD tends to increase the width of the pulses as well as their energies. Besides, chaotic patterns and bifurcation points on the minimum length of the fiber owing to the impact of TOD are also reported in a nutshell.

Polarization dynamics of ultrafast solitons

“…In order to model our system, we resort to a non-Lagrangian approach for simulating coupled complex Ginzburg-Landau equations for the two components of the electric wave vector as for the first state-of-polarization [20]:…”

“…In order to identify the appropriate dynamics, different models were developed for such lasers. These include the numerical evolution of the scalar Ginzburg-Landau equations [20][21][22][23] or analytical solutions for these equations [24]. Some numerical works have focused on the state-of-polarization dynamics of the output of ultrafast lasers [25][26][27][28][29][30][31][32][33][34] and others described the state-of-polarization during the propagation of the pulse inside the laser cavity [35][36][37].…”

Simple harmonic and damped motions of dissipative solitons in two-dimensional complex Ginzburg-Landau equation supported by an external V-shaped potential

“…The Complex Ginzburg-Landau (CGL) equations are well known as the basic model of pattern formation in the various nonlinear dissipative media [1][2][3]. In the nonlinear physics area, CGL equations are universally applicable nonlinear dynamics model that introduces a cubic-quintic term to provide saturation for growth in any achievable physical system [4,5]. The CGL equations have been widely used in nonlinear optical system, where passively mode-locked laser systems and optical transmission lines are two of the massive important applications [6].…”