Effects of Dissipative Terms on Dissipative Soliton Resonance Curve

Aladji Kamagaté,Adama Konaté,Olivier Asseu,Penetjiligué Adama Soro

doi:10.4236/opj.2017.73005

Abstract

Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. Using the method of collective variable approach, we have found an approximate relation between the parameters of the normalized complex cubic-quintic Ginzburg-Landau equation where the resonance manifests itself. Comparisons between the results obtained by collective variable approach, and those obtained by the method of moments show good qualitative agreement. This choice also helps to see the influence of the active terms on the resonance curve, so can be very useful in constructing passively mode-locked laser that generate solitons with the highest possible energies.

Highlights

One of the most perceptible features of solitons in dissipative systems is that they exist only when there is a continuous energy supply from an external source
Using the method of collective variable approach, we have found an approximate relation between the parameters of the normalized complex cubic-quintic Ginzburg-Landau equation where the resonance manifests itself
Thanks to collective variable approach, we have found a simple analytic expression for the resonance curve which is in good qualitative agreement with in [7]

Summary

Introduction

One of the most perceptible features of solitons in dissipative systems is that they exist only when there is a continuous energy supply from an external source. Finding the solutions of the CGLE or the region of parameters where DSR exists for a given set of parameters and a given initial conditions is an extremely lengthy and costly task It requires an enormous number of numerical simulations. In the case of DSR, this task can be simplified with approximations of the pulse shape, finding the set of parameters which predicts the areas where resonances can be found

Resonance Curve from a Collective Variable Approach

Influence of Dissipative Terms on Dissipative Curve

Conclusion