Strength and weaknesses of modeling the dynamics of mode-locked lasers by means of collective coordinates

Abstract

We address the efficiency of theoretical tools used in the development and optimization of mode-locked fiber lasers. Our discussion is based on the practical case of modeling the dynamics of a dispersion-managed fiber laser. One conventional approach uses discrete propagation equations, followed by the analysis of the numerical results through a collective coordinate projection. We compare the latter with our dynamical collective coordinate approach (DCCA), which combines both modeling and analysis in a compact form. We show that for single pulse dynamics, the DCCA allows a much quicker solution mapping in the space of cavity parameters than the conventional approach, along with a good accuracy. We also discuss the weaknesses of the DCCA, in particular when multiple pulsing bifurcations occur.

Paths from stationary to chaos in passively mode-locked fiber lasers: research progress of soliton pulsations and soliton explosions

“…It is necessary to establish a more general model for studying the instability of passively mode-locked fiber lasers. Researchers may define soliton pulsations and soliton explosions with more extensive degrees of freedom and explain the physical mechanism of their production in passively mode-locked fiber lasers by adding the set coordinate to the simulation models [184][185][186][187]. (b) The control of the generation of soliton pulsations and soliton explosions: among the numerous mode-locking techniques, the NPR technique has been widely studied due to its simplicity.…”

“…Researchers recently proposed using the time-lens technique to study the real-time time evolution characteristics of ultrafast nonlinear phenomena [189][190][191][192][193][194]. It has been applied to the research on the incoherent soliton evolution in optical turbulence [192] and the appearance of random respiration in modulation instability [187]. Using a combination of the DFT technique and the time-lens technique, the real-time spectrum and temporal properties of the soliton build-up process [59,181] and creeping solitons [91] were obtained.…”

Impact of Raman scattering on pulse dynamics in a fiber laser with narrow gain bandwidth

“…Then, we gradually increased the pump power, until entering the multi-pulse regime. To have a clear overview of the way the stable state evolves with a gradual raise of the pump power denoted hereafter as P p , we used a method of characterization of light pulses, called the moments method, briefly presented in appendix B, which allows us to determine in a relatively reliable way the major parameters of each pulse generated by the laser (once the pulse field ψ is known by numerically solving the propagation equation ( 2)) [12,29].…”

“…We consider a standard dispersion-managed cavity, which is quite similar to the fiber laser setups investigated in previous works [9,10,12,18]. The laser architecture is shown in figure 1.…”

“…Conversely, RS is generally regarded as having a negligible effect on light fields of low power and a narrow spectrum (compared to the bandwidth of Raman gain). Such light fields are generated in numerous mode-locked fiber lasers operating in the regime of moderate peak power [6][7][8][9][10][11][12]. These lasers can generate a large variety of mono-and multi-pulse structures, which have been so far considered as being virtually insensitive to RS, because of their narrow spectrum and their low peak power.…”