Fast and slowly evolving vector solitons in mode-locked fibre lasers

Abstract

We report on a new vector model of an erbium-doped fibre laser mode locked with carbon nanotubes. This model goes beyond the limitations of the previously used models based on either coupled nonlinear Schrödinger or Ginzburg-Landau equations. Unlike the previous models, it accounts for the vector nature of the interaction between an optical field and an erbium-doped active medium, slow relaxation dynamics of erbium ions, linear birefringence in a fibre, linear and circular birefringence of a laser cavity caused by in-cavity polarization controller and light-induced anisotropy caused by elliptically polarized pump field. Interplay of aforementioned factors changes coherent coupling of two polarization modes at a long time scale and so results in a new family of vector solitons (VSs) with fast and slowly evolving states of polarization. The observed VSs can be of interest in secure communications, trapping and manipulation of atoms and nanoparticles, control of magnetization in data storage devices and many other areas.

Bright and dark vector rogue waves

“…Based on the weak interaction model (WIM), such scenario of RWs emergence has been recently outlined theoretically based on the nonlinear Schrödinger (NLS) equation [11]. We support the concept in this paper by providing an experimental evidence of a new type of the energy landscape created by the interaction of the orthogonal states of polarisation (SOPs) and leading to the polarisation trapping or escape from the trapping which is triggered by polarisation instabilities [12]- [13]. We demonstrate that tuning the in-cavity and the pump polarisation controllers, i.e.…”

“…coupled oscillators with the dynamic coupling strength [15]. With accounting for the SOP, orthogonally polarised SOPs can be treated as coupled oscillators as well [12,13]. This provided a very good test bed for study synchronisation regimes of the orthogonal SOPs in a mode-locked fibre laser with a saturable absorber as a function of the laser parameters (power and ellipticity of the pump wave, and in-cavity birefringence) tunable by the pump laser current driver, polarisation controller for pump wave and in-cavity polarisation controller [5][6][7][8].…”

“…We show that tuning in-cavity and the pump polarisation controllers, i.e. the cavity birefringence and the ellipticity of the pump wave, enable, in terms of the theory of the coupled oscillators, changing the coupling strength between two orthogonal SOPs and detuning between their oscillation frequencies that is finally result in polarisation trapping or escape from the trapping triggered by polarisation instabilities [12]- [13]. The revealed conditions for emergence of new class of the rogue waves can potentially find applications for controlling synchronisation scenarios along with rogue wave emergence in the ensemble of coupled oscillators that mimic a wide range of the coupled systems such as multimode and coupled lasers, electrical power grids, communication networks, human brain, and financial markets.…”

Slow deterministic vector rogue waves

“…) and I ss [17,18]; α 1 is the total absorption of erbium ions at the lasing wavelength, α 0 is CNT absorption coefficients at the lasing wavelength, α 3 is the ratio of saturation powers for CNT and erbium doped fiber, α 2 is the total insertion losses in cavity, β is the birefringence strength (2β=2πL/L b , L b is the beat length); γ=γ k LI ss (γ k is the Kerr coupling constant), δ is the ellipticity of the pump wave, ε=τ R /τ Er is the ratio of the round-trip time τ R to the lifetime of erbium ions at the first excited level…”

“…Evolution of the laser SOPs and population of the first excited level in Er 3+ doped active medium has been modeled by using the equations developed by Sergeyev et al [17,18]:…”