Nonlinear Dynamics in Semiconductor Lasers - Abstract
Self-pulsing (SP) or self-Q-switching of the output power of Er- Yb-doped fibre lasers at frequencies of 10?100 kHz has been extensively studied for more than two decades to address issues related to the increased output power and regimes tunability. The experimentally obtained results demonstrated a variety of the self-pulsing regimes that stimulated the development of different theoretical approaches to the SP modelling. The approaches include contribution of the different effects to SP: (i) saturable absorber effect caused by unpumped section of active fibre, (ii) the presence of clustered erbium ions, (iii) the stimulated Brillouin scattering, (iv) self-phase modulation, (v) coherence and anti-coherence resonance (CR an ACR) scenario with multimode and polarization instabilities as an external noise source, (vi) the pump-to-signal intensity noise transfer (PSINT), (vii) power-dependent thermo-induced lensing in Er-doped fibre. The X-ray-absorption fine structure spectroscopy (XAFS) confirmed just a short-range coordination order (SRCO) of erbium ions rather than ions pair clustering. In high concentration LIEKKI TM, SRCO is suppressed however SP still present. The PSINT can contribute to low-frequency self-pulsing but only slightly above the first lasing threshold. Though the CR and ACR are feasible scenarios, there is no model of the CR and ACR-induced self-pulsing. Saturable effect of an unpumped active fibre, Brillouin scattering, and self-phase modulation have a high threshold and so can be considered as the feasible scenarios of SP for high power Er- and Yb-doped fibre lasers only. The power-dependent thermo-induced lensing can result in the low-threshold self-pulsing but it can?t address the complexity of the experimentally observed self-pulsing regimes. To address aforementioned challenges of self-pulsing complexity, we present here a new theoretical approach based on a further generalization of new vector model of Er-doped fibre recently developed by the author. This model can be considered as an extension of the Kuramoto equations based theory of synchronization of coupled phase oscillators to the case of dynamically changing coupling strength. We demonstrate that by tuning the laser parameters (power and ellipticity of the pump wave, and in-cavity birefringence) we can change the synchronization scenarios from the phase locking to the phase entrainment and to the chaotic phase drift. This corresponds to the tunable vector self-pulsing in Er-doped fibre laser where in addition to the pump power (S0), the normalized Stokes parameters (s1, s2, s3) are evolving on different trajectories on the Poincare sphere (stable focus, limit cycle, double scroll spiral attractor etc.). We apply linear stability along saddle index analysis to find conditions for emerging complex vector attractors on the Poincare sphere as a function of the laser parameters. Analysis validated by extensive numerical simulations gives an opportunity to explain experimental results on complex self-pulsing regimes in fiber lasers obtained by many authors during the last 20 years.