New nonlinear regimes of pulse generation in mode- locked fiber lasers

Mode-locked fiber lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes. The complex interplay among the effects of gain/loss, dispersion and nonlinearity in a fiber cavity can be used to shape the pulses and manipulate and control the light dynamics and, hence, lead to different mode-locking regimes. Major steps forward in pulse energy and peak power performance of passively mode-locked fiber lasers have been made with the recent discovery of new nonlinear regimes of pulse generation, namely, dissipative solitons in all-normal-dispersion cavities and parabolic self-similar pulses (similaritons) in passive and active fibers. Despite substantial research in this field, qualitatively new phenomena are still being discovered. In this talk, we review recent progress in the research on nonlinear mechanisms of pulse generation in passively mode-locked fiber lasers. These include similariton mode-locking, a mode-locking regime featuring pulses with a triangular distribution of the intensity, and spectral compression arising from nonlinear pulse propagation. We also report on the possibility of achieving various regimes of advanced temporal waveform generation in a mode-locked fiber laser by inclusion of a spectral filter into the laser cavity.

Quantization of the Inhomogeneous Bianchi I model:quasi-Heisenberg picture

The quantization scheme is suggested for a spatially inhomogeneous 1+1 Bianchi I model. The scheme consists in quantization of the equations of motion and gives the operator (so called quasi-Heisenberg) equations describing explicit evolution of a system. Some particular gauge suitable for quantization is proposed. The Wheeler-DeWitt equation is considered in the vicinity of zero scale factor and it is used to construct a space where the quasi-Heisenberg operators act. Spatial discretization as a UV regularization procedure is suggested for the equations of motion.

Dissipative parametric modulation instability and pattern formation in nonlinear optical systems

We present the essential features of the dissipative parametric instability, in the universal complex Ginzburg- Landau equation. Dissipative parametric instability is excited through a parametric modulation of frequency dependent losses in a zig-zag fashion in the spectral domain. Such damping is introduced respectively for spectral components in the +ΔF and in the -ΔF region in alternating fashion, where F can represent wavenumber or temporal frequency depending on the applications. Such a spectral modulation can destabilize the homogeneous stationary solution of the system leading to growth of spectral sidebands and to the consequent pattern formation: both stable and unstable patterns in one- and in two-dimensional systems can be excited. The dissipative parametric instability provides an useful and interesting tool for the control of pattern formation in nonlinear optical systems with potentially interesting applications in technological applications, like the design of mode- locked lasers emitting pulse trains with tunable repetition rate; but it could also find realizations in nanophotonics circuits or in dissipative polaritonic Bose-Einstein condensates.