Spectral Sidebands and Multi-Pulse Formation in Passively Mode Locked Lasers

Pulse formation in passively mode locked lasers is often accompanied with dispersive waves that form of spectral sidebands due to spatial inhomogoneities in the laser cavity. Here we present an explicit calculation of the amplitude, frequency, and precise shape of the sidebands accompanying a soliton-like pulse. We then extend the study to the global steady state of mode locked laser with a variable number of pulses, and present experimental results in a mode locked fiber laser that confirm the theory. The strong correlation between the temporal width of the sidebands and the measured spacing between the pulses in multipulse operation suggests that the sidebands have an important role in the inter-pulse interaction.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Haus/Gross-Pitaevskii equation for random lasers

We report on experimental tests of the trend of random laserlinewidth versus pumping power as predicted by an Haus master equation that is formally identical to the one-dimensional Gross- Pitaevskii equation in an harmonic potential. Experiments are done by employing picosecond pumped dispersions of Titaniumdioxide particles in dye-doped methanol. The derivation of the master equations is also detailed and shown to be in agreement with experiments analytically predicting the value of the threshold linewidth

Dynamical models for dissipative localized waves of the complex Ginzburg-Landau equation

Finite-dimensional dynamical models for solitons of the cubic-quintic complex Ginzburg-Landau equation CGLE are derived. The models describe the evolution of the pulse parameters, such as the maximum amplitude, pulse width, and chirp. A clear correspondence between attractors of the finite-dimensional dynamical systems and localized waves of the continuous dissipative system is demonstrated. It is shown that stationary solitons of the CGLE correspond to fixed points, while pulsating solitons are associated with stable limit cycles. The models show that a transformation from a stationary soliton to a pulsating soliton is the result of a Hopf bifurcation in the reduced dynamical system. The appearance of moving fronts kinks in the CGLE is related to the loss of stability of the limit cycles. Bifurcation boundaries and pulse behavior in the regions between the boundaries, for a wide range of system parameters, are found from analysis of the reduced dynamical models. We also provide a comparison between various models and their correspondence to the exact results

Pinned modes in two-dimensional lossy lattices with local gain and nonlinearity

We introduce a system with one or two amplified nonlinear sites ("hot spots", HSs) embedded into a two-dimensional linear lossy lattice. The system describes an array of evanescently coupled optical or plasmonic waveguides, with gain applied at selected HS cores. The subject of the analysis is discrete solitons pinned to the HSs. The shape of the localized modes is found in quasi-analytical and numerical forms, using a truncated lattice for the analytical consideration. Stability eigenvalues are computed numerically, and the results are supplemented by direct numerical simulations. In the case of self-focusing nonlinearity, the modes pinned to a single HS are stable or unstable when the nonlinearity includes the cubic loss or gain, respectively. If the nonlinearity is self-defocusing, the unsaturated cubic gain acting at the HS supports stable modes in a small parametric area, while weak cubic loss gives rise to a bistability of the discrete solitons. Symmetric and antisymmetric modes pinned to a symmetric set of two HSs are considered too.Comment: Philosophical Transactions of the Royal Society A, in press (a special issue on "Localized structures in dissipative media"