Instabilities, pattern formation, localized solutions, mode-locking and stochastic effects in nonlinear optical systems and beyond

Abstract

In this thesis the results of scientific research about dierent nonlinear phenomena with particular emphasis to photonic systems are presented. Works about dissipation induced modulation instabilities with applications for signal amplification in nonlinear optics and mode-locking in lasers constitute the main part of the thesis. The dissipa-tive instabilities studied are of two kinds, parametric instabilities induced by a periodic variation of spectral losses and instabilities induced by non varying but spectrally asym-metric losses. Although the main achievements are theoretical successful collaboration with experimentalists are reported too. Other results presented in this thesis concern a new fundamental theory of active mode-locking in lasers having a more general validity than Haus’ one and hence useful for describing mode-locked lasers with a fast gain dynamics such as semiconductor or quantum cascade lasers; the prediction of the novel theoretical model have been successfully compared with experimental findings. Theo-retical studies are also presented about collective phenomena, such as synchronization and localization, in coupled excitable lasers with saturable absorber and localized so-lutions on the non-vanishing background of the two-dimensional nonlinear Schr¨odinger equation with periodic potential: the Bogoliubov-de Gennes bullets.