Titre de la dissertation: « Numerical and analytical investigation of stochastic dynamics in driven nonlinear optical resonators ».

Promoteur: Monsieur Bjorn Maes

 Résumé de la dissertation: Usually, the dynamics of a physical system are influenced by random fluctuations, commonly referred to as noise. Surprisingly, noise can have a positive effect, giving rise to novel and intriguing dynamics within the system. In this study, we focus on nonlinear optical resonators characterized by an intensity-dependent refractive index, a phenomenon known as the « Kerr effect. » Our investigation reveals that stochastic fluctuations in the optical field can engender a variety of compelling phenomena.Firstly, we demonstrate that thermal fluctuations arising from the system’s temperature can trigger periodic transitions between the two stable states of a single resonator. These periodic transitions result in a frequency shift of the outgoing power compared to the input frequency driving the resonator.Secondly, we examine the thermal radiation emitted by coupled resonators when only one of them is driven. Our analysis reveals that the thermal radiation spectra traverse various distinct regimes contingent upon the intensity of the driving. We also introduce an analytical model capable of predicting the spectral shape within specific regimes.Thirdly, we delve into the realm of non-instantaneous nonlinear responses. We note that such responses significantly reshape the system’s dynamics leading to new regimes compared to instantaneous scenarios. Notably, we unveil that these systems exhibit spiking behavior, i.e., abrupt and transient responses arising from external perturbations. We illustrate how noise can act as the perturbation that triggers these spikes and we elucidate the different dynamical regimes. This system can generate spike trains at low input powers with a periodicity determined by the delay time of the nonlinear response.In conclusion, our study sheds light on the intricate interplay between noise and the dynamics of Kerr optical resonators. These findings find validation through experimental results of collaborators, showcasing self-sustained oscillations in coupled non-instantaneous Kerr resonators.