Control of dynamical regimes in optical microresonators exploiting parametric interaction

Microresonators have the ability of strongly enhancing the propagating optical field, enabling nonlinear phenomena, such as bi-stability, self-pulsing and chaotic regimes, at very low powers. It is fundamental to comprehend the mechanisms that generate such dynamics, which are crucial for micro-cavities-based applications in communications, sensing and metrology. The aim of this work is to develop a scheme for the control of nonlinear regimes in microresonators, assuming the interplay between the ultra-fast Kerr effect and a slow intensity-dependent nonlinearity, such as thermo-optical effect. The framework of the coupled-mode theory is applied to model the system, while the bifurcation theory is used to investigate a configuration in which the power and frequency of a weak signal can control the behaviour of a strong pump. In this regards, this study demonstrates that the effect of a parametric interaction, specifically the four-wave mixing, plays a fundamental role in influencing the nature of the stationary states observed in a micro-cavity. The results show possible new strategies for enhanced, low-power, all-optical control of sensors, oscillators and chaos-controlled devices. Moreover, the outcomes provide new understanding of the effect of coherent wave mixing in the thermal stability regions of optical micro-cavities, including optical micro-combs.