We experimentally investigate the interplay of Turing and Faraday (modulational) instabilities in a bistable passive nonlinear resonator. The Faraday branch is induced via parametric resonance owing to a periodic modulation of the resonator dispersion. We show that the bistable switching dynamics is dramatically affected by the competition between the two instability mechanisms, which dictates two completely novel scenarios. At low detunings from resonance switching occurs between the stable stationary lower branch and the Faraday-unstable upper branch, whereas at high detunings we observe the crossover between the Turing and Faraday periodic structures. The results are well explained in terms of the universal Lugiato-Lefever model.
We present the theory of modulation instability induced by spectrally dependent losses (optical filters) in passive driven nonlinear fiber ring resonators. Starting from an Ikeda map description of the propagation equation and boundary conditions, we derive a mean field model - a generalised Lugiato-Lefever equation - which reproduces with great accuracy the predictions of the map. The effects on instability gain and comb generation of the different control parameters such as dispersion, cavity detuning, filter spectral position and bandwidth are discussed.
The concept of synthetic dimensions in photonics has attracted rapidly growing interest in the past few years. Among a variety of photonic systems, the ring resonator system under dynamic modulation has been investigated in depth both in theory and experiment, and has proven to be a powerful way to build synthetic frequency dimensions. In this tutorial, we start with a pedagogical introduction to the theoretical approaches in describing the dynamically modulated ring resonator system, and then review experimental methods in building such a system. Moreover, we discuss important physical phenomena in synthetic dimensions, including nontrivial topological physics. Our tutorial provides a pathway towards studying the dynamically modulated ring resonator system, understanding synthetic dimensions in photonics, and discusses future prospects for both fundamental research and practical applications using synthetic dimensions.
We analyze the consequences of dissipative heating in driven Kerr microresonators theoretically and numerically, using a thermal Lugiato-Lefever model. We show that thermal sensitivity modifies the stability range of continuous wave in a way that blocks direct access to broadband frequency-comb forming waveforms, and we propose a deterministic access path that bypasses the thermal instability barrier. We describe a novel thermal instability that leads to thermooptical oscillations via a Hopf bifurcation.
We present a theoretical and numerical study of light propagation in graded-index (GRIN) multimode fibers where the core diameter has been periodically modulated along the propagation direction. The additional degree of freedom represented by the modulation permits to modify the intrinsic spatiotemporal dynamics which appears in multimode fibers. More precisely, we show that modulating the core diameter at a periodicity close to the self-imaging distance allows to induce a Moir{e}-like pattern, which modifies the geometric parametric instability gain observed in homogeneous GRIN fibers.
The realization of spontaneous symmetry breaking (SSB) requires a system that exhibits a near perfect symmetry. SSB manifests itself through a pitchfork bifurcation, but that bifurcation is fragile, and perturbed by any asymmetry or imperfections. Consequently, exploiting SSB for real-world applications is challenging and often requires cumbersome stabilization techniques. Here, we reveal a novel method that automatically leads to symmetric conditions, and demonstrate its practical application in coherently-driven, two-mode, passive Kerr resonators. More specifically, we show that introducing a $pi$-phase defect between the modes of a driven nonlinear resonator makes SSB immune to asymmetries by means of a period-doubled dynamics of the systems modal evolution. The two-roundtrip evolution induces a self-symmetrization of the system through averaging of the parameters, hence enabling the realization of SSB with unprecedented robustness. This mechanism is universal: all symmetry-broken solutions of driven Kerr resonators have a period-doubled counterpart. We experimentally demonstrate this universality by considering the polarization symmetry breaking of several different nonlinear structures found in normal and anomalous dispersion fiber cavities, including homogeneous states, polarization domain walls, and bright vector cavity solitons.