Irina Balakireva

Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes

We present a stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs in whispering gallery mode resonators pumped in the anomalous dispersion regime. This article is the second part of a research work whose rst part was devoted to the regime of normal dispersion, and was presented in ref. [1]. The case of anomalous dispersion is indeed the most interesting from the theoretical point of view, because of the considerable variety of dynamical behaviors that can be observed. From a technological point of view, it is also the most relevant because it corresponds to the regime where Kerr combs are predominantly generated, studied, and used for dierent applications. In this article, we analyze the connection between the spatial patterns and the bifurcation structure of the eigenvalues associated to the various equilibria of the system. The bifurcation map evidences a considerable richness from a dynamical standpoint. We study in detail the emergence of superand sub-critical Turing patterns in the system. We determine the areas were bright isolated cavity solitons emerge, and we show that soliton molecules can emerge as well. Very complex temporal patterns can actually be observed in the system, where solitons (or soliton complexes) co-exist with or without mutual interactions. Our investigations also unveil the mechanism leading to the phenomenon of breathing solitons. Two routes to chaos in the system are identied, namely a route via the so called secondary combs, and another via soliton breathers. The Kerr combs corresponding to all these temporal patterns are analyzed in detail, and a discussion is led about the possibility to gain synthetic comprehension of the observed spectra out of the dynamical complexity of the system.

Azimuthal Turing Patterns, Bright and Dark Cavity Solitons in Kerr Combs Generated With Whispering-Gallery-Mode Resonators

We investigate the formation of cavity solitons in crystalline whispering-gallery-mode disk resonators that are pumped in different dispersion regimes. In the Fourier domain, these dissipative structures correspond to specific types of mode-locked Kerr optical frequency combs. Depending on the sign of the second-order chromatic dispersion and on the pumping conditions, we show that either bright or dark cavity solitons can emerge, and we show that these two regimes are associated with characteristic spectral signatures that can be discriminated experimentally. We use the Lugiato-Lefever spatiotemporal formalism to investigate the temporal dynamics leading to the formation of these azimuthal solitons, as well as the emergence of Turing patterns. The theoretical results are in excellent agreement with experimental measurements that are obtained using calcium and magnesium fluoride disk resonators pumped near 1550 nm.

Phase noise performance comparison between optoelectronic oscillators based on optical delay lines and whispering gallery mode resonators.

We investigate the phase noise performance of optoelectronic oscillators when the optical energy storage elements are in the following three configurations: a high-Q whispering gallery mode resonator, an optical delay-line and a combination of both elements. The stability properties of these various optical elements are first characterized, and then systematically compared in the optical and in the microwave frequency domains. Subsequently, the spectral purity of the oscillator is theoretically and experimentally examined for each case. When the resonator is used as both delay and filtering element inside the delay-line based oscillator, the generated spurious modes are highly rejected. A spur rejection by more than 53 dB has been demonstrated for the first-neighboring spur.

A taxonomy of optical dissipative structures in whispering-gallery mode resonators with Kerr nonlinearity

In this paper, the research related to the formation of optical dissipative structures in Kerr-nonlinear whispering-gallery mode resonators pumped with continuous-wave lasers is reviewed. Pattern formation in these systems can be analysed using the paradigmatic Lugiato–Lefever model, which is a partial differential equation ruling the dynamics of the intra-cavity laser field. Various dissipative structures such as Turing rolls, solitons, breathers and spatio-temporal chaos can emerge in the resonator depending on the laser power and frequency. The bifurcation analysis enables a classification of these patterns, and also permits identification of their basins of attraction. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)’.

Optical Kerr frequency combs: Modelling and applications

Whispering gallery mode resonators have generated a broad interest in recent years. From a fundamental point of view, they enable to investigate various phenomena related light-matter interactions, as well as the dynamics of photons confined in nonlinear media, from both the classical and quantum perspectives. From the applied viewpoint, WGM resonators are considered as a core photonic component in the emerging discipline of microwave photonics. They are considered as promising central elements for optical filtering, add-drop systems, miniature solid-state lasers, efficient light modulators, and so on. Both aerospace and communication engineering are expected to be the areas where the impact of WGM technology will be the strongest. We provide in this communication an overview of the field as well as of the various perspectives on the challenges that will have to be met in this new discipline.

Kerr comb generation from the perspective of spatial dissipative structures

The theoretical understanding of Kerr combs has been the object of extensive efforts worldwide in the last ten years. Several insights have been provided since then into this problem and have enabled significant progress for the optimization and tailoring of these combs. Here, we investigate the formation of dissipative structures in crystalline whispering-gallery mode disk resonators that are pumped in different dispersion regimes. In the Fourier domain, these dissipative structures correspond to specific types of mode-locked Kerr optical frequency combs. Depending on the sign of the second-order chromatic dispersion and on the pumping conditions, we show that either bright or dark cavity solitons can emerge, and we show these two regimes are associated with characteristic spectral signatures that can be discriminated experimentally. We use the Lugiato-Lefever spatiotemporal formalism to investigate the temporal dynamics leading to the formation of these azimuthal solitons, as well as the emergence of Turing patterns. The theoretical results are in excellent agreement with experimental measurements that are obtained using calcium and magnesium fluoride disk resonators pumped near 1550 nm.

Temporal dynamics of Kerr frequency combs in whispering-gallery mode resonators

Based on a modal description of the evolution of the modes amplitude in a whispering-gallery mode resonator, we numerically study the generation of Kerr combs. We show that a stable primary comb appear for pump power slightly above threshold, enabling potential applications in metrology. For high input power however, chaotic signals are observed.

On phase locking phenomena in Kerr combs

Based on a modal description of the evolution Kerr combs in a whispering-gallery mode resonator, we numerically investigate the phase bhavior of the different spectral lines of the spectrum. We show that a stable phase relation exists between adjacent modes in primary combs. This result is of great interest for metrological applications where one phase noise is an issue. For high input power however, chaotic signals are observed.