Stephane Coen

Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model.

A generalized Lugiato-Lefever equation is numerically solved with a Newton-Raphson method to model Kerr frequency combs. We obtain excellent agreement with past experiments, even for an octave-spanning comb. Simulations are much faster than with any other technique despite including more modes than ever before. Our study reveals that Kerr combs are associated with temporal cavity solitons and dispersive waves, and opens up new avenues for the understanding of Kerr-comb formation.

Universal scaling laws of Kerr frequency combs

Using the known solutions of the Lugiato-Lefever equation, we derive universal trends of Kerr frequency combs. In particular, normalized properties of temporal cavity soliton solutions lead us to a simple analytic estimate of the maximum attainable bandwidth for given pump resonator parameters. The result is validated via comparison with past experiments encompassing a diverse range of resonator configurations and parameters.

Ultraweak long-range interactions of solitons observed over astronomical distances

Recirculating temporal optical cavity solitons in a coherently driven passive optical fibre ring resonator allows pairs of solitons to interact over distances 8,000 times their width. This finding highlights the extreme stability, robustness and coherence of the process, and of solitons in general.

Coherence properties of Kerr frequency combs

We use numerical simulations based on an extended Lugiato-Lefever equation (LLE) to investigate the stability properties of Kerr frequency combs generated in microresonators. In particular, we show that an ensemble average calculated over sequences of output fields separated by a fixed number of resonator roundtrips allows the coherence of Kerr combs to be quantified in terms of the complex degree of first-order coherence. We identify different regimes of comb coherence, linked to the solutions of the LLE. Our approach provides a practical and unambiguous way of assessing the stability of Kerr combs that is directly connected to an accessible experimental quantity.

Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons

Optical tweezers use laser light to trap and move microscopic particles in space. Here we demonstrate a similar control over ultrashort light pulses, but in time. Our experiment involves temporal cavity solitons that are stored in a passive loop of optical fibre pumped by a continuous wave holding laser beam. The cavity solitons are trapped into specific time slots through a phase modulation of the holding beam, and moved around in time by manipulating the phase profile. We report both continuous and discrete manipulations of the temporal positions of picosecond light pulses, with the ability to simultaneously and independently control several pulses within a train. We also study the transient drifting dynamics and show complete agreement with theoretical predictions. Our study demonstrates how the unique particle-like characteristics of cavity solitons can be leveraged to achieve unprecedented control over light. These results could have significant ramifications for optical information processing.

Observation of dispersive wave emission by temporal cavity solitons

Here we report, for the first time to our knowledge, direct experimental observations of dispersive wave (DW) emission by temporal cavity solitons (CSs). We expect that a better understanding of this process will lead to larger Kerr frequency comb bandwidths akin to what has been achieved in supercontinuum generation, and thereby our study has strong practical implications for the many technological and scientific applications of Kerr combs.

Walk-Off-Induced Modulation Instability, Temporal Pattern Formation, and Frequency Comb Generation in Cavity-Enhanced Second-Harmonic Generation.

We derive a time-domain mean-field equation to model the full temporal and spectral dynamics of light in singly resonant cavity-enhanced second-harmonic generation systems. We show that the temporal walk-off between the fundamental and the second-harmonic fields plays a decisive role under realistic conditions, giving rise to rich, previously unidentified nonlinear behavior. Through linear stability analysis and numerical simulations, we discover a new kind of quadratic modulation instability which leads to the formation of optical frequency combs and associated time-domain dissipative structures. Our numerical simulations show excellent agreement with recent experimental observations of frequency combs in quadratic nonlinear media [Phys. Rev. A 91, 063839 (2015)]. Thus, in addition to unveiling a new, experimentally accessible regime of nonlinear dynamics, our work enables predictive modeling of frequency comb generation in cavity-enhanced second-harmonic generation systems. We expect our findings to have wide impact on the study of temporal and spectral dynamics in a diverse range of dispersive, quadratically nonlinear resonators.

Observations of spatiotemporal instabilities of temporal cavity solitons

Localized dissipative structures (LDS) have been predicted to display a rich array of instabilities, yet systematic experimental studies have remained scarce. We have used a synchronously-driven optical fiber ring resonator to experimentally study LDS instabilities in the strong-driving regime of the AC-driven nonlinear Schrodinger equation (also known as the Lugiato-Lefever model). Through continuous variation of a single control parameter, we have observed a string of theoretically predicted instability modes, including irregular oscillations and chaotic collapses. Beyond a critical point, we observe behaviour reminiscent of a phase transition: LDSs trigger localized domains of spatiotemporal chaos that invade the surrounding homogeneous state. Our findings directly confirm a number of theoretical predictions, and they highlight that complex LDS instabilities can play a role in experimental systems.Temporal cavity solitons (CSs) are pulses of light that can persist in coherently driven passive resonators, such as fiber ring resonators and monolithic microresonators. It has been theoretically predicted that they can exhibit rich instability dynamics, yet experimental observations have remained scarce. Here, we report on the observations of complex spatiotemporal instabilities of temporal CSs in a synchronously driven fiber ring resonator. Through continuous variation of a single control parameter, we observe a string of predicted instabilities, including irregular oscillations (breathing) and chaotic collapses. Beyond a critical point, we find behavior reminiscent of a phase transition: CSs trigger localized domains of spatiotemporal chaos that invade the surrounding continuous wave background. Our findings directly confirm a number of theoretical predictions, and they highlight that complex CS instabilities can play a role in experimental systems.

Frequency comb formation in doubly resonant second-harmonic generation

We theoretically study the generation of optical frequency combs and corresponding pulse trains in doubly resonant intracavity second-harmonic generation (SHG). We find that, despite the large temporal walk-off characteristic of realistic cavity systems, the nonlinear dynamics can be accurately and efficiently modeled using a pair of coupled mean-field equations. Through rigorous stability analysis of the systems steady-state continuous-wave solutions, we demonstrate that walk-off can give rise to an unexplored regime of temporal modulation instability. Numerical simulations performed in this regime reveal rich dynamical behaviors, including the emergence of temporal patterns that correspond to coherent optical frequency combs. We also demonstrate that the two coupled equations that govern the doubly resonant cavity behavior can, under typical conditions, be reduced to a single mean-field equation akin to that describing the dynamics of singly-resonant-cavity SHG [F. Leo et al., Phys. Rev. Lett. 116, 033901 (2016)]. This reduced approach allows us to derive a simple expression for the modulation instability gain, thus permitting us to acquire significant insight into the underlying physics. We anticipate that our work will have a wide impact on the study of frequency combs in emerging doubly resonant cavity SHG platforms, including quadratically nonlinear microresonators.

Single envelope equation modeling of multi-octave comb arrays in microresonators with quadratic and cubic nonlinearities

We numerically study, by means of the single envelope equation, the generation of optical frequency combs ranging from the visible to the mid-infrared spectral regions in resonators with quadratic and cubic nonlinearities. Phase-matched quadratic wave-mixing processes among the comb lines can be activated by low-power continuous wave pumping in the near infrared of a radially poled lithium niobate whispering gallery resonator. We examine both separate and coexisting intracavity doubly resonant second-harmonic generation and parametric oscillation processes and find that modulation instabilities may lead to the formation of coupled comb arrays extending over multiple octaves. In the temporal domain, the frequency combs may correspond to pulse trains or even to a single pulse circulating in the cavity.