François Leo

Silicon-Based Photonic Integration Beyond the Telecommunication Wavelength Range

In this paper we discuss silicon-based photonic integrated circuit technology for applications beyond the telecommunication wavelength range. Silicon-on-insulator and germanium-on-silicon passive waveguide circuits are described, as well as the integration of III-V semiconductors, IV-VI colloidal nanoparticles and GeSn alloys on these circuits for increasing the functionality. The strong nonlinearity of silicon combined with the low nonlinear absorption in the mid-infrared is exploited to generate picosecond pulse based supercontinuum sources, optical parametric oscillators and wavelength translators connecting the telecommunication wavelength range and the mid-infrared.

Silicon-based heterogeneous photonic integrated circuits for the mid-infrared

In this paper we present our recent work on mid-infrared photonic integrated circuits for spectroscopic sensing applications. We discuss the use of silicon-based photonic integrated circuits for this purpose and detail how a variety of optical functions in the mid-infrared besides passive waveguiding and filtering can be realized, either relying on nonlinear optics or on the integration of other materials such as GaSb-based compound semiconductors, GeSn epitaxy and PbS colloidal nanoparticles.

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.

Second-harmonic-assisted four-wave mixing in chip-based microresonator frequency comb generation

Simultaneous Kerr comb formation and second-harmonic generation with on-chip microresonators can greatly facilitate comb self-referencing for optical clocks and frequency metrology. Moreover, the presence of both second- and third-order nonlinearities results in complex cavity dynamics that is of high scientific interest but is still far from being well-understood. Here, we demonstrate that the interaction between the fundamental and the second-harmonic waves can provide an entirely new way of phase matching for four-wave mixing in optical microresonators, enabling the generation of optical frequency combs in the normal dispersion regime under conditions where comb creation is ordinarily prohibited. We derive new coupled time-domain mean-field equations and obtain simulation results showing good qualitative agreement with our experimental observations. Our findings provide a novel way of overcoming the dispersion limit for simultaneous Kerr comb formation and second-harmonic generation, which might prove to be especially important in the near-visible to visible range where several atomic transitions commonly used for the stabilization of optical clocks are located and where the large normal material dispersion is likely to dominate.

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.

Universal mechanism for the binding of temporal cavity solitons

Temporal cavity solitons (CSs) are pulses of light that can persist in coherently driven passive resonators, such as fiber ring resonators and monolithic Kerr microresonators. While these solitons can in principle occupy arbitrary positions, multisoliton configurations often appear rigidly frozen in time, seemingly insensitive to noise. Here, we elucidate this behavior by presenting theoretical and experimental evidence of a universal mechanism through which temporal CSs can form robust long-range bound states. These bound states require perturbations to the strict Lugiato–Lefever mean-field description of temporal CSs. Binding occurs when the perturbation excites a narrowband resonance in the soliton spectrum, which gives long oscillatory tails to the CSs. Those tails can then interlock for a discrete set of temporal separations between the solitons. The universality of this mechanism is demonstrated in fiber ring cavities by providing experimental observations of long-range bound states ensuing from three different perturbations: third-order dispersion (dispersive wave generation), the periodic nature of the cavity (Kelly sidebands), and the random birefringence of the resonator. Subpicosecond resolution of bound-state separations and their dynamics are obtained by using the dispersive Fourier transform technique. Good agreement with theoretical models, including a new vector mean-field model, is also reported. Our work provides a framework to better understand the many soliton bound states observed in externally driven, passive Kerr resonators, including the soliton crystals reported in microresonators.

Coexistence of Multiple Nonlinear States in a Tristable Passive Kerr Resonator

Pattern formation in optical devices known as passive Kerr resonators has been studied for decades, but recent theoretical work has suggested the existence of entirely new dynamics when operated in the highly nonlinear regime. New experiments confirm these predictions, which could lead to innovative new sources of laser-like light and provide new insight into nonlinear dynamics and pattern formation.

Real time observations of soliton bound states, with multiple binding mechanisms, in passive nonlinear cavities

We resolve in real-time the dynamics of bound states of temporal cavity solitons in a passive driven nonlinear resonator, and identify several new binding mechanisms involving Gordon/Kelly sidebands, birefringence, and dispersive waves.