Analysis of the dispersive Fourier transform dataset using dynamic mode decomposition: evidence of multiple vibrational modes and their interplay in a three-soliton molecule.

We demonstrate that the dynamic mode decomposition technique can effectively reduce the amount of noise in the dispersive Fourier transform dataset and allow for finer quantitative analysis of the experimental data. We therefore show that the oscillation pattern of a soliton molecule actually results from the interplay of several elementary vibration modes.

Subharmonic instabilities in Kerr microcombs.

We report experimental observation of subharmonic mode excitation in primary Kerr optical frequency combs generated using crystalline whispering-gallery mode resonators. We show that the subcombs can be controlled and span a single or multiple free spectral ranges around the primary comb modes. In the spatial domain, the resulting multiscale combs correspond to an amplitude modulation of intracavity roll patterns. We perform a theoretical analysis based on eigenvalue decomposition that evidences the mechanism leading to the excitation of these combs.

Superlocalization Reveals Long-Range Synchronization of Vibrating Soliton Molecules.

We implement a superlocalization method in the time domain that allows the observation of the external motion of soliton molecules in a fiber ring cavity laser with unprecedented accuracy. In particular, we demonstrate the synchronization of two oscillating soliton molecules separated by several nanoseconds, with intermolecular oscillations following the same pattern as the intramolecular motion of the individual molecules. These experimental findings indicate an interplay between the different interaction mechanisms that coexist inside the laser cavity, despite their very different characteristic ranges, timescales, strengths, and physical origins.

Fluctuations and correlations in Kerr optical frequency combs with additive Gaussian noise.

We investigate the effects of environmental stochastic fluctuations on Kerr optical frequency combs. This spatially extended dynamical system can be accurately studied using the Lugiato-Lefever equation, and we show that when additive noise is accounted for, the correlations of the modal field fluctuations can be determined theoretically. We propose a general theory for the computation of these field fluctuations and correlations, which is successfully compared to numerical simulations.

Heterodyne interferometry applied to the characterization of nonlinear integrated waveguides.

We demonstrate that heterodyne interferometry makes it possible to accurately measure minute nonlinear phase shifts with little constraint on the propagation loss or chromatic dispersion. We apply this technique to characterize the effective nonlinearity of silicon nitride rib waveguides in the normal and anomalous dispersion regimes.

Saturable plasmonic metasurfaces for laser mode locking.

Metamaterials are artificial materials made of subwavelength elementary cells that give rise to unexpected wave properties that do not exist naturally. However, these properties are generally achieved due to 3D patterning, which is hardly feasible at short wavelengths in the visible and near-infrared regions targeted by most photonic applications. To overcome this limitation, metasurfaces, which are the 2D counterparts of metamaterials, have emerged as promising platforms that are compatible with planar nanotechnologies and thus mass production, which platforms the properties of a metamaterial into a 2D sheet. In the linear regime, wavefront manipulation for lensing, holography, and polarization control has been achieved recently. Interest in metasurfaces operating in the nonlinear regime has also increased due to the ability of metasurfaces to efficiently convert incident light into harmonic frequencies with unusual polarization properties. However, to date, the nonlinear absorption of metasurfaces has been mostly ignored. Here, we demonstrate that plasmonic metasurfaces behave as saturable absorbers with modulation performances superior to the modulation performance of other 2D materials and exhibit unusual polarimetric nonlinear transfer functions. We quantify the link between saturable absorption, the plasmonic resonances of the unit cell and their distribution in a 2D metasurface, and finally provide a practical implementation by integrating the metasurfaces into a fiber laser cavity operating in pulsed regimes driven by the metasurface properties. As such, this work provides new perspectives on ultrathin nonlinear saturable absorbers for applications where tunable nonlinear transfer functions are needed, such as in ultrafast lasers or neuromorphic circuits.

On the transition to secondary Kerr combs in whispering-gallery mode resonators.

We demonstrate that extended dissipative structures in Kerr-nonlinear whispering-gallery mode resonators undergo a spatiotemporal instability, as the pumping parameters are varied. We show that the dynamics of the patterns beyond this bifurcation yield specific Kerr comb and sub-comb spectra that can be subjected to a phase of frequency-locking when optimal conditions are met. Our numerical results are found to be in agreement with experimental measurements.

Dependence of quality factor on surface roughness in crystalline whispering-gallery mode resonators.

We present an experimental study of the variation of quality factor (Q-factor) of WGM resonators as a function of surface roughness. We consider mm-size whispering-gallery mode resonators manufactured with fluoride crystals, featuring Q-factors of the order of 1 billion at 1550 nm. The experimental procedure consists of repeated polishing steps, after which the surface roughness is evaluated using profilometry by white-light phase-shifting interferometry, while the Q-factors are determined using the cavity-ring-down method. This protocol permits us to establish an explicit curve linking the Q-factor of the disk-resonator to the surface roughness of the rim. We have performed measurements with four different crystals, namely, magnesium, calcium, strontium, and lithium fluoride. We have thereby found that the variations of Q-factor as a function of surface roughness is universal, in the sense that it is globally independent of the bulk material under consideration. We also discuss our experimental results in the light of theoretical estimates of surface scattering Q-factors already published in the literature.

Spectro-temporal dynamics of Kerr combs with parametric seeding.

We report a joint theoretical and experimental investigation of the parametric seeding of a primary Kerr optical frequency comb. Electro-optic modulation sidebands matching multiple free-spectral ranges of an ultrahigh-Q millimeter-size magnesium fluoride disk resonator are used as seed signals. These seed signals interact through four-wave mixing with the spectral components of a stable primary comb and give rise to complex spectro-temporal patterns. We show that the new frequency combs feature multiscale frequency spacing, with major frequency gaps in the order of a few hundred gigahertz, and minor frequency spacing in the order of a few tens of gigahertz. The experimental results are in agreement with numerical simulations using the Lugiato-Lefever equation. We expect such versatile and coherent optical frequency combs to have potential applications in optical communications systems where frequency management assigns predefined spectral windows at the emitter stage.

Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor.

We report the fabrication for the first time of a strontium fluoride (SrF(2)) whispering-gallery mode resonator with quality factor in excess of 1 billion. The millimeter-size disk-resonator is polished until the surface roughness decreases down to a root-mean square value of 1.2 nm, as measured with a vertical scanning profilometer. We also demonstrate that this ultrahigh Q resonator allows for the generation of a normal-dispersion Kerr optical frequency comb at 1550 nm.

Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications.

Optical Kerr frequency combs are known to be effective coherent multiwavelength sources for ultrahigh capacity fiber communications. These combs are the frequency-domain counterparts of a wide variety of spatiotemporal dissipative structures, such as cavity solitons, chaos, or Turing patterns (rolls). In this Letter, we demonstrate that Turing patterns, which correspond to the so-called primary combs in the spectral domain, are optimally coherent in the sense that for the same pump power they provide the most robust carriers for coherent data transmission in fiber communications using advanced modulation formats. Our model is based on a stochastic Lugiato-Lefever equation which accounts for laser pump frequency jitter and amplified spontaneous emission noise induced by the erbium-doped fiber amplifier. Using crystalline whispering-gallery-mode resonators with quality factor Q∼10^{9} for the comb generation, we show that when the noise is accounted for, the coherence of a primary comb is significantly higher than the coherence of their solitonic or chaotic counterparts for the same pump power. In order to confirm this theoretical finding, we perform an optical fiber transmission experiment using advanced modulation formats, and we show that the coherence of the primary comb is high enough to enable data transmission of up to 144 Gbit/s per comb line, the highest value achieved with a Kerr comb so far. This performance evidences that compact crystalline photonic systems have the potential to play a key role in a new generation of coherent fiber communication networks, alongside fully integrated systems.

Mixed-mode oscillations in slow-fast delayed optoelectronic systems.

In this article, we investigate the dynamical behavior of breathers in optoelectronic oscillators from the standpoint of mixed-mode oscillations. In the phase space, these breathers are composite oscillations that are damped to the attractive branches of an invariant manifold. Our study shows that the emergence of breather dynamics is linked to the apparition of inflection points in the phase space, and we develop an analytical framework based on the Liénard reduction form in order to provide an analytical insight into this phenomenology. Our theoretical results are in excellent agreement with experimental measurements.

Phase steps and resonator detuning measurements in microresonator frequency combs.

Experiments and theoretical modelling yielded significant progress toward understanding of Kerr-effect induced optical frequency comb generation in microresonators. However, the simultaneous Kerr-mediated interaction of hundreds or thousands of optical comb frequencies with the same number of resonator modes leads to complicated nonlinear dynamics that are far from fully understood. An important prerequisite for modelling the comb formation process is the knowledge of phase and amplitude of the comb modes as well as the detuning from their respective microresonator modes. Here, we present comprehensive measurements that fully characterize optical microcomb states. We introduce a way of measuring resonator dispersion and detuning of comb modes in a hot resonator while generating an optical frequency comb. The presented phase measurements show unpredicted comb states with discrete π and π/2 steps in the comb phases that are not observed in conventional optical frequency combs.

Routes to spatiotemporal chaos in Kerr optical frequency combs.

We investigate the various routes to spatiotemporal chaos in Kerr optical frequency combs, obtained through pumping an ultra-high Q-factor whispering-gallery mode resonator with a continuous-wave laser. The Lugiato-Lefever model is used to build bifurcation diagrams with regards to the parameters that are externally controllable, namely, the frequency and the power of the pumping laser. We show that the spatiotemporal chaos emerging from Turing patterns and solitons display distinctive dynamical features. Experimental spectra of chaotic Kerr combs are also presented for both cases, in excellent agreement with theoretical spectra.

On the robustness of phase locking in Kerr optical frequency combs.

We theoretically investigate the phase locking phenomena between the spectral components of Kerr optical frequency combs in the dynamical regime of Turing patterns. We show that these Turing patterns display a particularly strong and robust phase locking, originating from a cascade of phase locked triplets which asymptotically lead to a global phase locking between the modes. The local and global phase locking relationships defining the shape of the comb are analytically determined. Our analysis also shows that solitons display a much weaker phase locking that can be destroyed more easily than in the Turing pattern regime. Our results indicate that Turing patterns are generally the most suitable for applications requiring the highest stability. Experimental generation of such combs is also discussed in detail, and is in excellent agreement with the numerical simulations.

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.

Microwave photonics systems based on whispering-gallery-mode resonators.

Microwave photonics systems rely fundamentally on the interaction between microwave and optical signals. These systems are extremely promising for various areas of technology and applied science, such as aerospace and communication engineering, sensing, metrology, nonlinear photonics, and quantum optics. In this article, we present the principal techniques used in our lab to build microwave photonics systems based on ultra-high Q whispering gallery mode resonators. First detailed in this article is the protocol for resonator polishing, which is based on a grind-and-polish technique close to the ones used to polish optical components such as lenses or telescope mirrors. Then, a white light interferometric profilometer measures surface roughness, which is a key parameter to characterize the quality of the polishing. In order to launch light in the resonator, a tapered silica fiber with diameter in the micrometer range is used. To reach such small diameters, we adopt the "flame-brushing" technique, using simultaneously computer-controlled motors to pull the fiber apart, and a blowtorch to heat the fiber area to be tapered. The resonator and the tapered fiber are later approached to one another to visualize the resonance signal of the whispering gallery modes using a wavelength-scanning laser. By increasing the optical power in the resonator, nonlinear phenomena are triggered until the formation of a Kerr optical frequency comb is observed with a spectrum made of equidistant spectral lines. These Kerr comb spectra have exceptional characteristics that are suitable for several applications in science and technology. We consider the application related to ultra-stable microwave frequency synthesis and demonstrate the generation of a Kerr comb with GHz intermodal frequency.

Demonstration of a reef knot microfiber resonator.

We propose a new way to realize a microfiber optical resonator by implementing the topology of a reef knot using two microfibers. We describe how this structure, which includes 4 ports and can serve as an add-drop filter, can be fabricated. Resonances in an all-silica reef knot are measured and good fits are obtained from a simple resonator model. We also show the feasibility of assembling a hybrid silica-chalcogenide reef knot structure.