Sub-Hz Closed-Loop Electro-Optomechanical Oscillator with Gallium Phosphide Photonic Crystal Integrated on SoI Circuitry.

We report on a new approach of a low phase noise electro-optomechanical oscillator directly working in the GHz frequency range. The developed nanoscale oscillator is a one-dimensional photonic crystal made of gallium phosphide (GaP), heterogeneously integrated on silicon-on-insulator circuitry. Based on the strong interaction between the optical mode at the telecommunication wavelength and the mechanical mode in GHz, ultra-pure mechanical oscillations are enabled and directly imprinted on an optical carrier. Further stabilization is achieved with a delayed optoelectronic feedback loop using integrated electro-mechanical self-injection. We achieve a short-term stability of 0.7 Hz linewidth and a long-term stability with an Allan deviation below 10-7 Hz/Hz at 10 s averaging time, which represents an important step toward fully integrated optomechanical oscillators. Integrability and the low phase noise of this oscillator address some of the most important needs of optoelectronic oscillators and pave the way toward on-chip integrated microwave oscillators for microwave applications such as RADARs.

Merging and disconnecting resonance tongues in a pulsing excitable microlaser with delayed optical feedback.

Excitability, encountered in numerous fields from biology to neurosciences and optics, is a general phenomenon characterized by an all-or-none response of a system to an external perturbation of a given strength. When subject to delayed feedback, excitable systems can sustain multistable pulsing regimes, which are either regular or irregular time sequences of pulses reappearing every delay time. Here, we investigate an excitable microlaser subject to delayed optical feedback and study the emergence of complex pulsing dynamics, including periodic, quasiperiodic, and irregular pulsing regimes. This work is motivated by experimental observations showing these different types of pulsing dynamics. A suitable mathematical model, written as a system of delay differential equations, is investigated through an in-depth bifurcation analysis. We demonstrate that resonance tongues play a key role in the emergence of complex dynamics, including non-equidistant periodic pulsing solutions and chaotic pulsing. The structure of resonance tongues is shown to depend very sensitively on the pump parameter. Successive saddle transitions of bounding saddle-node bifurcations constitute a merging process that results in unexpectedly large regions of locked dynamics, which subsequently disconnect from the relevant torus bifurcation curve; the existence of such unconnected regions of periodic pulsing is in excellent agreement with experimental observations. As we show, the transition to unconnected resonance regions is due to a general mechanism: the interaction of resonance tongues locally at an extremum of the rotation number on a torus bifurcation curve. We present and illustrate the two generic cases of disconnecting and disappearing resonance tongues. Moreover, we show how a pair of a maximum and a minimum of the rotation number appears naturally when two curves of torus bifurcation undergo a saddle transition (where they connect differently).

Ultra-low-noise microwave to optics conversion in gallium phosphide.

Mechanical resonators can act as excellent intermediaries to interface single photons in the microwave and optical domains due to their high quality factors. Nevertheless, the optical pump required to overcome the large energy difference between the frequencies can add significant noise to the transduced signal. Here we exploit the remarkable properties of thin-film gallium phosphide to demonstrate bi-directional on-chip conversion between microwave and optical frequencies, realized by piezoelectric actuation of a Gigahertz-frequency optomechanical resonator. The large optomechanical coupling and the suppression of two-photon absorption in the material allows us to operate the device at optomechanical cooperativities greatly exceeding one. Alternatively, when using a pulsed upconversion pump, we demonstrate that we induce less than one thermal noise phonon. We include a high-impedance on-chip matching resonator to mediate the mechanical load with the 50-Ω source. Our results establish gallium phosphide as a versatile platform for ultra-low-noise conversion of photons between microwave and optical frequencies.

Floquet Control of Optomechanical Bistability in Multimode Systems.

Cavity optomechanical systems make possible the fine manipulation of mechanical degrees of freedom with light, adding functionality and having broad appeal in photonic technologies. We show that distinct mechanical modes can be exploited with a temporally modulated Floquet drive to steer between distinct steady states induced by changes of cavity radiation pressure. We investigate the additional influence of the thermo-optic nonlinearity on these dynamics and find that it can suppress or amplify the control mechanism in contrast to its often performance-limiting character. Our results provide new techniques for the characterization of thermal properties of optomechanical systems and their control, sensing and computational applications.

Random number generation with a chaotic electromechanical resonator.

Chaos enables the emergence of randomness in deterministic physical systems. Therefore it can be exploited for the conception of true random number generators mandatory in classical cryptography applications. Meanwhile, nanomechanical oscillators, at the core of many on-board functionalities such as sensing, reveal as excellent candidates to behave chaotically. This is made possible thanks to intrinsic mechanical nonlinearities emerging at the nanoscale. Here we present a platform gathering a nanomechanical oscillator and its integrated capacitive actuation. Using a modulation of the resonant force induced by the electrodes, we demonstrate chaotic dynamics and study how it depends on the dissipation of the system. The randomness of a binary sequence generated from a chaotic time trace is evaluated and discussed such that the generic parameters enabling successful random number generation can be established. This demonstration makes use of concepts which are sufficiently general to be applied to the next generation of nano-electro-optomechanical systems.

Vibrational Resonance Amplification in a Thermo-Optic Optomechanical Nanocavity.

Vibrational resonance is a generic phenomenon found in many different bistable systems whereby a weak low-frequency signal is amplified by use of an additional nonresonant high-frequency modulation. The realization of weak signal enhancement in integrated nonlinear optical nanocavities is of great interest for nanophotonic applications where optical signals may be of low power. Here, we report experimental observation of vibrational resonance in a thermo-optically bistable photonic crystal optomechanical resonator with an amplification up to +16 dB. The characterization of the bistability can interestingly be done using a mechanical resonance of the membrane, which is submitted to a strong thermoelastic coupling with the cavity.

Weak signal enhancement by nonlinear resonance control in a forced nano-electromechanical resonator.

Driven non-linear resonators can display sharp resonances or even multistable behaviours amenable to induce strong enhancements of weak signals. Such enhancements can make use of the phenomenon of vibrational resonance, whereby a weak low-frequency signal applied to a bistable resonator can be amplified by driving the non-linear oscillator with another appropriately-adjusted non-resonant high-frequency field. Here we demonstrate experimentally and theoretically a significant resonant enhancement of a weak signal by use of a vibrational force, yet in a monostable system consisting of a driven nano-electromechanical nonlinear resonator. The oscillator is subjected to a strong quasi-resonant drive and to two additional tones: a weak signal at lower frequency and a non-resonant driving at an intermediate frequency. We analyse this phenomenon in terms of coherent nonlinear resonance manipulation. Our results illustrate a general mechanism which might have applications in the fields of microwave signal amplification or sensing for instance.

Gallium Phosphide as a Piezoelectric Platform for Quantum Optomechanics.

Recent years have seen extraordinary progress in creating quantum states of mechanical oscillators, leading to great interest in potential applications for such systems in both fundamental as well as applied quantum science. One example is the use of these devices as transducers between otherwise disparate quantum systems. In this regard, a promising approach is to build integrated piezoelectric optomechanical devices that are then coupled to microwave circuits. Optical absorption, low quality factors, and other challenges have up to now prevented operation in the quantum regime, however. Here, we design and characterize such a piezoelectric optomechanical device fabricated from gallium phosphide in which a 2.9 GHz mechanical mode is coupled to a high quality factor optical resonator in the telecom band. The large electronic band gap and the resulting low optical absorption of this new material, on par with devices fabricated from silicon, allows us to demonstrate quantum behavior of the structure. This not only opens the way for realizing noise-free quantum transduction between microwaves and optics, but in principle also from various color centers with optical transitions in the near visible to the telecom band.

Pulse train interaction and control in a microcavity laser with delayed optical feedback.

We report experimental and theoretical results on the pulse train dynamics in an excitable semiconductor microcavity laser with an integrated saturable absorber and delayed optical feedback. We show how short optical control pulses can trigger, erase, or retime regenerative pulse trains in the external cavity. Both repulsive and attractive interactions between pulses are observed, and are explained in terms of the internal dynamics of the carriers. A bifurcation analysis of a model consisting of a system of nonlinear delay differential equations shows that arbitrary sequences of coexisting pulse trains are very long transients towards weakly stable periodic solutions with equidistant pulses in the external cavity.

Intrinsic Properties of Suspended MoS2 on SiO2/Si Pillar Arrays for Nanomechanics and Optics.

Semiconducting two-dimensional (2D) materials, such as transition-metal dichalcogenides (TMDs), are emerging in nanomechanics, optoelectronics, and thermal transport. In each of these fields, perfect control over 2D material properties including strain, doping, and heating is necessary, especially on the nanoscale. Here, we study clean devices consisting of membranes of single-layer MoS2 suspended on pillar arrays. Using Raman and photoluminescence spectroscopy, we have been able to extract, separate, and simulate the different contributions on the nanoscale and to correlate these to the pillar array design. This control has been used to design a periodic MoS2 mechanical membrane with a high reproducibility and to perform optomechanical measurements on arrays of similar resonators with a high-quality factor of 600 at ambient temperature, hence opening the way to multiresonator applications with 2D materials. At the same time, this study constitutes a reference for the future development of well-controlled optical emissions within 2D materials on periodic arrays with reproducible behavior. We measured a strong reduction of the MoS2 band gap induced by the strain generated from the pillars. A transition from direct to indirect band gap was observed in isolated tent structures made of MoS2 and pinched by a pillar. In fully suspended devices, simulations were performed allowing both the extraction of the thermal conductance and doping of the layer. Using the correlation between the influences of strain and doping on the MoS2 Raman spectrum, we have developed a simple, elegant method to extract the local strain in suspended and nonsuspended parts of a membrane. This opens the way to experimenting with tunable coupling between light emission and vibration.

Phase Stochastic Resonance in a Forced Nanoelectromechanical Membrane.

Stochastic resonance is a general phenomenon usually observed in one-dimensional, amplitude modulated, bistable systems. We show experimentally the emergence of phase stochastic resonance in the bidimensional response of a forced nanoelectromechanical membrane by evidencing the enhancement of a weak phase modulated signal thanks to the addition of phase noise. Based on a general forced Duffing oscillator model, we demonstrate experimentally and theoretically that phase noise acts multiplicatively, inducing important physical consequences. These results may open interesting prospects for phase noise metrology or coherent signal transmission applications in nanomechanical oscillators. Moreover, our approach, due to its general character, may apply to various systems.

High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs.

Light scattering by a two-dimensional photonic-crystal slab (PCS) can result in marked interference effects associated with Fano resonances. Such devices offer appealing alternatives to distributed Bragg reflectors and filters for various applications, such as optical wavelength and polarization filters, reflectors, semiconductor lasers, photodetectors, bio-sensors and non-linear optical components. Suspended PCS also have natural applications in the field of optomechanics, where the mechanical modes of a suspended slab interact via radiation pressure with the optical field of a high-finesse cavity. The reflectivity and transmission properties of a defect-free suspended PCS around normal incidence can be used to couple out-of-plane mechanical modes to an optical field by integrating it in a free-space cavity. Here we demonstrate the successful implementation of a PCS reflector on a high-tensile stress Si3N4 nanomembrane. We illustrate the physical process underlying the high reflectivity by measuring the photonic-crystal band diagram. Moreover, we introduce a clear theoretical description of the membrane scattering properties in the presence of optical losses. By embedding the PCS inside a high-finesse cavity, we fully characterize its optical properties. The spectrally, angular- and polarization-resolved measurements demonstrate the wide tunability of the membrane's reflectivity, from nearly 0 to 99.9470±0.0025%, and show that material absorption is not the main source of optical loss. Moreover, the cavity storage time demonstrated in this work exceeds the mechanical period of low-order mechanical drum modes. This so-called resolved-sideband condition is a prerequisite to achieve quantum control of the mechanical resonator with light.

High Q factor InP photonic crystal nanobeam cavities on silicon wire waveguides.

High-quality (Q) factor indium phosphide (InP)-based 1D photonic crystal nanobeam cavities are fabricated on silicon on insulator waveguides. Through the optimization of the fabrication process, the intrinsic Q factor of these fully encapsulated nanocavities is demonstrated to attain values higher than 100,000. Experimental and numerical investigations are carried out on the impact, on the Q factor, of the strength of the evanescent wave coupling between the cavity and the waveguide. We reveal that this coupling can result in a modification of the electromagnetic field distribution in the resonant mode, which gives rise up to a factor 4 reduction in the intrinsic Q factor for the structures under study.

Integrated III-V Photonic Crystal--Si waveguide platform with tailored optomechanical coupling.

Optomechanical systems, in which the vibrations of a mechanical resonator are coupled to an electromagnetic radiation, have permitted the investigation of a wealth of novel physical effects. To fully exploit these phenomena in realistic circuits and to achieve different functionalities on a single chip, the integration of optomechanical resonators is mandatory. Here, we propose a novel approach to heterogeneously integrate arrays of two-dimensional photonic crystal defect cavities on top of silicon-on-insulator waveguides. The optomechanical response of these devices is investigated and evidences an optomechanical coupling involving both dispersive and dissipative mechanisms. By controlling the optical coupling between the waveguide and the photonic crystal, we were able to vary and understand the relative strength of these couplings. This scalable platform allows for an unprecedented control on the optomechanical coupling mechanisms, with a potential benefit in cooling experiments, and for the development of multi-element optomechanical circuits in the framework of optomechanically-driven signal-processing applications.

Thermal management in hybrid InP/silicon photonic crystal nanobeam laser.

Thermal properties of InP-based quantum well photonic crystal nanobeam lasers heterogeneously integrated on silicon on insulator waveguides are studied. We show both numerically and experimentally the reduction of the thermal resistance of the III-V cavities by adjusting the composition of the layer which bonds the III-V materials to the silicon wafer and by adding an over-cladding on top of the cavities. Using a bonding layer made of benzocyclobutene and SiO(2) and an over-cladding of MgF(2), we found a decrease by a factor higher than 35 compared to air-suspended photonic crystal nanobeam cavities. Such optimized structures are demonstrated to operate under continuous wave pumping for several 10's of minutes despite the adverse effect of non-radiative surface recombination of carriers.

Deformable two-dimensional photonic crystal slab for cavity optomechanics.

We have designed photonic crystal suspended membranes with optimized optical and mechanical properties for cavity optomechanics. Such resonators sustain vibration modes in the megahertz range with quality factors of a few thousand. Thanks to a two-dimensional square lattice of holes, their reflectivity at normal incidence at 1064 nm reaches values as high as 95%. These two features, combined with the very low mass of the membrane, open the way to the use of such periodic structures as deformable end mirrors in Fabry-Perot cavities for the investigation of cavity optomechanical effects.

Surface-emitting mid-infrared quantum cascade lasers with high-contrast photonic crystal resonators.

We have developed surface-emitting single-mode quantum cascade lasers which employ high-contrast photonic-crystal resonators. The devices operate on band-edge states of the photonic band-structure. The mode profile and polarization characteristics of the band-edge modes are calculated by three-dimensional finite-difference time-domain simulation. Experimentally, the spectral properties, the far-field patterns, and the polarization characteristics of the lasers are determined and compared with simulations. The good agreement between the simulations and the experiments confirms that the hexapolar mode at the Gamma-point band-edge gives rise to lasing. By using a novel and advanced fabrication method, deep and vertical PhC holes are fabricated with no metal redeposition on the sidewalls, which improves the laser performance with respect to the current status. The angular of the output beam is approximately 15 masculine, and the side mode suppression ratio of the single mode emission is about 25 dB. The threshold current density at 78 K and the maximum operation temperature are 7.6 kA/cm2 and 220 K, respectively. The performance is mainly limited by the loss induced by surface plasmon waveguide, which can be overcome by using an optimized dielectric waveguide structure.

Dynamics of band-edge photonic crystal lasers.

Band-edge photonic crystal lasers were fabricated and their temporal characteristics were minutely analyzed using a high resolution up-conversion system. The InGaAs/InP photonic crystal laser operates at room temperature at 1.55 microm with turn on time ranging from 17ps to 30ps.