Multimode phonon lasing in cavity optomechanical systems enables the generation of coherent, multi-frequency mechanical signals with potential applications in RF signal processing, frequency combs, and sensing. However, achieving simultaneous self-sustained oscillations in multiple mechanical modes is often hindered by strong mode competition. Here, we demonstrate robust multimode phonon lasing in a silicon optomechanical nanobeam, driven by a self-pulsing (SP) mechanism originating from free-carrier dispersion and thermo-optic effects. Unlike previous approaches that rely on external pump modulation or the use of widely spectrally separated modes to mitigate the suppression of self-oscillations, our system supports lasing of two strongly competing in-plane flexural modes of the nanobeam under continuous-wave pumping. The SP cycle dynamically adapts to the mechanical perturbations, providing synchronized optical pumping even in the absence of harmonic frequency relations. This results in stable multimode operation across periodic, quasi-periodic, and chaotic regimes, all accurately predicted by numerical modeling. These findings establish SP as a passive and self-organized mechanism for coherent multi-frequency phonon generation in chip-scale platforms.

We present recent advances in the development and control of the nonlinear dynamics of individual and coupled one-dimensional optomechanical oscillators (OMOs), based on silicon optomechanical crystal cavities. These devices exhibit coherent mechanical oscillations at frequencies up to hundreds of MHz, driven by a self-sustained mechanism known as self-pulsing (SP). We experimentally demonstrate several individual and collective dynamical regimes that are essential steps toward realizing networks of weakly interacting OMOs with remotely controllable dynamics. In particular, we observe multimode mechanical lasing in a single OMO, spontaneous synchronization of weakly coupled OMOs, and injection locking of both individual and coupled OMOs to external RF tones. These results open the door to high-performance applications in sensing, time-keeping, and signal processing.

Multimode cavity optomechanics, where multiple mechanical degrees of freedom couple to optical cavity modes, provides a rich platform for exploring nonlinear dynamics and engineering complex interactions. In this work, we investigate the interplay between two mechanical modes with similar characteristics and a self-induced nonlinear modulation of intra-cavity power (self-pulsing) driven by free-carrier dispersion and thermo-optic effects in silicon. Notably, the self-pulsing dynamics adapts to the optomechanically induced perturbations from both mechanical modes, enabling simultaneous synchronous pumping and driving them into a stable state characterized by high-amplitude, self-sustained, and coherent oscillations. This result effectively overcomes the strong mode competition typically observed in modes with similar spatial distributions and frequency scales. Remarkably, this regime is achieved even when the mechanical frequencies do not satisfy a harmonic relation, leading to quasi-periodic or chaotic intra-cavity power dynamics, while the mechanical modes maintain coherent, high-amplitude oscillations. These results, supported by a numerical model that accurately predicts the dynamics of the system, open new pathways for the generation and control of multi-phonon coherent sources in chip-integrated silicon platforms.

Optomechanical oscillators stand out as high-performance and versatile candidates for serving as reference clocks in sequential photonic integrated circuits. Indeed, they have the unique capability of simultaneously generating mechanical tones and optical signal modulations at frequencies determined by their geometrical design. In this context, the concept of synchronization introduces a powerful means to precisely coordinate the dynamics of multiple oscillators in a controlled manner, therefore increasing efficiency and preventing errors in signal processing photonic systems or communication interfaces. In this work, we demonstrate the cascaded injection locking of a pair of silicon-based optomechanical crystal cavities acting as optomechanical oscillators to an external reference signal that subtly modulates the laser driving only one of them. In contrast to most previous implementations, both cavities support isolated optical resonances and interact by a weak mechanical interconnection. This configuration allows one cavity to be used for probing the mechanical perturbation generated by the oscillator that receives the external forcing. The combination of the obtained results, supported by a numerical model, with remote optical injection locking schemes discussed in the literature lays the groundwork for the distribution of reference signals within large networks of processing elements in future phonon–photon hybrid circuits.

Silicon one-dimensional optomechanical cavities offer a cost-effective and highly scalable solution for the study and implementation of non-linear phenomena. By modifying the refractive index of silicon through thermal or free-carrier effects, it becomes possible to optically drive these resonators into a state of high-amplitude and coherent self-sustained mechanical oscillation. The nonlinearity stemming from this amplification mechanism provides significant adaptability in adjusting the frequency of mechanical resonators, enabling experiments such as injection locking, synchronization, and the study of chaotic dynamics. In this work, we show different novel configurations for the synchronization between mechanical flexural modes of silicon nanobeams and their locking to an external reference signal. The results hold great promise for applications in the distribution of clock signals in future photonic integrated circuits, as well as for establishing extensive networks of optomechanical resonators for studying complex non-linear dynamics.

Nanomechanical resonators can serve as ultrasensitive, miniaturized force probes. While vertical structures such as nanopillars are ideal for this purpose, transducing their motion is challenging. Pillar-based photonic crystals (PhCs) offer a potential solution by integrating optical transduction within the pillars. However, achieving high-quality PhCs is hindered by inefficient vertical light confinement. Here, we present a full-silicon photonic crystal cavity based on nanopillars as a platform for applications in force sensing and biosensing areas. Its unit cell consists of a silicon pillar with a larger diameter at its top portion than at the bottom, which allows vertical light confinement and an energy band gap in the near-infrared range for transverse-magnetic polarization. We experimentally demonstrate optical cavities with Q factors exceeding 103, constructed by inserting a defect within a periodic arrangement of this type of pillars. Each nanopillar naturally behaves as a nanomechanical cantilever, making the fabricated geometries excellent optomechanical (OM) photonic crystal cavities in which the mechanical motion of each nanopillar composing the cavity can be optically transduced. These geometries display enhanced mechanical properties, cost-effectiveness, integration possibilities, and scalability. They also present an alternative in front of the widely used suspended Si beam OM cavities made on silicon-on-insulator substrates.

Nanomechanical resonators can serve as ultrasensitive, miniaturized force probes. While vertical structures like nanopillars are ideal for this purpose, transducing their motion is challenging. Pillar-based photonic crystals (PhCs) offer a potential solution by integrating optical transduction within the pillars. However, achieving high-quality PhCs is hindered by inefficient vertical light confinement. Here, we present a full-silicon 1D photonic crystal cavity based on nanopillars as a new platform with great potential for applications in force sensing and biosensing areas. Its unit cell consists of a silicon pillar with larger diameter at its top portion than at the bottom, which allows vertical light confinement and an energy bandgap in the near infrared range for transverse-magnetic (TM) polarization. We experimentally demonstrate optical cavities with Q-factors exceeding 1e3 constructed by inserting a defect within a periodic arrangement of this type of pillars. Given the fact that that each nanopillar naturally behaves as a nanomechanical cantilever, the fabricated geometries are excellent optomechanical (OM) photonic crystal cavities in which the mechanical motion of each nanopillar composing the cavity can be optically transduced. These novel geometries display enhanced mechanical properties, cost-effectiveness, integration possibilities, and scalability, and opens and new path in front of the widely used suspended Si beam OM cavities made on silicon-on-insulator.

Glass microspheres are of great interest for numerous industrial, biomedical, or standalone applications, but it remains challenging to evaluate their elastic and optical properties in a non-destructive way. In this work, we address this issue by using two complementary contactless techniques to obtain elastic and optical constants of glass microspheres with diameters ranging from 10 to 60 µm. The first technique we employ is Brillouin Light Scattering, which yields scattering with longitudinal acoustic phonons, the frequency of which is found to be 5% lower than that measured in the bulk material. The second technique involves exciting the optical whispering gallery modes of the microspheres, which allows us to transduce some of their vibrational modes. The combined data allow for extracting the refractive index and the elastic constants of the material. Our findings indicate that the values of those properties are reduced with respect to their bulk material counterpart due to an effective decrease of the density, resulting from the fabrication process. We propose the use of this combined method to extract elastic and optical parameters of glass materials in microsphere geometries and compare them with the values of the pristine material from which they are formed.

The remote synchronization of oscillators is essential for improving the performance, efficiency, and reliability of various systems and technologies, ranging from everyday telecommunications to cutting-edge scientific research and emerging technologies. In this work, we unequivocally demonstrate a master-slave type of synchronization between two self-sustained optomechanical crystal oscillators that interact solely through an external optical feedback stage. Several pieces of experimental evidence rule out the possibility of resonant forcing, and, in contrast to previous works, indicate that synchronization is achieved in the regime of natural dynamics suppression. Our experimental results are in agreement with the predictions of a numerical model describing the specific mechanical lasing dynamics of each oscillator and the unidirectional interaction between them. The outcomes of our study pave the way toward the synchronization of clock signals corresponding to far-placed processing elements in a future synchronous photonic integrated circuit.

The remote synchronization of oscillators is essential for improving the performance, efficiency, and reliability of various systems and technologies, ranging from everyday telecommunications to cutting-edge scientific research and emerging technologies. In this work, we unequivocally demonstrate a unidirectional type of synchronization between two self-sustained optomechanical crystal oscillators that interact solely through an external optical feedback stage. Several pieces of experimental evidence rule out the possibility of resonant forcing and, in contrast to previous works, indicate that synchronization is achieved in the regime of natural dynamics suppression. Our experimental results are in agreement with the predictions of a numerical model describing the specific mechanical lasing dynamics of each oscillator and the unidirectional interaction between them. The outcomes of our study pave the way toward the synchronization of clock signals corresponding to far-placed processing elements in a future synchronous photonic integrated circuit.

Locking of oscillators to ultra-stable external sources is of paramount importance for improving close-to-carrier phase noise in free running oscillators. In most of them, such as Micro-Electro-Mechanical-Systems or LC circuit-based oscillators, the locking frequency range is limited by the robustness of their natural frequency, which comes explicitly related with intrinsic parameters of the system. In this work we report the synchronization of an optically-driven self-pulsing limit-cycle taking place in a silicon optomechanical crystal cavity to an external harmonic signal that modulates the driving laser. Because of the extreme ductility of the natural self-pulsing frequency (several tens of MHz), the injection-locking mechanism is highly efficient and displays giant relative bandwidths exceeding 60%. The external modulation reveals itself as a knob to explore dynamical attractors that are otherwise elusive and, in particular, as a means to initialize a mechanical resonator into a state of self-sustained oscillations driven by radiation pressure forces. Moreover, we exploit the large anharmonicity of the studied limit-cycle to induce injection-locking to integer multiples and fractions of the frequency of the external reference, which can be used for frequency conversion purposes in nano-electro-opto-mechanical systems.

Controlling thermal energy transfer at the nanoscale has become critically important in many applications and thermal properties since it often limits device performance. In this work, we study the effects on thermal conductivity arising from the nanoscale structure of free-standing nanocrystalline silicon films and the increasing surface-to-volume ratio when fabricated into suspended optomechanical nanobeams. We characterize thermal transport in structures with different grain sizes and elucidate the relative impact of grain size and geometrical dimensions on thermal conductivity. We use a micro-time-domain thermoreflectance method to study the impact of the grain size distribution, from 10 to 400 nm, on the thermal conductivity in free-standing nanocrystalline silicon films considering surface phonon and grain boundary scattering. We find a drastic reduction in the thermal conductivity, down to values of 10 W.m^-1.K^-1 and below, which is just a fraction of the conductivity of single crystalline silicon. Decreasing the grain size further decreases the thermal conductivity. We also observe that this effect is smaller in OM nanostructures than in membranes due to the competition of surface scattering in decreasing thermal conductivity. Finally, we introduce a novel versatile contactless characterization technique that can be adapted to any structure supporting a thermally shifted optical resonance and use it to evaluate the thermal conductivity. This method can be used with optical resonances exhibiting different mode profiles and the data is shown to agrees quantitatively with the thermoreflectance measurements. This work opens the way to a more generalized thermal characterization of optomechanical cavities and to create hot-spots with engineered shapes at desired position in the structures as a means to study thermal transport in coupled photon-phonon structures.

Optomechanical crystal cavities (OMC) have rich perspectives for detecting and indirectly analysing biological particles, such as proteins, bacteria and viruses. In this work we demonstrate the working principle of OMCs operating under ambient conditions as a sensor of submicrometer particles by optically monitoring the frequency shift of thermally activated mechanical modes. The resonator has been specifically designed so that the cavity region supports a particular family of low modal-volume mechanical modes, commonly known as -pinch modes-. These involve the oscillation of only a couple of adjacent cavity cells that are relatively insensitive to perturbations in other parts of the resonator. The eigenfrequency of these modes decreases as the deformation is localized closer to the centre of the resonator. Thus, by identifying specific modes that undergo a frequency shift that amply exceeds the mechanical linewidth, it is possible to infer if there are particles deposited on the resonator, how many are there and their approximate position within the cavity region. OMCs have rich perspectives for detecting and indirectly analysing biological particles, such as proteins, viruses and bacteria.

Spontaneous locking of the phase of a coherent phonon source to an external reference is demonstrated in a deeply sideband-unresolved optomechanical system. The high-amplitude mechanical oscillations are driven by the anharmonic modulation of the radiation pressure force that result from an absorption-mediated free-carrier/temperature limit cycle, i.e., self-pulsing. Synchronization is observed when the pump laser driving the mechanical oscillator to a self-sustained state is modulated by a radiofrequency tone. We employ a pump-probe phonon detection scheme based on an independent optical cavity to observe only the mechanical oscillator dynamics. The lock range of the oscillation frequency, i.e., the Arnold tongue, is experimentally determined over a range of external reference strengths, evidencing the possibility to tune the oscillator frequency for a range up to 350 kHz. The stability of the coherent phonon source is evaluated via its phase noise, with a maximum achieved suppression of 44 dBc/Hz at 1 kHz offset for a 100 MHz mechanical resonator. Introducing a weak modulation in the excitation laser reveals as a further knob to trigger, control and stabilize the dynamical solutions of self-pulsing based optomechanical oscillators, thus enhancing their potential as acoustic wave sources in a single-layer silicon platform.

The resonant enhancement of mechanical and optical interaction in optomechanical cavities enables their use as extremely sensitive displacement and force detectors. In this Letter, we demonstrate a hybrid magnetometer that exploits the coupling between the resonant excitation of spin waves in a ferromagnetic insulator and the resonant excitation of the breathing mechanical modes of a glass microsphere deposited on top. The interaction is mediated by magnetostriction in the ferromagnetic material and the consequent mechanical driving of the microsphere. The magnetometer response thus relies on the spectral overlap between the ferromagnetic resonance and the mechanical modes of the sphere, leading to a peak sensitivity of 850  pT Hz^{-1/2} at 206 MHz when the overlap is maximized. By externally tuning the ferromagnetic resonance frequency with a static magnetic field, we demonstrate sensitivity values at resonance around a few nT Hz^{-1/2} up to the gigahertz range. Our results show that our hybrid system can be used to build a high-speed sensor of oscillating magnetic fields.

Nanocrystalline materials exhibit properties that can differ substantially from those of their single crystal counterparts. As such, they provide ways to enhance and optimise their functionality for devices and applications. Here we report on the optical, mechanical and thermal properties of nanocrystalline silicon probed by means of optomechanical nanobeams to extract information of the dynamics of optical absorption, mechanical losses, heat generation and dissipation. The optomechanical nanobeams are fabricated using nanocrystalline films prepared by annealing amorphous silicon layers at different temperatures. The resulting crystallite sizes and the stress in the films can be controlled by the annealing temperature and time and, consequently, the properties of the films can be tuned relatively freely, as demonstrated here by means of electron microscopy and Raman scattering. We show that the nanocrystallite size and the volume fraction of the grain boundaries play a key role in the dissipation rates through non-linear optical and thermal processes. Promising optical (13000) and mechanical (1700) quality factors were found in the optomechanical cavity realised in the nanocrystalline Si resulting from annealing at 950 C. The enhanced absorption and recombination rates via the intra-gap states and the reduced thermal conductivity boost the potential to exploit these non-linear effects in applications, including NEMS, phonon lasing and chaos-based devices.

This folder contains the raw data from which the graphs in paper Mechanical oscillations in lasing microsphere, DOI: 10.1063/1.4997182, have been obtained.

Nanocrystalline silicon is a material that shows highly interesting properties for both electronic and photonic applications. Recently, it has also been employed as the core material for building optomechanical systems, showing some novel features. In this work we provide insight in the optical, mechanical and thermal properties of nanocrystalline silicon as a material platform of optomechanical crystal cavities. The results of this work, extracted by means of a combination of complementary experimental techniques, can be useful to evaluate the potential benefits as well as disadvantages of this material highly relevant for the development of nano-opto-electro-mechanical systems (NOEMS). We show that the specific microscopic nature of the nanocrystalline material has a dominant effect in the optical and mechanical losses and in the thermal properties. More specifically, we find strong correlations between the measured parameters and the volume fraction of grain boundaries, which has been tuned by adjusting the annealing temperature of the layers.

The resonant enhancement of mechanical and optical interaction in optomechanical cavities enables their use as extremely sensitive displacement and force detectors. In this work we demonstrate a hybrid magnetometer that exploits the coupling between the resonant excitation of spin waves in a ferromagnetic insulator and the resonant excitation of the breathing mechanical modes of a glass microsphere deposited on top. The interaction is mediated by magnetostriction in the ferromagnetic material and the consequent mechanical driving of the microsphere. The magnetometer response thus relies on the spectral overlap between the ferromagnetic resonance and the mechanical modes of the sphere, leading to a peak sensitivity better than 900 pT Hz$^{-1/2}$ at 206 MHz when the overlap is maximized. By externally tuning the ferromagnetic resonance frequency with a static magnetic field we demonstrate sensitivity values at resonance around a few nT Hz$^{-1/2}$ up to the GHz range. Our results show that our hybrid system can be used to build high-speed sensor of oscillating magnetic fields.

The synchronization of coupled oscillators is a phenomenon found throughout nature. Mechanical oscillators are paradigmatic examples, but synchronizing their nanoscaled versions is challenging. We report synchronization of the mechanical dynamics of a pair of optomechanical crystal cavities that, in contrast to previous works performed in similar objects, are intercoupled with a mechanical link and support independent optical modes. In this regime they oscillate in antiphase, which is in agreement with the predictions of our numerical model that considers reactive coupling. We also show how to temporarily disable synchronization of the coupled system by actuating one of the cavities with a heating laser, so that both cavities oscillate independently. Our results can be upscaled to more than two cavities and pave the way towards realizing integrated networks of synchronized mechanical oscillators.