Nanoscale Resonators Research Articles

Modeling of nonlocal Caputo–Fabrizio integral models in a nanoscale resonator

In the present work, the nonlocal integral constitutive laws for application to nano-beams, are investigated in a general setting. Evidence of boundary effects are enlightened by theoretical analysis and numerical computations. The proposed compensation procedures efficiently analyzes the thermoelastic interaction in a nanoscale resonator in the context of two-temperature three-phase lag model of thermoelasticity involving Caputo Fabrizio (CF) derivative where both the ends of the nanoscale beam is clamped. Employing the Laplace transform as a tool, the solutions for conductive temperature, thermodynamic temperature, stress and deflection have been determined. The corresponding solutions in the space-time domain is obtained by incorporating the numerical inversion of the Laplace transform using Riemann-sum approximation technique. According to the graphical representations corresponding to the numerical results, effectiveness of the recently proposed theory is demonstrated due to the presence of nonlocal CF order and the nonsingular kernel.

Ultra-high Q resonances based on zero group-velocity modes accompanied by bound states in the continuum in 2D photonic crystal slabs

Optical resonators made of 2D photonic crystal (PhC) slabs provide efficient ways to manipulate light at the nanoscale through small group-velocity modes with low radiation losses. The resonant modes in periodic photonic lattices are predominantly limited by nonleaky guided modes at the boundary of the Brillouin zone below the light cone. Here, we propose a mechanism for ultra-high Q resonators based on the bound states in the continuum (BICs) above the light cone that have zero-group velocity (ZGV) at an arbitrary Bloch wavevector. By means of the mode expansion method, the construction and evolution of avoided crossings and Friedrich-Wintgen BICs are theoretically investigated at the same time. By tuning geometric parameters of the PhC slab, the coalescence of eigenfrequencies for a pair of BIC and ZGV modes is achieved, indicating that the waveguide modes are confined longitudinally by small group-velocity propagation and transversely by BICs. Using this mechanism, we engineer ultra-high Q nanoscale resonators that can significantly suppress the radiative losses, despite the operating frequencies above the light cone and the momenta at the generic k point. Our work suggests that the designed devices possess potential applications in low-threshold lasers and enhanced nonlinear effects.

Colloidal Self-Assembly of Silver Nanoparticle Clusters for Optical Metasurfaces.

Optical metasurfaces are two-dimensional assemblies of nanoscale optical resonators and could constitute the next generation of ultrathin optical components. The development of methods to manufacture these nanostructures on a large scale is still a challenge, while most performance demonstrations were obtained with lithographically fabricated metasurfaces that are restricted to small scales. Self-assembly fabrication routes are promising alternatives and have been used to produce original nanoresonators. Reports of self-assembled metasurface fabrication, however, are still scarce. Here, we show that an emulsion-based formulation approach can be used both for the fabrication of complex colloidal resonators, presenting a strong interaction with light, in particular due to simultaneous magnetic and electric modes of resonance, and for their deposition in homogeneous films. This fabrication technique involves emulsification of an aqueous suspension of silver nanoparticles in an oil phase, followed by controlled drying of the emulsion, and produces silver colloidal clusters. We show that the drying process can be controlled in a liquid emulsion, producing a metafluid, as well as in a sedimented emulsion, producing a metasurface. The structural control of the synthesized colloidal clusters is demonstrated with electron microscopy and X-ray scattering techniques. Using a polarization-resolved multiangle light scattering setup in the visible wavelength range, we conduct a comprehensive angular and spectroscopic study of the optical resonant scattering of the nanoresonators in a metafluid and show that they present strong optical magnetic resonances and directional forward-scattering patterns, with scattering efficiencies of up to 4. The metasurfaces consist of homogeneous films, of variable surface density, of colloidal clusters that have the same extinction properties on the surface and in the fluid. This experimental approach allows for large-scale production of metasurfaces.

Hyperbolic Polaritonic Rulers Based on van der Waals α-MoO3 Waveguides and Resonators.

Low-dimensional, strongly anisotropic nanomaterials can support hyperbolic phonon polaritons, which feature strong light-matter interactions that can enhance their capabilities in sensing and metrology tasks. In this work, we report hyperbolic polaritonic rulers, based on microscale α-phase molybdenum trioxide (α-MoO3) waveguides and resonators suspended over an ultraflat gold substrate, which exhibit near-field polaritonic characteristics that are exceptionally sensitive to device geometry. Using scanning near-field optical microscopy, we show that these systems support strongly confined image polariton modes that exhibit ideal antisymmetric gap polariton dispersion, which is highly sensitive to air gap dimensions and can be described and predicted using a simple analytic model. Dielectric constants used for modeling are accurately extracted using near-field optical measurements of α-MoO3 waveguides in contact with the gold substrate. We also find that for nanoscale resonators supporting in-plane Fabry-Perot modes, the mode order strongly depends on the air gap dimension in a manner that enables a simple readout of the gap dimension with nanometer precision.

Small-Scale Dynamic Behavior of Embedded Beams Under Moving Force in Complex Environments

Forced and free dynamic responses of nanobeams resting on a three-parameter foundation subjected to a moving force in magneto-hygro-thermal conditions are investigated based on the nonlocal strain gradient theory. Also, a detailed parametric study is conducted to identify the impact of slender ratio, axial and distributed tangential loads on the vibration characteristics and dynamic phenomena of the small-scale system. Comparative studies with existing results in the literature are performed to ensure the accuracy of the presented model and solution approach. Analytical and numerical methods are implemented to detect the effects of foundation coefficients, environmental conditions, geometrical and scale parameters on the dynamic amplification factor, critical moving force velocity, cancellation, and maximum free response mechanisms of the system. The outcomes revealed that the critical moving force velocity is enhanced by ascending the slender ratio, elastic, and shear moduli of the foundation. It is found that when the damping factor is considered for the foundation, it is feasible to prevent the occurrence of the cancellation phenomenon. Also, it is concluded that by fine-tuning scale parameters and environmental conditions, unwanted vibration of the system can be suppressed. The attained results of this study can be helpful in the vibration control of nanoscale actuators, switches, and resonators.

Energy Transfer into Period-Tripled States in Coupled Electromechanical Modes at Internal Resonance

A demonstration of a new way to transfer energy between coupled modes in a nanoscale resonator presents novel opportunities for information applications that go beyond the standard binary representation.

Precision Calibration of the Duffing Oscillator with Phase Control

The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to an external excitation. When changing the amplitude or frequency of the external excitation, a sudden jump in the response function reveals the nonlinear dynamics prominently. However, this bistability leaves part of the full response function unobserved, which limits the precise measurement of the system parameters. Here, we exploit the often unknown fact that the response of a Duffing oscillator with nonlinear damping is a unique function of its phase. By actively stabilizing the oscillator's phase we map out the full response function. This phase control allows us to precisely determine the system parameters. Our results are particularly important for characterizing nanoscale resonators, where nonlinear effects are observed readily and which hold great promise for next generation of ultrasensitive force and mass measurements. We demonstrate our approach experimentally with an optically levitated particle in high vacuum.

A tunable nonlinear plasmonic multiplexer/demultiplexer device based on nanoscale ring resonators

A tunable nonlinear plasmonic multiplexer/demultiplexer device based on nanoscale ring resonators

Nonlocal Timoshenko modeling effectiveness for carbon nanotube-based mass sensors

Carbon nanotubes (CNTs) have been considered for a wide range of nanotechnology applications due to their unique mechanical, thermal, and electrical properties. One of the most notable nanotechnology applications is the frequency shift-based carbon nanotube mass sensor, which has motivated the development of reliable reduced-order models. As such, this research effort focuses on a carbon nanotube-based mass sensor that utilizes Timoshenko beam theory to extend the usability of these models to short and stout structures. Additionally, Eringen's nonlocal elasticity is considered to account for certain nanoscale phenomena. To the authors' knowledge, this is the first time a CNT-based mass sensor modeled with the nonlocal Timoshenko beam theory with a complex-shaped deposited particle has been studied. Considering Timoshenko beam theory and Eringen's nonlocal theory, the Hamilton's principle is utilized to derive the governing equations of motion, boundary conditions, and continuity conditions accounting for a single deposited nanoparticle. Then, it is shown that the obtained frequency shift of the sensor is dependent on the rotary inertia, shear effects, nonlocal parameter, and particle mass, geometry, and location. The variation of each of these parameters leads to a holistic characterization of the proposed system. The discrepancies and limits of applicability between Timoshenko and Euler-Bernoulli models are deeply explored and discussed, particularly for short and stout structures. It is shown that the Euler-Bernoulli model leads to an overprediction of the frequency shifts compared to Timoshenko beam theory, especially for higher modes. The nonlocal Timoshenko-based model is valuable because short and stout structures were found to be preferred for mass sensing applications, since they lead to a higher sensitivity. Other researchers can utilize these findings for the design, modeling, and analysis of nanoscale sensors and resonators.

3D-printed nanoscale resonators

3D-printed nanoscale resonators

Electro-superlubric springs for continuously tunable resonators and oscillators

Resonators and resonator-based oscillators are used in most electronics systems and they are classified as either mechanical or electrical, with fixed or difficult-to-tune resonant frequencies. Here, we propose an electro-superlubric spring, whose restoring force between two contacting sliding solid surfaces in the structural superlubric state is linearly dependent on the sliding displacement from the balanced position. We use theoretical analysis and finite element methods to study the restoring force and stability. The stiffness of this electro-superlubric spring is proportional to the square of the applied electric bias, facilitating continuous tuning from zero to several megahertz or gigahertz for the microscale or nanoscale resonators, respectively. Furthermore, we propose an electro-superlubric oscillator that is easily operated by varying a pair of harmonic voltages. The resonant frequency, resonant amplitude, quality factor, and maximum resonant speed can be continuously tuned via the applied voltage and bias. These results indicate significant potential in the applications of electro-superlubric resonators and oscillators.

Frequency shifts and thermoelastic damping in different types of Nano-/Micro-scale beams with sandiness and voids under three thermoelasticity theories

The present work focuses on the analytical study of thermoelastic damping (TED) and frequency shift (FS) in micro-scale beams and TED in nano-scale beams. The considered thermoelastic beam is homogeneous, isotropic, and consists of sandiness and voids (TESV). TED and FS of the beam are studied under four types of distinct boundary conditions, viz. clamped-clamped (CC), simply supported-simply supported (SS), Cantilever, and clamped-simply supported (CSS), considering different types of practical engineering applications. Newton–Raphson method is used to numerically evaluate the first two eigenvalues of each type of beam. The expressions of the characteristic roots are also provided. Based on the linear Euler–Bernoulli theory, the closed-form expressions for the beams’ transverse vibrations are derived. Analytical expressions for the deflection, change in temperature, and void volume fraction are also obtained, followed by TED and FS analysis for the considered boundaries. Three theories of thermoelasticity, viz. the Classical dynamical coupled (CL), Lord–Shulman (LS), and Green–Lindsay (GL) thermoelasticity theories are considered in this problem. The influences of thermal relaxation times owing to the three thermoelasticity theories, voids, sandiness, micro & nano dimensions of the beam, and the first two modes (M1 & M2) on the TED and FS are illustrated graphically. Critical thickness (CrTh) and critical length (CrLt) of all four beams under the influence of the existing parameters are meticulously analyzed. Some special cases of this problem are discussed, and the obtained outcomes are validated with well-established results found in the extant literature. In-depth analysis of the effects of thermoelastic coupling and other existing parameters on the natural frequency of micro-/nano-scale resonators, among other applications, is quintessential for designing and optimizing frequency-sensitive nanoelectromechanical systems (NEMS) and microelectromechanical systems (MEMS). Hence, the present analysis may have significant application and contribution in areas utilizing NEMS/MEMS devices.

Nonlinear dynamic control of GaAs nanomechanical resonators using lasers

The ability to control, manipulate, and read out nanomechanical resonators is of great significance for many applications. In this work, we start by constructing a nonlinear dynamic model that is deduced from the fundamental beam-photon–electron interaction and energy band theories, with the aim of describing a complicated cavity-free optomechanical coupling process. Based on the model established, we first reveal the manipulation of a resonator’s response, including softening and hardening effects due to laser injection. By driving the laser parametrically, we comprehensively investigate the control of the resonator’s dynamics, in particular, in the nonlinear regime. It is found that both the laser power and frequency can be used to directly manipulate the NEMS resonator’s dynamics, e.g., by amplitude amplification, periodicity changes, and periodic–chaotic state conversion. We then provide bifurcation diagrams, which evidence a deterministic evolution of dynamics. Finally, we perform a special study of the control of chaotic states of the nanomechanical resonator using laser parametric driving. The maximal Lyapunov exponents together with time series calculation show that the chaotic states can be controlled at a few specific frequency points of the injecting laser. This work not only provides guidance for using lasers to control nanoscale resonators, but also sheds light on the exploration of novel applications based on nonlinear NEMS resonators.

The effects of nonlinear damping on degenerate parametric amplification

This paper considers the dynamic response of a single degree of freedom system with nonlinear stiffness and nonlinear damping that is subjected to both resonant direct excitation and resonant parametric excitation, with a general phase between the two. This generalizes and expands on previous studies of nonlinear effects on parametric amplification, notably by including the effects of nonlinear damping, which is commonly observed in a large variety of systems, including micro- and nano-scale resonators. Using the method of averaging, a thorough parameter study is carried out that describes the effects of the amplitudes and relative phase of the two forms of excitation. The effects of nonlinear damping on the parametric gain are first derived. The transitions among various topological forms of the frequency response curves, which can include isolae, dual peaks, and loops, are determined, and bifurcation analyses in parameter spaces of interest are carried out. In general, these results provide a complete picture of the system response and allow one to select drive conditions of interest that avoid bistability while providing maximum amplitude gain, maximum phase sensitivity, or a flat resonant peak, in systems with nonlinear damping.

Thermoelastic modeling and comparative analysis of biomass sensors under rippling deformation and magnetic field

This study is intended for investigating the linear and nonlinear responses of carbon nanotube-based mass sensors in thermal and magnetic environment. For accurate modeling, the carbon nanotube rippling deformation effect is considered and various representations for the thermal expansion are examined and compared to each other. By utilizing Euler-Bernoulli beam theory assumptions and Eringen's nonlocal elasticity theory, the nonlinear reduced-order model is developed on the basis of the extended Hamilton's principle. The results show that the natural and resonant frequencies and frequency shifts of the system are strongly dependent on the magnetic field and thermal expansion representation. The method of multiple scale is used to determine the modulation equation including the von Karman and rippling nonlinearities. The results show a very good agreement between the perturbation solution and the numerical integration results for specific conditions of the forcing, temperature difference, and quality factor. A comparative study between the linear and nonlinear mass sensing approaches is performed to show their limits of applicability. It is demonstrated that the linear approach may result in erroneous detection of the deposited mass. The obtained results indicate that the longitudinal magnetic field enhances the dynamic stability of the carbon nanotube mechanical resonator in the pre-buckling oscillation regime, while the dynamic stability of the nanoscale resonator is decreased in the presence of the magnetic field for the post-buckling configuration. Also, the ripple-based nonlinearity is accompanied by an increase in the mass responsivity of the resonator. On the contrary, mass sensitivity of the carbon nanotube resonator is diminished by considering the von Kármán geometric nonlinearity. This study shows the importance of considering the nonlinear effects on the system's sensitivity from frequency and amplitude sensing techniques.

Coherent and Purcell-Enhanced Emission from Erbium Dopants in a Cryogenic High- Q Resonator

The stability and outstanding coherence of dopants and other atom-like defects in tailored host crystals make them a leading platform for the implementation of distributed quantum information processing and sensing in quantum networks. Albeit the required efficient light-matter coupling can be achieved via the integration into nanoscale resonators, in this approach the proximity of interfaces is detrimental to the coherence of even the least-sensitive emitters. Here, we establish an alternative: By integrating a 19 micrometer thin erbium-doped crystal into a cryogenic Fabry-Perot resonator with a quality factor of nine million, we can demonstrate 59(6)-fold enhancement of the emission rate, corresponding to a two-level Purcell factor of 530(50), while preserving lifetime-limited optical coherence up to 0.54(1) ms. With its emission at the minimal-loss wavelength of optical fibers and its outcoupling efficiency of 46(8) %, our system enables coherent and efficient nodes for long-distance quantum networks.

Generation of Pure OAM Beams with a Single State of Polarization by Antenna-Decorated Microdisk Resonators

We report waveguide-addressed plasmonic-photonic resonators that generate beams of controlled orbital angular momentum and spin angular momentum content upon driving through a waveguide. From phase-gradient metasurfaces, we borrow the idea of carefully combining multiple nanoscale resonators in a repeat unit, from which we build periodic rings that decorate microdisk resonators. We describe the general mode structure of microdisk cavities perturbed by antenna arrays on the basis of a quasinormal mode formalism and present a strategy to simultaneously control the orbital and spin angular momentum content of light outcoupled to the far field. We propose a realization that uses silicon nitride disks and aluminum nanorod antennas. We find excellent polarization and orbital angular momentum (OAM) purity, as benchmarked by polarization-resolved interferometric Fourier microscopy on single devices.

Broadband phononic frequency comb generation in a parametrically excited capacitive micromachined ultrasonic transducer

Optical frequency combs consisting of evenly spaced discrete frequencies have been used for a number of applications such as frequency metrology, range finding and molecular fingerprinting. Recently, the acoustic equivalent of these frequency combs, known as phononic frequency combs (PFCs), have been demonstrated in micro and nanoscale resonators. However, such demonstrations are restricted to PFC generation in high-Q mechanical resonators under carefully controlled operating conditions with limited practical applications. In this work, we demonstrate a novel method of generating PFCs with a parametrically driven capacitive micromachined ultrasonic transducer (CMUT) operating in a fluid medium. The proposed system consists of an electrically driven CMUT array that forms part of a resonant RLC circuit of frequency w0. By applying two drive tones of frequency w0 and w0+Δ, we are able to generate broadband acoustic frequency combs via a parametric four-wave mixing process. The intensity and number of combs generated is strongly dependent on the relative strength of the two driving tones whereas the comb spacing is determined by the frequency difference Δ between the drive signals. We also briefly discuss a potential application of PFCs in extended non-ambiguous range (NAR) distance metrology with interferometric resolution.

Numerical analysis of tunable nonlinear plasmonic router based on nanoscale ring resonators

In the advanced plasmonics integrated circuits (PICs) there has been outstanding, continuing interest in developing routers to harness light-matter interactions in nanoscale dimensions with wanted optical properties. In this regard, herein, we introduce an all-optical router based on nanometer ring resonator which surface plasmon resonance (SPR) and nonlinear materials are used simultaneously to enhance high performance range. By changing the radius of the ring resonator and the intensity of the light we achieved control of the parameters and the routing. The results of routing and shifting the central frequency with light intensity and radius of the ring resonator are studied. The performance of the router indicates that a ring is required for each ports, which changes the control parameters to change its central frequency, as well as we can be said the use of switches and filters as other design features. These routers have advantages such as nano scale size, low light intensity, fast response time, integratable and etc., which are highly used in all-optical circuits, image processing and today's modern technology. In our simulation, we consider transmission or reflection of light in each ports based on the finite difference time domain (FDTD).

Energy relaxation pathways between light-matter states revealed by coherent two-dimensional spectroscopy

Coupling matter excitations to electromagnetic modes inside nano-scale optical resonators leads to the formation of hybrid light-matter states, so-called polaritons, allowing the controlled manipulation of material properties. Here, we investigate the photo-induced dynamics of a prototypical strongly-coupled molecular exciton-microcavity system using broadband two-dimensional Fourier transform spectroscopy and unravel the mechanistic details of its ultrafast photo-induced dynamics. We find evidence for a direct energy relaxation pathway from the upper to the lower polariton state that initially bypasses the excitonic manifold of states, which is often assumed to act as an intermediate energy reservoir, under certain experimental conditions. This observation provides new insight into polariton photophysics and could potentially aid the development of applications that rely on controlling the energy relaxation mechanism, such as in solar energy harvesting, manipulating chemical reactivity, the creation of Bose–Einstein condensates and quantum computing.