Mechanical Frequency Shift Research Articles

Ultrasensitive optomechanical strain sensor

We demonstrate an ultrasensitive optomechanical strain sensor based on a SiN membrane and a Fabry-Perot cavity, enabling the measurements of both static and dynamic strain by monitoring reflected light fluctuations using a single-frequency laser. The SiN membrane offers high-quality-factor mechanical resonances that are sensitive to minute strain fluctuations. The two-beam Fabry-Perot cavity is constructed to interrogate the motion state of the SiN membrane. A static strain resolution of 4.00 nɛ is achieved by measuring mechanical resonance frequency shifts of the SiN membrane. The best dynamic resolution is 4.47 pɛHz-1/2, which is close to that of the sensor using high-finesse cavity and optical frequency comb, overcoming the dependence of ultrasensitive strain sensors on narrow-linewidth laser and high-finesse cavity with frequency locking equipment. This work opens up a promising avenue for a new generation of ultrasensitive strain sensors.

Detection of individual metallic nanoparticles via plasmon-mediated optomechanical coupling.

Characterization of individual nanoparticles is a challenge due to the diffraction limit. To overcome this constraint we investigate the transfer of their optical properties to a mechanical degree of freedom of a larger object. From finite-difference time-domain computations, we estimate the mechanical frequency shift caused by metallic nanoparticles traveling through a microfluidic channel. Due to plasmonic effects we find relative shifts on the order of 1% for a 1 mW incident optical power for particles with radius ranging from 25 to 150 nm. The extreme sensitivity of this detection scheme enables real-time and in situ observation of optical dynamics at nanoscale.

Optical spring effect enhanced by optical parametric amplifier

We experimentally demonstrate that the optical spring effect can be modified using an optical parametric amplifier in an opto-mechanical cavity. The theoretical analysis shows that both the gain and phase of the optical parametric amplifier can modify the frequency of a mechanical resonator in an opto-mechanical cavity. This modification could be used to tune the frequency of peak sensitivity of gravitational wave detectors. The experimental results show a factor of 1.2 ± 0.8 increase in mechanical resonator frequency shift induced by optical spring by tuning the optical parametric amplifier gain.

Fluid–structure model for disks vibrating at ultra-high frequency in a compressible viscous fluid

Radial mechanical modes of miniature disk-shaped resonators are promising candidates for probing the ultra-high-frequency rheological properties of liquids. However, the lack of an analytical fluid–structure model hinders the inference of liquid properties from the experimental measurement of such radial vibrations. Here, we develop analytical models for the case of a disk vibrating in a compressible viscous liquid. Closed-form expressions for the mechanical quality factor and resonant frequency shift upon immersion are obtained and compared with the results of numerical modeling for a few significant cases. At frequencies above 1 GHz, our model points out the significance of compressibility effects.

Quantum sensing proposal using a hybrid optomechanical system

The optomechanical system has developed a significant breakthrough in quantum science, especially since it can further improve the precision and sensitivity of the measurement in the quantum region. Here, we study a feasible optomechanical proposal in a hybrid quantum system, which can ensure a quantum sensor with further enhanced sensitivity. With the joint assistance of microwave modifying and optical parametric amplification, the effective line width of this supermode is further reduced around the critical point, and it can therefore result in a resolvable spectrum to display a much weaker mechanical frequency shift, which is perhaps induced by a tiny mass or charged particles in this system. We also hope there might be some useful applications for this attempt in the area of quantum measurement.

Optomechanically induced thermal bistability in an optical microresonator

Optomechanical systems have attracted considerable attention due to their wide applications in hybrid transduction systems, sensors, and quantum measurements. Classical optomechanical systems have various dynamical regimes that depend on the parameters, and the situation can be even more complicated when incorporated with other nonlinearities, such as the thermal nonlinearity that is common in optical resonators. Here, we experimentally and theoretically study the thermal bistability induced by optomechanical effect in a whispering-gallery mode microresonator. The mechanical oscillation modulates the intracavity photon number and modifies the thermal stability of states under a blue-detuned pump laser. Utilizing a silica microtip to suppress the mechanical motion, we identify the regions where the optical cavity temperature and detuning change due to the onset of oscillation and characterize the shifts in the detuning quantitatively. Hysteretic response in the mechanical frequency shifts (optical spring effect) to the pump wavelength is also observed to confirm the presence of bistability. The thermal dynamics discussed here is essentially different from the optomechanical heating and cooling of the effective temperature of the mechanical oscillator. This discovery shows that the thermal nonlinearity, which has been used for locking the pump frequency in the optomechanical systems, may also make some detuning states thermally unstable. Our study demonstrates an approach to characterize the detuning of the pump laser in an optomechanical resonator with thermal nonlinearity and also lays the groundwork for further understanding of dynamical effects induced by optomechanical effects.

Ultra-high resolution mass sensing based on an optomechanical nonlinearity

Ultra-high resolution mass sensing used to be realized by measuring the changed mechanical oscillation frequency by a small mass that should be detected. In this work we present a different approach of mass sensing without directly measuring such mechanical frequency change but relying on the modified light field due to a previously less explored nonlinear mechanism of optomechanical interaction. The concerned optomechanical setup used for the mass sensing is driven by a sufficiently strong two-tone field satisfying a condition that the difference of these two drive frequencies matches the frequency of the mechanical oscillation, so that a nonlinear effect will come into being and lock the mechanical motion under the radiation pressure into a series of fixed orbits. A small mass attached to the mechanical resonator slightly changes the mechanical frequency, thus violating the exact frequency match condition. Such small change can be detected by the amplitude modification on the higher order sidebands of the cavity field. Even given a moderate mechanical quality factor for the setup, the added mass can still be detected to the levels corresponding to a mechanical frequency shift from 5 to 7 order less than the mechanical damping rate. Because the output cavity field difference for very close values of mechanical frequency is not blurred by thermal noise, such mass sensing can be well performed at room temperature. The previous tough requirements for ultra-high resolution mass sensing can be significantly relaxed by the method.

Research on the reflection-type ELC-based optomechanical metamaterial.

In this paper, we propose a new kind of optomechanical metamaterial based on a planar ELC-type absorbing structure fabricated on the low-loss flexible substrate. The nonlinear coupling mechanism and nonlinear response phenomenon of the proposed optomechanical metamaterial driven by electromagnetic induced force are analyzed theoretically. The mechanical deformation/displacement and the mechanical resonance frequency shift of the metamaterial unit deposed on the flexible substrate are also numerically and experimentally demonstrated to reveal the coupling phenomenon of electromagnetic field and mechanical field. These results will help researchers to further understand the multi-physics interactions of optomechanical metamaterials and will promote the developments of new type of metasurface for high-efficiency dynamic electromagnetic wave controlling and formatting.

High harmonic optomechanical oscillations in the lithium niobate photonic crystal nanocavity

We explore the optomechanical coupling in an on-chip lithium niobate (LN) photonic crystal nanocavity. A mechanical frequency shift and nonlinear mechanical oscillations are observed with the intracavity power increasing. A 14th harmonic oscillation is generated at the intracavity power of 430 μW in the LN photonic crystal, which potentially can function as a mechanical frequency comb. The photonic crystal structure also shows the positive temperature coefficient of frequency, while the LN crystal has a negative intrinsic temperature coefficient. These characters of optomechanics in LN may play important roles in photon-phonon coupling or detector systems such as sensitive displacement and the mass and force detection.

Nano-Optomechanical Systems (NOMS) for Gas Chromatography Sensing

Nano-optomechanical systems (NOMS) achieve high-precision measurement of displacement which enables very high sensitivity through mechanical resonance-shift sensing. A recent breakthrough [1] has shown that NOMS devices can operate in high-damping environment without sacrificing their frequency stability and sensing resolution. This is because stability losses from lower quality factor (Q) are offset by stability gains from a larger intrinsic signal-to-noise ratio.We take advantage of this excellent stability to do atmospheric pressure resonant mechanical gas sensing with high sensitivity using NOMS [2]. In particular, we have set up a traditional gas chromatograph to output to a NOMS detector and shown parts-per-billion level detection [2]. By modifying the NOMS devices to make the silicon cantilevers porous, we have improved sensitivity by a further factor of 10 [3].The next challenge, and opportunity, in using NOMS for mass sensing, is to separate the gas loading signals that affect both the mechanical and optical resonances in high optomechanical-coupling devices [4]. This is because, at high coupling, changes in optical resonance produce changes in mechanical resonance and vice versa. This effect can be used to amplify the sensing signal obtained when measuring mechanical frequency changes. In fact, it scales particularly well with high-finesse optical cavities and could lead to a situation where evanescent field gas loading on the optical cavity is transduced as a mechanical frequency shift with orders of magnitude better mass sensitivity than could be realized from the NEMS alone or the optical cavity alone. As an example, our present mass loading sensitivity is around 50 kDa [5]; improving the cavity linewidth merely by a factor of 10 should shrink that mass sensitivity by a factor of 1000, bringing it down to 50 Da. This level of sensitivity would allow studying chemical adsorption and desorption of individual gas chromatography molecules on the sensor surface and could provide a simple path for obtaining orthogonal information in gas chromatography detectors.[1] S. K. Roy, V. T. K. Sauer, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, Improving mechanical sensor performance through larger damping. Science 360, eaar5220 (2018); doi: 10.1126/science.aar5220.[2] A. Venkatasubramanian, et al., Nano-optomechanical systems for gas chromatography. Nano Lett. 16, 6975-6981 (2016); doi: 10.1021/acs.nanolett.6b03066.[3] A. Venkatasubramanian, et al., Porous nanophotonic optomechanical beams for enhanced mass adsorption. ACS sensors 4, 1197-1202 (2018); doi: 10.1021/acssensors.8b01366.[4] M. P. Maksymowych, J. N. Westwood-Bachman, A. Venkatasubramanian, and W. K. Hiebert, Optomechanical spring enhanced mass sensing. Appl. Phys. Lett. 115, 101103 (2019); doi: 10.1063/1.5117159[5] Da = Dalton = 1 amu = 1 atomic mass unit ~ 1.66 x 10-27 kg.

Nanomechanical characterization of quantum interference in a topological insulator nanowire

Aharonov–Bohm conductance oscillations emerge as a result of gapless surface states in topological insulator nanowires. This quantum interference accompanies a change in the number of transverse one-dimensional modes in transport, and the density of states of such nanowires is also expected to show Aharonov–Bohm oscillations. Here, we demonstrate a novel characterization of topological phase in Bi2Se3 nanowire via nanomechanical resonance measurements. The nanowire is configured as an electromechanical resonator such that its mechanical vibration is associated with its quantum capacitance. In this way, the number of one-dimensional transverse modes is reflected in the resonant frequency, thereby revealing Aharonov–Bohm oscillations. Simultaneous measurements of DC conductance and mechanical resonant frequency shifts show the expected oscillations, and our model based on the gapless Dirac fermion with impurity scattering explains the observed quantum oscillations successfully. Our results suggest that the nanomechanical technique would be applicable to a variety of Dirac materials.

Optomechanical spring enhanced mass sensing

On-chip nano-optomechanical systems (NOMS) have demonstrated a zeptogram-level mass sensitivity and are promising candidates for low-cost implementations in areas such as metabolite quantitation and chemical analysis. High responsivity and sensitivity call for substantial optomechanical coupling and cavity finesse, resulting in detuning-dependent stiffness and mechanical damping via optomechanical back-action. Since mass loading (or temperature or force change) can alter both mechanical and cavity properties, mechanical frequency shifts induced by loading can encompass both effects. Precision sensing requires understanding and quantifying the source of the frequency tuning. Here, we show the deconvolution of direct loading and optomechanical stiffness change on the mechanical eigenfrequency as a function of detuning for a nano-optomechanical sensor in gaseous sensing experiments. Responses were generally dominated by shifts in optical stiffness and resulted in a mass loading signal amplification by as much as a factor of 2.5. This establishes an alternative possible route toward better mass sensitivity in NOMS while confirming the importance of incorporating optical stiffness effects for precision mass sensing.

Noise suppression of mechanical oscillations in a microcavity for ultrasensitive detection.

Optical microcavities have been widely applied as sensitive detectors due to ultrahigh quality factors and small mode volumes. Besides considering the optical mode as the sensing signal, the optomechanical oscillations induced by the optical spring effect also perform as an elegant sensing signal. However, the minimal size of a detectable analyte is limited by the relatively weak light-matter interaction compared to the experimental noises. To improve the detection limit, many methods have been developed to either enhance device sensitivities or suppress experimental noises. In this work, we present a way to lower the detection limit by suppressing experimental noises of the mechanical frequency by 3 orders of magnitude. Utilizing a fiber tip as a benchmark analyte attaching onto the cavity, the mechanical frequency shift reflects the changes of the optical mode detuning of the cavity, predicting an effective tool for ultrasensitive detection.

Quantum signatures in quadratic optomechanics

We analyze quantum effects occurring in optomechanical systems where the coupling between an optical mode and a mechanical mode is quadratic in displacement (membrane-in-the-middle geometry). We show that it is possible to observe quantum effects in these systems without achieving the single-photon strong coupling regime. We find that zero-point energy causes a mechanical frequency shift, and we propose an experimental way to measure it. Further, we show that it is possible to determine the phonon statistics from the cavity transmission, and propose a way to infer the resonator's temperature based on this feature. For completeness, we revisit the case of an isolated system and show that different types of mechanical quantum states can be created, depending on the initial cavity state. In this situation, mechanical motion undergoes collapse and revivals, and we compute the collapse and revival times, as well as the degree of squeezing.

Realization of a highly sensitive mass sensor in a quadratically coupled optomechanical system

We propose and analyze an efficient scheme for realizing high-sensitive mass sensor in a quadratically coupled optomechanical system via nonlinear second-order sideband process. This is achieved by exploiting a well-established optomechanical circumstance, where a degenerate parametric amplifier (DPA) is embedded into a membrane-in-the-middle cavity driven by a strong control field and a weak probe pulse. Beyond the conventional linearized approximation, we derive analytical expressions for the efficiency of a second-order sideband and the sensitivity of a mass sensor by using a perturbation method. In this scheme, an added mass deposited on the dielectric membrane can be measured by monitoring the efficiency variation of second-order sideband generation. Using experimentally achievable parameters, we identify the conditions under which nonlinear gain of DPA allows us to enhance the efficiency of a second-order sideband and improve the sensitivity of a mass sensor beyond what is achievable in the linearly coupled optomechanical system based on the detection of mechanical frequency shift. More importantly, we also find that the maximum efficiency of a second-order sideband and the optimum sensitivity of a mass sensor simultaneously serve as an efficient detection for the added mass of a membrane when a control field and nonlinear gain of DPA become strong. The present proposal offers a practical opportunity to design an all-optical nonlinear mass sensor at the picogram level.

Mass sensing by quantum criticality.

Mass sensing connects mass variation to a frequency shift of a mechanical oscillator, whose limitation is determined by its mechanical frequency resolution. Here we propose a method to enlarge a minute mechanical frequency shift, which is smaller than the linewidth of the mechanical oscillator, into a huge frequency shift of the normal mode. Explicitly, a frequency shift of about 20Hz of the mechanical oscillator would be magnified to be a 1MHz frequency shift in the normal mode, which increases it by 5 orders of magnitude. This enhancement relies on the sensitivity appearing near the quantum critical point of the electromechanical system. We show that a mechanical frequency shift of 1Hz could be resolved with a mechanical resonance frequency ωb=11×2π MHz. Namely, an ultrasensitive mechanical mass sensor of the resolution Δm/m∼2Δωb/ωb∼10-8 could be achieved. Our method has potential application in mass sensing and other techniques based on the frequency shift of a mechanical oscillator.

Trapping and Optomechanical Sensing of Particles with a Nanobeam Photonic Crystal Cavity

Particle trapping and sensing serve as important tools for non-invasive studies of individual molecule or cell in bio-photonics. For such applications, it is required that the optical power to trap and detect particles is as low as possible, since large optical power would have side effects on biological particles. In this work, we proposed to deploy a nanobeam photonic crystal cavity for particle trapping and opto-mechanical sensing. For particles captured at 300 K, the input optical power was predicted to be as low as 48.8 μW by calculating the optical force and potential of a polystyrene particle with a radius of 150 nm when the trapping cavity was set in an aqueous environment. Moreover, both the optical and mechanical frequency shifts for particles with different sizes were calculated, which can be detected and distinguished by the optomechanical coupling between the particle and the designed cavity. The relative variation of the mechanical frequency achieved approximately 400%, which indicated better particle sensing compared with the variation of the optical frequency (±0.06%). Therefore, our proposed cavity shows promising potential as functional components in future particle trapping and manipulating applications in lab-on-chip.

Nanomechanical Plasmon Spectroscopy of Single Gold Nanoparticles

We experimentally demonstrate the effect of the localized surface plasmon resonance (LSPR) of a single gold nanoparticle (AuNP) of 100 nm in diameter on the mechanical resonance frequency of a free-standing silicon nitride membrane by means of optomechanical transduction. We discover that a key effect to explain the coupling in these systems is the extinction cross section enhancement due to the excitation of the LSPR at selected wavelengths. In order to validate this coupling, we have developed a fixed wavelength interferometric readout system with an integrated tunable laser source, which allows us to perform the first experimental demonstration of nanomechanical spectroscopy of deposited AuNPs onto the membrane, discerning in between single particles and dimers by the mechanical frequency shift. We have also introduced three-axis mechanical scanners with nanometer-scale resolution in our experimental setup to selectively study single nanoparticles or small clusters. Whereas the single particles are polarization-insensitive, the gold dimers have a clearly defined polarization angle dependency as expected by theory. Finally, we found an unexpected long-distance (∼200 nm) coupling of the LSPR of separated AuNPs coming out from the guided light by the silicon nitride membrane.

Coherent optical propagation and ultrahigh resolution mass sensor based on photonic molecules optomechanics

We theoretically demonstrate the coherent optical propagation properties based on a photonic molecules optomechanics. With choosing a suitable detuning of the pump field from optomechanical cavity resonance, both the slow- and fast-light effect of the probe field appear in the system. The coupling strength of the two cavities play a key role, which affords a quantum channel and influences the width of the transparency window. Based on the photonic molecules optomechanical system, a high resolution mass sensor is also proposed. The mass of external nanoparticles deposited onto the cavity can be measured straightforward via tracking the mechanical resonance frequency shifts due to mass changes in the probe transmission spectrum. Compared with the single-cavity optomechanics mass sensors, the mass resolution is improved significantly due to the cavity–cavity coupling. The photonic molecules optomechanics provide a new platform for on-chip applications in quantum information processing and ultrahigh resolution sensor devices.

Coherent optical propagation properties and ultrahigh resolution mass sensing based on double whispering gallery modes cavity optomechanics

Whispering gallery mode (WGM) cavities due to their high quality factors, small mode volumes, and simple fabrications, have potential applications in photonic devices and ultrasensitive mass sensing. Cavity optomechanic systems based on WGM cavities have progressed enormously in recent years due to the fact that they reveal and explore fundamental quantum physics and pave the way for potential applications of optomechanical devices. However, WGM based cavity optomechanics still lies in a single optical mode coupled to a single mechanical mode. Here in this paper, in order to reveal more quantum phenomena and realize remarkable applications, we present a typical multimode cavity optomechanical system composed of two WGM cavities, of which one WGM cavity is an optomechanical cavity driven by a pump laser and a probe laser and the other cavity is an ordinary WGM cavity only driven with a pump laser. The two WGM cavities are coupled with each other via exchanging energy, and the coupling strength depends on the distance between the two cavities. With the standard method of quantum optics and the quantum Langevin equations, the coherent optical spectra are derived. The coherent optical propagation properties and the phenomenon of optomechanically induced transparency based slow-light effect are demonstrated theoretically via manipulating the coupling strength of the two cavities. The results based on the two-WGM cavity optomechanical system are also compared with those based on the single cavity optomechanical system, and the results indicate that the cavity-cavity coupling plays a key role in the system, which indicates a quantum channel, and influences the width of the transparency window. We further theoretically propose a mass sensor based on the double WGM cavity optomechanical system. To implement mass sensing, the first step is to determine the original frequency of the resonator. With adjusting the detuning parameters and the cavity-cavity coupling strength, a straightforward method to measure the resonance frequency of the WGM optomechanical resonator is proposed. The resonance frequency of the mechanical resonator can be determined from the probe transmission spectrum, and the coupling strength between the two cavities will enhance both the line width and the intensity, which will be beneficial to implementing mass sensing. The mass of external nanoparticles deposited onto the WGM optomechanical cavity can be measured conveniently by tracking the mechanical resonance frequency shifts due to the fact that mass changes in the probe transmission spectrum. Compared with those of single-cavity optomechanical mass sensors, the mass sensitivity and resolution are improved significantly due to the cavity-cavity coupling. This double WGM cavity optomechanical system provides a new platform for exploring the on-chip applications in optical storage and ultrahigh resolution sensing devices.