Sensitivity of optical mass sensor enhanced by optomechanical coupling

We present a novel approach using an ultrasensitive mass sensor to evaluate adsorbed mass in cavity optomechanics. The group delay of a transmitted signal field pulse can be adjusted by varying the optomechanical cooperativity, which depends on the effective mass of a mechanical resonator. We derive the linear relationship between the group delay and the adsorbed mass, and define the mass sensitivity of the proposed mass sensor. The results show that the mass sensitivity is determined by the temporal resolution of the evolution of the transmitted signal field pulse. Finally, we demonstrate a mass sensor at the attogram scale for measuring gold nanoparticles.

In general, PZT thick films fabricated through screen printing show porosity ranging from 10% to 40%. Unfortunately, these high porosities of thick films greatly affect the electromechanical characteristics of PZT thick film cantilevers. In this paper, we report a systematic analysis on the effect of thick film porosity on the electromechanical characteristics of the PZT thick film cantilevers in order to make the PZT thick film cantilever a highly controllable micro mass sensor or micro self actuator. The theoretical calculations of mass sensitivity and actuating force of the optimal PZT thick film cantilevers are presented with respect to the material properties and geometry of PZT thick films, which are based on experimentally verified material properties and geometrical parameters. The 400 × 300 cantilever with 20% porosity of active material was evaluated to be reliable as an optimal mass sensor and self actuator. The thick film cantilever indicates both high mass sensitivity (~48 pg/Hz), the same as sensitive thin film cantilever sensors, and high actuating force (~1.7 N), similar to strong bulk cantilevers. From the results of the modeling, it was found that the harmonic oscillation response according to material properties including the porosity, and geometry of the fabricated thick film cantilever, is quite controllable and predictable, thus enhancing the actuating force and mass sensitivity. Also, it was confirmed that controlling the porosity of PZT thick films is more efficient than controlling the cantilever geometry to increase the cantilever resonating force. However, optimizing the geometric constituents is more effective than controlling the densification of PZT thick films to increase the mass sensitivity of the cantilevers.

A multipartite quantum system is entangled when its state cannot be factorized into a product of states or a mixture of such products. Quantum information schemes that exploit this purely quantum mechanical feature have been devised initially for systems with two discrete quantum levels (i.e., qubits), and afterward, extended to continuous-variable (CV) systems characterized by observables with continuous spectra, such as the position and momentum of a particle, or the quadratures of an electromagnetic field. Optomechanical systems, such as a driven optical cavity with vibrating end-mirrors or a classical coherent field scattering sidebands off a freely suspended mirror, hold a promise of being candidates for CV quantum information processing applications. As in most other proposals, light is the information carrier; the difference lies in the choice of a micromirror as a quantum storage device. Desired quantum states can be encoded in acoustic modes. The optomechanical coupling, owing to which quantum state transfer between radiation and mirror is possible, is realized via the radiation pressure effect, which consists in momentum transfer between field and mirror during the scattering process. The use of the vibrational modes of a micromirror as a quantum state encoder system is somehow unexpected because this is a macroscopic ensemble of atoms expected to behave rather classically. However, there are proposals that show that, in principle, the vibrational occupation number of even such a large collection of atoms in a solid can be reduced close to zero, which signifies a clear transition from the classical to the quantum regime. Remarkable progress has been made to experimentally cool the resonator by a few orders of magnitude to quite low occupation numbers. However, in order to approach the quantum limit, one needs to integrate small, light, and flexible micromechanical elements into high-finesse cavities (which are typically much more rigid and massive), which is technically challenging. Furthermore, the mechanical quality factor has to be quite high, but present microfabrication techniques yield a mechanical quality factor scaling down for smaller and smaller microresonators. This chapter starts with developing a general framework for treating the dynamics of a driven optical cavity with a vibrating end-mirror system in which two cooling techniques have been recently demonstrated: (i) cold-damping quantum feedback, where the oscillator position is measured through a phase-sensitive detection of the cavity output and the resulting photocurrent is used for a real-time correction of the dynamics, and (ii) backaction or self-cooling, in which the off-resonant operation of the cavity results in a retarded back action on the mechanical system, and hence, in a “self”-modification of its dynamics. The two situations are illustrated in Fig. 24.1. Analytical results for the final phonon number are obtained for both schemes and their applicability within today's state-of-the-art laboratory setups is analyzed.

A photonic and phononic crystal (phoxonic crystal PxC) is a periodically patterned material that can at the same time localize optical and mechanical modes. Here we theoretically model one-dimensional PxC in diamond and find high quality mechanical resonances with very high frequencies > 10 GHz and optical properties comparable to those of PxC in other materials. The simultaneous confinement of photons and phonons leads to an optomechanical interaction that we calculate in a perturbation approach. The optomechanical coupling strengths reach values in the MHz range. We identify design rules to simultaneously achieve high optical and mechanical quality factors along with strong optomechanical coupling.

Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic radiation. The radiation-pressure force can be used for cooling atomic motion. Laser cooling was experimentally realized in the 1980s and has since become an extraordinarily important technique. Many applications have been enabled by laser cooling, including optical atomic clocks, precision measurements of the gravitational field, and systematic studies of quantum many-body physics in trapped clouds of atoms. Since the advent of both optical microcavities and advanced nanofabrication techniques, the optomechanical interaction could be studied in mesoscopic mechannical resonator. In 2005, Kippenberg et al. discovered that optical microtoroid resonators with their high optical finesse at the same time contain mechanical modes and thus are able to display optomechanical effects, in particular, radiation-pressure-induced self-oscillations. During the last decade, cavity optomechanics has advanced rapidly and optomechanical coupling has been reported in numerous novel systems. Furthermore, a number of remarkable optomechanical phenomena have been demonstrated in experiments, such as amplifying and cooling of phonon modes, optomechanically induced transparency, strong coupling between mechanical oscillator and optical cavity, optical wavelength conversion, conversion between optical light and microwave, optomechanical light storage and optomechanically induced non-reciprocity. In future, both in the field of precision sensing, classical and quantum information processing, cavity optomechanics will play an increasingly important role.

Graphene sheet (GS) is a two-dimensional (2D) material with extremely favorable mass sensor properties. In this paper, a linear elastic 2D plate model is applied to study the potential of a nanoscale mass sensor on individual GS. The simulated natural frequency was compared with the results obtained from the Rayleigh's energy method. The effects of the attached mass, aspect ratio, and the layer number of the GS on the natural frequency are investigated in detail. Initial tension due to the fabrication process and temperature is also studied, which has effects on the frequency and frequency shift. The results show that the sensitivity of the mass sensor with smaller dimension is higher. The resolution of mass sensor can reach 1 zg and the sensitivity of seven-layer graphene mass sensor is the highest. Lower temperature has higher sensitivity and initial tension due to the fabrication process has little influence on the mass sensor. The conclusion is useful for the design of mass sensor with high resolution.

The low mass and high quality factors that nanomechanical resonators exhibit lead to exceptional sensitivity in the frequency domain. This is especially appealing for the design of ultrasensitive force and mass sensors. The sensitivity of a nanomechanical mass and force sensor depends on its mass and quality factor; a low resonator mass and a higher quality factor reduce both the minimum resolvable mass and force. Graphene, a single atomic layer thick membrane is an ideal candidate for nanoelectromechanical resonators due to its extremely low mass and high stiffness. Here, we show that by employing the intrinsic piezoresistivity of graphene to transduce its motion in nanoelectromechanical systems, we approach a force resolution of 16.3 ± 0.8 aN/Hz(1/2) and a minimum detectable mass of 1.41 ± 0.02 zeptograms (10(-21) g) at ambient temperature. Quality factors of the driven response of the order of 10(3) at pressures ∼10(-6) Torr on several devices are also observed. Moreover, we demonstrate this at ambient temperature on chemical-vapor-deposition-grown graphene to allow for scale-up, thus demonstrating its potential for applications requiring exquisite force and mass resolution such as mass spectroscopy and magnetic resonance force microscopy.

This work demonstrates mass measurement of individual submicron air-borne particles using resonant micromechanical nano-balances. Thermally actuated high-frequency single crystalline silicon resonators fabricated using a single mask process have been used as mass sensors. Mass sensitivity of the resonators have been characterized using artificially generated airborne particles of known size and composition. Mass sensitivities as high as 1.6 kHz/pg have been demonstrated for devices with resonant frequencies in the tens of MHz range. The measured mass sensitivities are in good agreement with the calculated values based on the resonator physical dimensions. Due to the high mass sensitivities, the shift in the resonator frequencies caused by individual particles as small as ~200 nm in diameter is distinguishable. Counting and individual mass measurement of single arbitrary particles in air samples from a cleanroom have also been demonstrated. The results in this work present the possibility of implementation of low-cost and small-size instruments for airborne particle mass and size distribution analysis in highly controlled environments (e.g., for cleanroom classification) or for environmental applications.

We have realized a distributed mass-sensor using micro-cantilevers. The micro-cantilevers were actuated using piezoelectric ZnO thin films. The micro-cantilevers layer stack consists of Si/SiO2/Pt/ZnO/Pt layers for self-actuation of devices. The mass sensing performance was evaluated by laser Doppler vibrometer. Experimentally, micro-cantilever length was varied in the 100–300- $\mu \text{m}$ range, and it is established that mass-sensitivity increases with reducing length of cantilevers. New relationship has been derived between mass sensitivity (S) and cantilever length (l), which follows the modified power law as S $\propto 1/l^{2.8}$ . Remarkable mass-sensitivity (S = 0.3138 Hz/pg) was obtained for a smallest size cantilever, which has dimensions $100\,\,\times \,\,50\,\,\times \,\,8.3 \mu \text{m}^{3}$ . Optimal mass sensor shows high-quality factor (Q ~ 234) at room temperature and one atmospheric pressure. Such ZnO-based mass sensors are biocompatible, safe, and promising candidate for chemical and bio-sensing applications. [2018-0243]

We study the cavity mode frequencies of a Fabry–Pérot cavity containing two vibrating dielectric membranes. We derive the equations for the mode resonances and provide approximate analytical solutions for them as a function of the membrane positions, which act as an excellent approximation when the relative and center-of-mass position of the two membranes are much smaller than the cavity length. With these analytical solutions, one finds that extremely large optomechanical coupling of the membrane relative motion can be achieved in the limit of highly reflective membranes when the two membranes are placed very close to a resonance of the inner cavity formed by them. We also study the cavity finesse of the system and verify that, under the conditions of large coupling, it is not appreciably affected by the presence of the two membranes. The achievable large values of the ratio between the optomechanical coupling and the cavity decay rate, , make this two-membrane system the simplest promising platform for implementing cavity optomechanics in the strong coupling regime.

In this study, in order to develop the composition ceramics for low loss multilayer ceramic actuator for ultrasonic nozzle and ultrasonic vibrator applications, Pb(Mn1/3Nb2/3)O3Pb(Ni1/3Nb2/3)O3Pb(Zr1/2Ti1/2)O3 (abbreviated as PMN-PNN-PZT) ceramics were fabricated using Li2CO3, Na2CO3 and ZnO as sintering aids. And then, their piezoelectric and dielectric properties according to the amount of ZnO addition were investigated. The addition of ZnO improved density, dielectric constant, electromechanical coupling factor, mechanical quality factor and piezoelectric d constant of PMN-PNN-PZT ceramics due to the increase of sinterability and accepter doping effect. Electromechanical coupling factor(kp) and mechanical quality factor(Qm) of PMN-PNN-PZT ceramics increased with ZnO amount up to 0.4 wt% and then decreased. At the sintering temperature of 900degC and 0.4 wt% ZnO addition, density, dielectric constant, electromechanical coupling factor(kp), mechanical quality factor(Qm) and piezoelectric d33 constant showed the optimum value of 7.876 g/cm3, 1299, 0.612, 1151 and 369 pC/N, respectively, for low loss multilayer ceramic actuator application.

Enhanced sensitivity of bimetallic optical fiber SPR sensor based on MoS2 nanosheets

The effect of shape on the mechanical quality factor, Q, of a micromachined cantilever resonator has been investigated with a focus on the energy loss in the resonator, which is due to the internal friction of moving parts. Theoretical modeling and numerical simulations based on FEM were performed on a test structure. The relative value of Q was calculated by summing the squares of the stress on each constituent element of the beam when the curvature of either the support base or the resonating beam was varied. Test structures were fabricated and the mechanical quality factor was measured. The theoretical and experimental results agree well, which shows that stress distribution is an important factor determining Q. It was found that the curvature of the supporting base has little effect on Q, but that the curvature of the beam has a considerable effect.

Optical devices based on new sensing principle are widely used in biochemical and medical area. Nowadays, mass sensing based on monitoring the frequency shifts induced by added mass in oscillators is a well-known and widely used technique. It is interesting to note that for nanoscience and nanotechnology applications there is a strong demand for very sensitive mass sensors, being the target a sensor for single molecule detection. The desired mass resolution for very few or even single molecule detection, has to be below the femtogram range. Considering the strong interaction between high co-localized optical mode and mechanical mode in optomechanical crystal (OMC) cavities, we investigate OMC splitnanobeam cavities in silicon operating near at the 1550nm to achieve high optomechanical coupling rate and ultra-small motion mass. Theoretical investigations of the optical and mechanical characteristic for the proposed cavity are carried out. By adjusting the structural parameters, the cavity’s effective motion mass below 10fg and mechanical frequency exceed 10GHz. The transmission spectrum of the cavity is sensitive to the sample which located on the center of the cavity. We conducted the fabrication and the characterization of this cavity sensor on the silicon-on-insulator (SOI) chip. By using vertical coupling between the tapered fiber and the SOI chip, we measured the transmission spectrum of the cavity, and verify this cavity is promising for ultimate precision mass sensing and detection.

Fabrication and characterization of low loss MOMS resonators for cavity opto-mechanics