Real-time mapping of small forces with micrometer resolution is essential for studying soft and biological matter. However, existing techniques are slow, limited in spatial sampling or require non-planar substrates that can perturb cell behavior. Here we present silicon sensor arrays for rapid surface force mapping that operate using the elasto-optically induced wavelength shift in thin polymer-cladded optical ring resonators. Using a nano-indenter, we demonstrate that the sensor array reaches a force resolution down to 12 µN and shows a linear response. We present both a five-ring linear array and a 10×5 two-dimensional array at 15 µm pitch, and demonstrate the feasibility of localization and force mapping of a spherical nanoindentation tip. Combined measurement of forces by nano-indenter and the optical ring resonator sensor presents a methodology for calibrating this type of photonic force sensor. Moreover, good correspondence between measurements and finite element simulations provides evidence for the proposed operation mechanism. The shown combination of biocompatible claddings, strong opto-mechanical coupling, and foundry-ready photonics, presents a route towards scalable, real-time force mapping for soft-matter metrology, tactile interfaces, and in vitro mechanobiology.

We uncover a chain of nonlinear modal interactions in softly clamped nanostring resonators. The process involves the sequential coupling of five mechanical modes, during frequency sweeps, yielding a broad nonlinear response with nearly constant amplitude. We demonstrate that soft clamping enables this cascaded energy transfer and amplifies the effective geometric nonlinearity of the driven mode by an order of magnitude. Analytical and finite element-based reduced-order models capture the key features of the coupling cascade and clarify its underlying mechanism. The phenomenon is generic in nonlinear vibrational systems and can be tailored through soft-clamping design strategies.

Photonic ultrasound sensors promise unparalleled spatial and temporal resolution in ultrasound imaging due to their size-independent noise figure, high sensitivity, and broad bandwidth. Optical materials can further improve performance and stability, but achieving small size, high sensitivity, and wide bandwidth remains challenging. This work introduces amorphous silicon carbide (a-SiC) for ultrasound sensing, offering strong optical confinement, low propagation loss, and high stability for miniaturized microring sensors. We demonstrate a compact detection system with a 20-transducers linear array coupled to a single bus waveguide. The sensors achieve an optical finesse of 1320 and intrinsic sensitivity of 78 fm kPa⁻¹, leading to a noise-equivalent pressure below 55mPa/Hz, calibrated from 3.36 MHz to 30 MHz. High-resolution imaging of fine structures validates real-world applicability. a-SiC is also easily integrated on most substrates due to its low deposition temperature. Our results position a-SiC as a promising solution for optical ultrasound sensing, combining miniaturization, low-loss, and high-sensitivity.

Accurate localization and delivery of biomolecules are pivotal for building tools to understand biology. The interactions of biomolecules with atomically flat 2D surfaces offer a means to realize both the localization and delivery, yet experimental utilization of such interactions has remained elusive. By combining single-molecule detection methods with computational approaches, we comprehensively characterize the interactions of individual DNA molecules with hexagonal boron nitride (hBN) surfaces. Our experiments directly show that, upon binding to a hBN surface, a DNA molecule retains its ability to diffuse along the surface. Further, we show that the magnitude and direction of such diffusion can be controlled by the DNA length, the surface topography, and atomic defects. We observe that the diffusion speed of the biomolecules is significantly lower than indicated by molecular dynamic simulations. Through computational analysis, we present the model based on temporary trapping by atomic defects that accounts for those observations. By fabricating a narrow hBN ribbon structure, we achieve pseudo-1D confinement, demonstrating its potential for nanofluidic guiding of biomolecules.

Schlieren imaging is a widely applied optical technique for visualizing small refractive index changes in transparent media. An emerging application of schlieren is real-time monitoring and optimization of ultrasound pressure fields for acoustic levitation applications. However, the typically nonlinear relationship between the schlieren intensity and the pressure field complicates deducing the latter from the former. Here, we propose a method to remove this nonlinear relationship, thereby permitting a more quantitative analysis of the pressure variations in the levitation field. By exploiting the harmonic nature of the pressure field using phase-shifted stroboscopic schlieren images we extract the linear part of the schlieren intensity. This linear part is proportional to the instantaneous pressure gradient. The method is successfully employed experimentally and validated by comparing it to simulated acoustic levitation fields. Thereby, our work paves the way towards an improved quantitative analysis of periodic schlieren images that is easily implemented and is particularly suitable for the analysis of ultrasound pressure fields for acoustic levitation applications.

Nanomechanical resonances of two-dimensional (2D) materials are sensitive probes for condensedmatter physics, offering new insights into magnetic and electronic phase transitions. Despite extensive research, the influence of the spin dynamics near a phase transition on the nonlinear dynamics of 2D membranes has remained largely unexplored. Here, we investigate nonlinear magneto-mechanical coupling to antiferromagnetic order in suspended FePS3-based heterostructure membranes. By monitoring the motion of these membranes as a function of temperature, we observe characteristic features in both nonlinear stiffness and damping close to the Néel temperature TN. We account for these experimental observations with an analytical magnetostriction model in which these nonlinearities emerge from a coupling between mechanical and magnetic oscillations, demonstrating that magneto-elasticity can lead to nonlinear damping. Our findings thus provide insights into the thermodynamics and magneto-mechanical energy dissipation mechanisms in nanomechanical resonators due to the material’s phase change and magnetic order relaxation.

Crystal defects in hexagonal boron nitride (hBN) are emerging as versatile nanoscale optical probes with a wide application profile, spanning the fields of nanophotonics, biosensing, bioimaging, and quantum information processing. However, generating these crystal defects as reliable optical emitters remains challenging due to the need for deterministic defect placement and precise control of the emission area. Here, we demonstrate an approach that integrates microspheres with hBN crystal lattices to enhance both hBN defect generation and optical signal readout. This technique harnesses microspheres to amplify light–matter interactions at the nanoscale through two mechanisms: focused femtosecond (fs) laser irradiation into a photonic nanojet (PNJ) for highly localized defect generation and enhanced light collection via the whispering gallery mode (WGM) effect. Our microsphere-assisted defect generation method reduces the emission area by a factor of 5 and increases the fluorescence collection efficiency by approximately 10 times compared to microsphere-free samples. These advancements in defect generation precision and signal collection efficiency open new possibilities for optical emitter manipulation in hBN, with potential applications in quantum technologies and nanoscale sensing.

A quantitative understanding of the microscopic mechanisms responsible for damping in van der Waals nanomechanical resonators remains elusive. In this work, we investigate van der Waals magnets, where the thermal expansion coefficient exhibits an anomaly at the magnetic phase transition due to magnetoelastic coupling. Thermal expansion mediates the coupling between mechanical strain and heat flow and determines the strength of thermoelastic damping (TED). Consequently, variations in the thermal expansion coefficient are reflected directly in TED, motivating our focus on this mechanism. We extend existing TED models to incorporate anisotropic thermal conduction, a critical property of van der Waals materials. By combining the thermodynamic properties of the resonator material with the anisotropic TED model, we examine dissipation as a function of temperature. Our findings reveal a pronounced impact of the phase transition on dissipation, along with transitions between distinct dissipation regimes controlled by geometry and the relative contributions of in-plane and out-of-plane thermal conductivity. These regimes are characterized by the resonant interplay between strain and in-plane or through-plane heat propagation. To validate our theory, we compare it to experimental data of the temperature-dependent mechanical resonances of FePS3 resonators.

Current temperature sensors require regular recalibration to maintain reliable temperature measurement. Photonic/quantum-based approaches have the potential to radically change the practice of thermometry through provision of in situ traceability, potentially through practical primary thermometry, without the need for sensor recalibration. This article gives an overview of the European Partnership in Metrology (EPM) project: Photonic and quantum sensors for practical integrated primary thermometry (PhoQuS-T), which aims to develop sensors based on photonic ring resonators and optomechanical resonators for robust, small-scale, integrated, and wide-range temperature measurement. The different phases of the project will be presented. The development of the integrated optical practical primary thermometer operating from 4 K to 500 K will be reached by a combination of different sensing techniques: with the optomechanical sensor, quantum thermometry below 10 K will provide a quantum reference for the optical noise thermometry (operating in the range 4 K to 300 K), whilst using the high-resolution photonic (ring resonator) sensor the temperature range to be extended from 80 K to 500 K. The important issues of robust fibre-to-chip coupling will be addressed, and application case studies of the developed sensors in ion-trap monitoring and quantum-based pressure standards will be discussed.

Miniaturized optomechanical devices are well-suited for applications in the automotive, aerospace, and biomedical sectors due to their compact size and lightweight design, which make them ideal for measuring small forces [1]. The significant refractive index contrast between the silicon waveguide core and the silicon dioxide cladding in silicon-on-insulator (SOI) structures enables submicron core dimensions. This design supports single-mode propagation at a wavelength of 1.55 µm, with strong optical confinement that allows for sharp bends with radii as small as a few micrometers [2]. Micro-optical-electromechanical systems (MOEMS) offer several advantages over traditional micro-electromechanical systems (MEMS), including higher optical sensitivity, simplicity, cost-effectiveness, and suitability for use in electromagnetically active environments and ultra-high vacuum conditions [3].

The unique properties of two-dimensional (2D) materials bring great promise to improve sensor performance and realise novel sensing principles. However, to enable their high-volume production, wafer-scale processes that allow integration with electronic readout circuits need to be developed. In this perspective, we review recent progress in on-chip 2D material sensors, and compare their performance to the state-of-the-art, with a focus on results achieved in the Graphene Flagship programme. We discuss transfer-based and transfer-free production flows and routes for complementary metal-oxide-semiconductor integration and prototype development. Finally, we give an outlook on the future of 2D material sensors, and sketch a roadmap towards realising their industrial and societal impact.

Ultrasound is widely used in medical imaging, and emerging photo-acoustic imaging is crucial for disease diagnosis. Currently, high-end photo-acoustic imaging systems rely on piezo-electric materials for detecting ultrasound waves, which come with sensitivity, noise, and bandwidth limitations. Advanced applications demand a large matrix of broadband, high-resolution, and scalable ultrasound sensors. Silicon photonic circuits have been introduced to meet these requirements by detecting ultrasound-induced deformation and stress in silicon waveguides. Although higher sensitivities could facilitate the exploration of new applications, the high stiffness of the waveguide materials constrains the intrinsic sensitivity of the silicon photonic circuits to ultrasound signals. Here, we explore the impact of the mechanical properties of a polymer cladding on the sensitivity of silicon photonic ultrasound sensors. Our model and experiments reveal that optimizing the polymer cladding's stiffness enhances the resonance wavelength sensitivity. Experimentally, we show a fourfold increase in the sensitivity compared to the sensors without a cladding polymer and, a twofold sensitivity increase compared to the sensors with a cladding polymer of saturated cross-linking density. Interestingly, comparing experiments with the optomechanical model suggests that the change in Young's Modulus alone cannot explain the sensitivity increase. In conclusion, polymer-coated silicon photonic ultrasound sensors exhibit potential for advanced photo-acoustic imaging applications. It offers the prospect of increasing the ultrasound detection sensitivity of silicon photonic ultrasound sensors while using CMOS-compatible processes. This paves the way to integrate the polymer-coated silicon photonic ultrasound sensors with electronics to utilize the sensors in advanced medical imaging applications.

High-frequency acoustic devices based on two-dimensional (2D) materials are emerging platforms to design and manipulate the spatiotemporal response of acoustic waves for next-generation sensing and contactless actuation applications. Conventional actuation methods, however, cannot be applied to all 2D materials, are frequency-limited or influenced by substrate interactions. Therefore, a universal, high-frequency, on-chip actuation technique is needed. Here, we demonstrate that surface acoustic waves (SAWs) can efficiently actuate suspended 2D materials by exciting suspended graphene membranes with high-frequency (375 MHz) Rayleigh waves and mapping the resulting vibration field with atomic force acoustic microscopy (AFAM), enabling direct visualization of wave propagation without substrate interference. Acoustic waves traveling from supported to suspended graphene experience a reduction in acoustic wavelength from 10 μm to ∼2 μm due to the decrease in effective bending rigidity, leading to a decrease in wave velocity on suspended graphene. By varying the excitation frequency through laser photothermal actuation (0-100 MHz) and SAW excitation (375 MHz), we observed a phase velocity change from ∼160 m/s to ∼700 m/s. This behavior is consistent with the nonlinear dispersion of acoustic waves, as predicted by plate theory, in suspended graphene membranes. The geometry and bending rigidity of the membrane thus play key roles in modulating the acoustic wave pattern and wavelength. This combined SAW actuation and AFAM visualization scheme advances the understanding of acoustic transport at the nanoscale limit and provides a route toward the manipulation of localized wavefields for on-chip patterning and transport over 2D materials surfaces.

Nonlinear dynamic simulations of mechanical resonators have been facilitated by the advent of computational techniques that generate nonlinear reduced order models (ROMs) using the finite element (FE) method. However, designing devices with specific nonlinear characteristics remains inefficient since it requires manual adjustment of the design parameters and can result in suboptimal designs. Here, we integrate an FE-based nonlinear ROM technique with a derivative-free optimization algorithm to enable the design of nonlinear mechanical resonators. The resulting methodology is used to optimize the support design of high-stress nanomechanical Si ₃N ₄ string resonators, in the presence of conflicting objectives such as simultaneous enhancement of Q-factor and nonlinear Duffing constant. To that end, we generate Pareto frontiers that highlight the trade-offs between optimization objectives and validate the results both numerically and experimentally. To further demonstrate the capability of multi-objective optimization for practical design challenges, we simultaneously optimize the design of nanoresonators for three key figure-of-merits in resonant sensing: power consumption, sensitivity and response time. The presented methodology can facilitate and accelerate designing (nano) mechanical resonators with optimized performance for a wide variety of applications. (Figure presented.)

Mass sensing using MEMS is crucial for detecting minute changes in mass with high sensitivity, enabling applications in environmental monitoring, medical diagnostics, and chemical detection. However, fluid damping in these environments is relatively high and can lead to reduction of the quality factor and sensitivity of these sensors. In this paper, we present a rotating ring resonator for mass sensing applications and investigate its nonlinear dynamics and bifurcation. The ring is supported by four slender beams and subjected to rotational base excitation. The shift in the nonlinear bifurcation point on the frequency response curve is used for mass sensing, which is significant because the device exhibits multiple nonlinear bifurcation points. The structure is designed and modelled to vibrate in a rotational in-plane mode, to provide lower damping and higher quality factor compared to cantilever-based mass sensors that operate in a translational out-of-plane mode. Moreover, the structure exhibits nonlinear resonance zones within the super harmonic regime, enabling mass detection at a particular fraction of the primary resonance zone. At lower excitation amplitudes, the linear response dominates, and the device also allows mass detection in the linear regime via resonance frequency shifts.

Suspended drums made of 2D materials hold potential for sensing applications. However, the industrialization of these applications is hindered by significant device-to-device variations presumably caused by non-uniform stress distributions induced by the fabrication process. Here, we introduce a methodology to determine the stress distribution from their mechanical resonance frequencies and corresponding mode shapes as measured by a laser Doppler vibrometer (LDV). To avoid limitations posed by the optical resolution of the LDV, we leverage a manufacturing process to create ultra-large graphene drums with diameters of up to 1000 μm. We solve the inverse problem of a Föppl–von Kármán plate model by an iterative procedure to obtain the stress distribution within the drums from the experimental data. Our results show that the generally used uniform pre-tension assumption overestimates the pre-stress value, exceeding the averaged stress obtained by more than 47%. Moreover, it is found that the reconstructed stress distributions are bi-axial, which likely originates from the transfer process. The introduced methodology allows one to estimate the tension distribution in drum resonators from their mechanical response and thereby paves the way for linking the used fabrication processes to the resulting device performance.

Since the performance of micro-electro-mechanical system (MEMS)-based microphones is approaching fundamental physical, design, and material limits, it has become challenging to improve them. Several works have demonstrated graphene’s suitability as a microphone diaphragm. The potential for achieving smaller, more sensitive, and scalable on-chip MEMS microphones is yet to be determined. To address large graphene sizes, graphene-polymer heterostructures have been proposed, but they compromise performance due to added polymer mass and stiffness. This work demonstrates the first wafer-scale integrated MEMS condenser microphones with diameters of 2R = 220–320 μm, thickness of 7 nm multi-layer graphene, that is suspended over a back-plate with a residual gap of 5 μm. The microphones are manufactured with MEMS compatible wafer-scale technologies without any transfer steps or polymer layers that are more prone to contaminate and wrinkle the graphene. Different designs, all electrically integrated are fabricated and characterized allowing us to study the effects of the introduction of a back-plate for capacitive read-out. The devices show high mechanical compliances C_m = 0.081–1.07 μmPa⁻¹ (10–100 × higher than the silicon reported in the state-of-the-art diaphragms) and pull-in voltages in the range of 2–9.5 V. In addition, to validate the proof of concept, we have electrically characterized the graphene microphone when subjected to sound actuation. An estimated sensitivity of S_1kHz = 24.3–321 mV Pa⁻¹ for a V_bias = 1.5 V was determined, which is 1.9–25.5 × higher than of state-of-the-art microphone devices while having a ~9 × smaller area. (Figure presented.).

Motion is all around us, the universe is full of moving matter and this motion is surprisingly predictable. The field of science and engineering that studies time-dependent motion in the presence of forces is called Dynamics. In this book we will introduce the core concepts in dynamics and provide a comprehensive toolset to predict and analyse planar 2D motion of point masses and rigid bodies. The material includes kinematic analysis, Newton’s laws, Euler’s laws, the equations of motion, work, energy, impulse and momentum. Vector-based methods are discussed for systematically solving essentially any problem in 2D dynamics. The book provides a bachelor level introduction for any science and engineering student that can serve as a basis for more advanced courses in dynamics.

Most microphones detect sound-pressure-induced motion of a membrane. In contrast, we introduce a microphone that operates by monitoring sound-pressure-induced modulation of the air compressibility. By driving a graphene membrane at resonance, the gas, that is trapped in a squeeze-film beneath it, is compressed at high frequency. Since the gas-film stiffness depends on the air pressure, the resonance frequency of the graphene is modulated by variations in sound pressure. We demonstrate that this squeeze-film microphone principle can be used to detect sound and music by tracking the membrane’s resonance frequency using a phase-locked loop. The squeeze-film microphone potentially offers advantages like increased dynamic range, lower susceptibility to pressure- induced failure and vibration-induced noise over conventional devices. Moreover, microphones might become much smaller, as demonstrated in this work with one that operates using a circular graphene membrane with an area that is more than 1000 times smaller than that of MEMS microphones.

As a consequence of their high strength, small thickness, and high flexibility, ultrathin graphene membranes show great potential for pressure and sound sensing applications. This study investigates the performance of multi-layer graphene membranes for microphone applications in the presence of air-loading. Since microphones need a flatband response over the full audible bandwidth, they require a sufficiently high mechanical resonance frequency. Reducing membrane thickness facilitates meeting this bandwidth requirement, and therefore, also allows increasing compliance and sensitivity of the membranes. However, at atmospheric pressure, air-loading effects can increase the effective mass, and thus, reduce the bandwidth of graphene and other 2D material-based microphones. To assess the severity of this performance-limiting effect, we characterize the acoustic response of multi-layer graphene membranes with a thickness of 8 nm in the pressure range from 30 to 1000 mbar, in air and helium environments. A bandwidth reduction by a factor ∼ 2.8 × for membranes with a diameter of 500 μm is observed. These measurements show that air-loading effects, which are usually negligible in conventional microphones, can lead to a substantial bandwidth reduction in ultrathin graphene microphones. With analytical and finite element models, we further analyze the performance limits of graphene microphones in the presence of air-loading effects.