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.

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.

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.

In atomically thin membranes, strain couples strongly to electrons, phonons, and photons. Although strain originating from uniform or global deformation has been widely studied, the impact of spatially localized mechanical perturbations on strain distribution remains less explored. Here, we investigate how localized tungsten carbide deposition via focused electron-beam-induced deposition (FEBID) modifies the strain landscape in suspended monolayer graphene membranes. Using spatially resolved mechanical resonance mode shape mapping and Raman spectroscopy, supported by finite element simulations, we find that the central deposit acts as a mechanically coupled local perturbation that redistributes the pre-existing strain into a more radially symmetric configuration with reduced angular anisotropy around the deposit. These findings demonstrate that FEBID-based local deposition can serve as a lithography-free approach for controlled strain modulation in suspended graphene, offering a practical platform for studying strain-coupled phenomena and designing strain-controlled nanoelectromechanical and optoelectronic systems.

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.

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.

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.

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].

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.)

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.

Correction to: Microsystems & Nanoengineering https://doi.org/10.1038/s41378-024-00656-x published online 21 February 2024 After publication of this article¹, it was brought to our attention that two pressure values were not correctly copied from the submitted original work to the published version. Correction 1 (from PDF, Page 4 of 9): “These membranes show resonance frequencies above the audible range (f₀₁ > 20 kHz) at 1 × 10³ mbar by piezo-shaker actuation”. The described phrase needs to be changed reporting the right pressure value of 1 × 10⁻³ mbar. The new phrase will be: “These membranes show resonance frequencies above the audible range (f₀₁ > 20 kHz) at 1 × 10⁻³ mbar by piezo-shaker actuation”. Correction 2 (from PDF, Page 4 of 9): “Energy losses and dampening are minimized due to the low pressure of 1 × 10³ mbar”. Again, the described phrase needs to be changed reporting the right pressure value of 1 × 10⁻³ mbar. The new phrase will be: “Energy losses and dampening are minimized due to the low pressure of 1 × 10⁻³ mbar”.

Acoustic levitation is an attractive and versatile technique that offers several advantages in terms of particle size, range, reconfigurability, and ease of use with respect to alternative levitating techniques. In this paper, we study the use of active damping to improve the response time and positioning precision of an acoustic levitator operating in air. We use a laser Doppler vibrometer to measure the velocity of a levitated particle. Using this information, a control algorithm is designed and implemented to provide active damping. By system identification and modeling, we demonstrate that the active damper mechanism is well-predictable by models and can be electronically reconfigured and controlled.