In the early years of numerical simulation methods, Fermi, Pasta, Ulam and Tsingou (FPUT) discovered that an undamped, weakly nonlinear equation describing the motion of a chain of masses and springs could show complex dynamics. Integration of these equations froma n initial displacement in the formof the fundamental mode resulted in significant mode coupling: energy was transferred from the fundamental mode to several other modes, before the energy would return to the initial condition. To date, very little observations of such behavior in mechanical vibrations have been reported. Recent developments in fabrication of high stress Silicon-Nitride (Si3N4) string resonators have shown that it is possible to generate resonators with extremely high Q-factors, proving a potential testbed for these mechanics. This research shows, through modal conversionof the FPUT potential, that one may observe significant FPUT behavior in systems with non-integer frequency ratios and certain coupling coefficients. In addition, it is shown that for the default FPUT beta-model, the effect of damping is negligible for fundamental mode Q-factors higher than 10,000. Simulations of the experimental frequency response of a high-Q Si3N4 string resonator show that the nonlinear dynamics of these resonators may be approximated by an analytical model that does not possess the required frequency ratios and coupling coefficients for FPUT behavior. Another string model, for which no mechanical equivalent has (yet) been found, may potentially show FPUT behavior. Several string-like resonator designs are tested using a numerical tool which can extract the modal coefficients. These resonators are modelled using simplified deformation models, which account only for axial deformation of the structure. The results for various string-like designs show that the eigenfrequencies and nonlinearity may be engineered easily, but these do not generate the required coupling coefficient for FPUT behavior.

Artificial intelligence has a strong need for faster and more energy-efficient solutions, especially for computation performed at the sensor edge. On-chip photonic neural networks (PNNs) offer a promising solution for high speeds and energy efficiency. A less explored side of PNNs is their application to time-series data, which is often the case for real-world sensor applications. While PNNs promise high speeds and energy-efficient solutions, no good use cases have been proposed. This report will first review the state of the art of PNNs. It will be seen that to solve time-series tasks, photonic continuous-time recurrent neural networks (CTRNNs) are required. The dynamics of CTRNNs are thoroughly explored to leverage obtained insights to recommend novel practical applications. This is done through simple examples, and applied to a real machine learning task. It was seen that on a real classification task the network learned two distinct fixed points corresponding to the classes. A link between the time constant of the continuous-time neurons and the temporal dynamics of the task is also found. Two general directions for novel applications are then proposed. Firstly, photonic PNNs can be slowed down to match the task. Opto-electronic PNNs allow for more control of the time constant, and on-chip photonic filter neurons are suggested. Secondly, the high speeds of photonic neural networks can also be directly leveraged. Extremely fast convergence of photonic CTRNNs can be utilized for Modern Hopfield networks, pathfinding algorithms, and time-dependent optimization problems such as for example Model Predictive Control.

Nanophotonics is the study of structures’ interaction with light with features at or below the nanometer scale. It has gained the interest of many researchers, as it can be used to control the flow of light very effectively in the design of, e.g., solar cells, highly efficient biosensors or lasers. The design of such devices can be non-intuitive and complex and therefore computational tools like topology optimization techniques have been used to improve their designs. However, the topology optimization methods used in the literature often use a density-based representation of the geometry, which often leads to jagged edges. It has been shown in the literature that jagged edges can deteriorate the accuracy of simulation results. Using a level-set method in combination with an enriched finite element method offers a smoother boundary representation than the often used density-based methods. This work aims to develop an analysis and level set optimization for 2D electromagnetic scattering and eigenvalue problems using an enriched finite element method. Furthermore, we showcase that even for a non-conforming discretization, the enriched finite element method achieves the same convergence properties as the standard finite element method with fitted meshes. Finally, we perform topology optimization on the design of both a 2D meta lens and 2D reflector, maximizing their ability to focus light onto a point, using a level set method to define the geometry in combination with the enriched method used in the analysis.

Hermeticity is a measure of how well a package is leak-tight. Many Micro-Electro-Mechanical Systems (MEMS) sensors, actuators, and microelectronic devices need a defined cavity environment for optimal performance, hence measuring the package leak rate is critical for lifetime prediction. MEMS devices are generally packaged through the wafer-bonding technique. The MEMS device is produced on a wafer with a cavity and bonded to a cap wafer to seal the hole. Reducing the cap wafer thickness allows it to deflect due to the cavity interior-exterior pressure differential. Consequently, if leakage occurs, the deflection will change. By measuring these deflections, it is possible to quantify leak rates. In order to use it as an in-line testing process, this research aims to determine the accuracy of the deflection method for determining the leak rates. To achieve this, our approach involved designing and leak testing test structures (or devices) using an experimental setup that can vary pressure, supply desired species inside a vacuum chamber, and measure deflection using an interferometer to determine leak rates. Deflections are converted to leak rates using a formulated analytical expression, subsequently utilized to determine the error involved in measuring leak rates. Using the experimental setup, the test devices were effectively characterized for sensitivity using pressure-induced deflection measurements, with experimental sensitivity values closely matching the theory. Further, air leak testing was performed on devices interconnected with nanometer-gap size leak channels to gain first-hand knowledge of leakage. Experimental leak rates matched well with analytical models, proving that flow through devices having leak channels can be characterized. Ultimately, the setup enabled successful helium leak testing of devices without any defined leak channels. The helium leak-tested samples were circular membranes of diameters: 2000, 1600, 1400, 1300, and 1100 μm with a thickness of 40 μm bonded to a cavity depth of 3.24 μm. Uncertainty analysis associated with leak rate measurement revealed that when considering a certain cavity depth and membrane thickness, the membrane with the largest diameter would exhibit the least amount of uncertainty. This was also observed through experiments, for the diameter of 2000 μm, a clear linear trend of deflection reduction due to the helium leakage was observed during a two-week period of deflection measurements. Whereas, for the diameter of 1100 μm, it was not possible to observe the same linear trend of deflection reduction, indicating that even more no.of.days is required to determine an accurate leak rate. In the end, a short analysis was made using the cavity design having the 2000 μm membrane, which had the least uncertainty in measuring the leak rate. This analysis aimed to ascertain the designed test structure’s usefulness in measuring leak rates of the MEMS packages. Based on the analysis, it was concluded that large-volume wafer-bonded MEMS packages (> 1 mm3) with an acceptable cavity pressure increase of 10 mbar could be tested using the deflection method and our proposed test structure design to guarantee their lifetime.

In a world increasingly dominated by technological advancements, the demand for high-quality microphones has never been more present. Seamless speech recognition and the development of userfriendly hearing aids remain significant challenges. State-of-the-art micro-electromechanical system (MEMS) microphones are reaching their bottlenecks in terms of thermo-acoustic noise, caused by the acoustic resistance of the parallel plate capacitor. This constrains the achievable signal-to-noise ratio (SNR). This thesis presents a novel solution to address these challenges through the application of silicon photonics technology in the development of a silicon photonic microphone. Silicon photonics is a technology that uses silicon as an optical medium to create photonic systems with sub-micrometre precision, which can be used to create ultra-sensitive sensing devices. The optical sensors are fabricated on standard silicon-on-insulator (SOI) wafers, allowing for seamless integration with the precise and cost-effective complementary metal-oxide-semiconductor (CMOS) process. The optomechanical sensitivity of the proposed microphone is derived for three different cladding materials that could be deposited on the wafer in the fabrication process. The thermal acoustic noise of the microphone is quantified. As the integrated photonic circuit does not require a backplate the design potentially reduces the thermal acoustic noise of current microphones by 44 %. The optimized design for the laboratory setup that is considered for this thesis can theoretically result in an SNR of 73.1 dB, which is roughly 5 dB more than the current state-of-the-art microphone technology.

Diamagnetic levitation presents a promising platform for realizing resonant sensors and energy harvesters. The technique offers mechanical isolation from the environment while operating with zero power consumption. This unique feature ensures exceptional sensitivity and accuracy in numerous applications. However, the presence of eddy currents in the levitating plate, induced by the alternating magnetic field, poses challenges, leading to increased damping and subsequently limiting the performance of levitating resonators. To address these issues, this study proposes a novel solution through the segmentation of diamagnetic plates. By dividing a pyrolytic graphite plate into smaller blocks, the flow of eddy currents is effectively restricted, resulting in reduced damping and significantly higher Q factors. By comparing the theoretical predictions using a FEM model from an earlier study with the measurements conducted the proposed technique is further validated. This comparative analysis demonstrates the effectiveness of the segmentation approach in mitigating damping due to eddy currents. Furthermore, the implementation of the proposed method led to remarkable results, with achieved Q factors exceeding 150 thousand.

In pursuit of extremely sensitive sensors, the dimensions of these sensors get smaller and smaller. Small scale resonators are commonly used as sensors by relating changes in the dynamic behaviour to a sensed quantity. Conventionally, the dynamics used for sensing are in the linear regime. But at smaller scales the dynamic range of the linear regime decreases. Therefore, it is of interest to investigate the dynamic behaviour in the nonlinear regime, as with the decreasing scale of the resonators this becomes inevitable. Especially, little is known about the frequency stability in this region. The frequency stability is an indication for the potential sensitivity that the resonator can have as sensor. By using phase locked loop (PLL) the frequency stability around the resonance frequency of nonlinear resonators can be obtained. This research contains attempts to control multilayer graphene drums around its fundamental resonance frequency with PLL. In addition, the frequency stability at these points are presented by measure of the Allan deviation. There are roughly two different distributions of the frequency stability over the frequency response obtained. One resonator shows behaviour attributed to internal resonance. This internal resonance is linked to an increase of nonlinear damping. Combining that with a simple simulation model, a relation was found between increased nonlinear damping and an improvement of frequency stability.

Research has shown concepts of phononic integrated circuits (PnICs) consisting of multiple acoustic waveguides and beam splitters. Traveling acoustic waves experience energy loss when moving. Minimizing these losses is critical for large and complex PnICs. By fabricating on-chip PnICs, it is possible to operate under vacuum and at low temperatures resulting in lower acoustic losses. Studies have shown on-chip data transport using straight acoustic waveguides fabricated inside suspended membrane phononic crystals. The use of high stress Silicon Nitride (SiN) has enabled the manufacturing of high aspect ratio suspended structures. This is achieved by stress keeping the membrane under tension resulting in a flat surface. Current acoustic beam splitter designs feature liquid and air for the wave supporting material. Making them not suitable for on-chip devices. Therefore, on-chip PnICs require a new type of splitter design. In this study, finite element methods are used to investigate if suspended SiN membranes offer a solution for on-chip acoustic beam splitting. The wave confinement of square and hexagonal lattice splitters are also compared to find the best performing design. Phononic bandstructures are constructed by performing eigenfrequency studies on various 2D phononic crystal unit cells. These bandstructures reach full GHz bandgaps with relative bandgap sizes of 57.3%. Symmetric beam splitters are then made by introducing line defects into the crystal structures. Multiple wave excitation locations, frequencies and waveguide widths are investigated to establish the highest wave confining splitter design. The final design consists of a y-shaped splitter inside a suspended SiN hexagonal lattice phononic crystal and achieves a wave confinement of 85.03% at an excitation frequency of 3.25GHz. The results show that suspended SiN membranes featuring hexagonal lattice phononic crystals offer a promising solution for on-chip beam splitting.

Suspended microchannel resonators are a kind of mechanical resonator with an embedded microchannel inside. This is done as for some samples it is convenient or even necessary to put the sample into a fluid. The sample can then travel through the channel and its mass can be determined. The channel also simplifies placement of the samples compared to regular nanomechanical resonators. By having this channel embedded within the resonator, it is then possible to place the resonator as a whole in a vacuum and so eliminate medium losses. The main purpose of these suspended microchannel resonators is mass spectrometry which has already been performed on viruses and biological cells and so could potentially be very useful for the medical field as well. Especially if suspended microchannel resonators can be used to measure individual proteins which has not been done before with these resonators. It would also be interesting to use these kinds of resonators in quantum mechanical experiments. This means that the performance of these suspended microchannel resonators needs to be improved. In order to accomplish this, a new kind of suspended microchannel resonator is introduced. The determination of these designs is strictly FEM based. The new resonator design, which is a doubly clamped beam, is made from pre-stressed silicon nitride which enables high Q-factors caused by an effect known as dissipation dilution. Dissipation dilution means diluting the energy losses of the system by increasing the stored energy which is increased by the initial stress in the silicon nitride. To increase this effect, the resonator is tapered towards the center. This is called strain engineering. Silicon nitride has been used in suspended microchannel resonators before but it did not result in higher Q-factors. Possibly due to clamping losses. The designs presented here offer a solution to that in the form of soft-clamping. This reduces the curvature near the boundaries to a minimum which means that the clamping losses are also reduced or eliminated. The combined effect of these features results in very high Q-factors as has already been reported for nanomechanical resonators. Through machine learning optimization it is possible to achieve 6E12 Hz in Qf product required for quantum mechanical experiments at room temperature and more than one order of magnitude improvement in mass sensitivity.

Vibration energy harvesters are especially interesting to use in an environment where there is one dominant vibration frequency present because then the harvesters can be designed to resonate at that specific frequency. To spread out the power yield over more frequencies a multi-modal harvester can be used which can resonate at multiple frequencies. A vibration with more than one sine wave can be manifested in a number of ways. The two frequencies can be present simultaneously, or they can alternate each other. How the energy harvesters react to these different vibration inputs is researched in this paper. Two fundamentally different multi-modal energy harvesters are used here. One which can be described by a coupled system of equations and one uncoupled. Two prototypes of an uncoupled and one coupled device are made and tested on an electromagnetic shaker. The vibration signals are sent to the shaker and the power output of the energy harvesters is measured using piezoelectric transducers mounted to the mechanisms. The results show that a phaseshift in the sine wave input signal generally results in a increase in power, where a decrease was assumed beforehand. When switching the input vibration from the first to the second eigenfrequency the power output does drop significantly, but the coupled mechanism has a substantially higher power output than the uncoupled device. And when the mechanisms are excited by a vibration with two eigenfrequencies at the same time no significant difference between the two can be observed, nor does the power output drop significantly. While the comparison between these two mechanisms is probably accurate, the quantitative conclusions must be taken with a grain of salt as it was noticed in a later stage of the research that the vibration signals were not consistent over the entire time period. At this point it is unclear if an overall better mechanism can be picked between the coupled and uncoupled one. However, it is shown that both have their distinct advantages where they outperform their counterpart, which can be used for designing a better energy harvester in future applications

Optical microscopes are fundamentally limited to a resolution of several hundreds of nanometers by the diffraction of light. Single-molecule localization microscopy (SMLM) circumvents this limit by sparsely exciting fluorescent molecules at different time instances. Single molecules can subsequently be localized with improved precision over the diffraction limit. Due to their high frame rate, single-photon avalanche diode (SPAD) arrays are imagers that can be used for SMLM. Most SPADs have to recharge after each photon arrival. During this recharging period, the SPAD is insensitive to more photon arrivals. As a result, SPAD arrays will measure zero or one photons for each pixel in each frame, whereas scientific complementary metal-oxide semiconductor (sCMOS) imagers and electron multiplying charge-coupled devices (EMCCD) have a discrete frame output. Here, we describe the photon arrivals in the image formation model of the SPAD array as a binomial process rather than as a Poissonian process. In addition, we quantify the minimum theoretical uncertainty of single-molecule localizations using a binomial Cramér-Rao lower bound and benchmark it with simulated and experimental data. We show that if the expected photon count is larger than one for all pixels within one standard deviation of a Gaussian point spread function, the binomial CRLB gives a 46% higher theoretical uncertainty than the Poissonian CRLB. Without saturation, which is the case for most SMLM applications, the binomial CRLB model gives the same uncertainty as the Poissonian CRLB. Therefore, the binomial CRLB can be used to predict and benchmark localization uncertainty for SMLM with SPAD arrays for all practical emitter intensities.

The exceptional material properties of bulk diamond like high stiffness, high thermal conductivity, wide optical transparency, chemical inertness and bio-compatibility make it the material of choice in many high-end applications. Most present-day diamond micro-devices are fabricated by costly and time-consuming top-down methods, such as focussed ion beam milling or reactive ion etching. Hence, bottom-up methods that incorporate selective seeding and chemical vapour deposition (CVD) to produce micro-patterned poly-crystalline diamond are of interest. The present work introduces two novel methods for the bottom-up synthesis of nanocrystalline diamond micro-structures. The first method is based on the precise dispensing of nanodiamond dispersions from a hollow AFM cantilever and is used to manufacture freestanding diamond micro-resonators which are analysed on their frequency response. The second method incorporates maskless lithography to create stencils for selective seeding and enables patterned diamond growth on the single digit micrometer scale. A future step of growing such micro-structures in electrically conductive diamond could open up a vast new range up applications.

Due to the demand for renewable energies, gasses likeH2 need to be detected with sensitive, accurate and fast detectors. The US Department of Energy has made a list of requirements that H2 sensors need to fullfill of which the minimum detectable concentration (0.1%) and the reaction time (one second) are challenging for current hydrogen sensors, particularly for low-power and low-cost mass-produced sensors. This thesis covers the design and simulation of a photonic crystal nanobeam cavity sensor, using the Pt-catalyzed WO3 as a H2 sensitive material. The thicknesses of both layers show a trade-off between the minimally detectable concentration and the reaction times, resulting in a cavity with sensitivity of almost 40 nm/RIU and a Q factor varying between 5e5 and 5e4 depending on how much catalyst is required to meet the one second reaction time performance target. Based on the conservative assumptions regarding the reaction times of the sensor, the 0.1% performance target is almost achieved. This means that if in practice, any of the layer thicknesses show to be more favourable than assumed in this thesis, together with the fact that for optical sensors there is no risk of sparks, the photonic crystal nanobeam cavity as a H2 sensor shows to be a good fit for a high performance, low-cost, mass-produced H2 sensor that meets the DoE performance targets.

This research explores the integration of Neural Architecture Search with Optical Neural Networks to optimize the efficiency and performance in traditional visual image classification tasks. The study introduces a new approach that applies Neural Architecture Search, a technique traditionally used to optimize the performance of Artificial Neural Networks, to the field of Optical Neural Networks.

Conventional Topology Optimization (TO) enables the inverse design of nanophotonic structures by specifying the objective and constraints without a predefined topological concept. Yet, extreme scenarios such as the design of a lightsail pose challenges that require new solutions. Here, a convolutional neural network (CNN) based TO methodology is extended to optimize a two-dimensional photonic crystal used to design a lightsail that aims to reach the nearest star (Alpha Centauri) within 20 years by achieving 20% of the speed of light. The CNN-TO performance is compared to a more conventional method of moving asymptotes (MMA) based TO by optimizing a photonic crystal unit-cell for the 2016 Starshot Initiative parameters. The CNN-TO requires up to 40% fewer iterations than MMA-TO to reach better performance under different operational conditions. The generated design turned out to be easy to fabricate, allowing them to be produced with optical lithography. Additionally, a study regarding the design challenges of the lightsail has been performed, which resulted in an optimization considering the functionality of the sail. Additionally, the study showed the sensitivity of the resulting design to varying objectives and materials. Therefore, underlining the necessity of considering multiple operating conditions (e.g. laser alignment and cooling) within the design process.

Micro- and nanoelectromechanical (MEM/NEM) resonators are used in numerous fields of engineering and are crucial for time keeping, synchronization, and sensing applications. These systems are subjected to energy dissipation, which is a limiting factor in the performance. Extensive understanding is essential when nonlinearities show up in both stiffness and dissipation, to design appropriately. Focusing on dissipative mechanisms, this paper explores the vibrational behavior of a suspended clamped-clamped beam fabricated from silicon-nitride in the nonlinear regime. This study reveals a notorious decay in ringdown, when the resonator is decoupled from its vibrational power. A sustained amplitude is observed for up to 8 seconds. Though the exact source of this anomaly remains elusive, it is suggested that it might include modal coupling and/or optomechanical effects

Nanomechanical resonators with low dissipation rates are ideal tools in fundamental science applications. They have been used in the field of cavity optomechanics for example in ground-state cooling, and in sensing applications, such as atomic resolution mass sensors. Their great sensitivity is due to their high Q-factor, which is a metric that shows how fast a system loses its energy. In ultra-high Q nanomechanical resonators, energy loss is limited to intrinsic and radiation losses, the latter is due to energy dissipation from the resonator into the substrate. Experiments have shown that the Q-factor of resonators with thin substrates are limited by radiation loss. However, the precise role of the substrate remains a topic that has not received much attention, but has significant implications for how we design nanomechanical microchips. Here we show that the resonator mode can couple to nearby substrate modes, which reduces the Q-factor. We found that the strength of this mode-coupling depends on the mode-shape of the substrate, with stronger coupling at anti-nodes of the mode-shape and hardly any coupling at the nodes. Furthermore, we show that clamping down the substrate with double-sided tape reduces the Q-factor of the resonators, this is explained by a reduction in Q of substrate modes due to the tape. Lastly, we found that in thin substrates, which have a higher density of modes, the Q-factor can be limited due to mode-coupling with the substrate. Our results demonstrate that the substrate choice, as it can strongly affect the Q-factor of resonators, should become an integral part of the resonator design phase. These results can likely be used by all types of nanomechanical resonators limited by radiation loss. We can use this knowledge to design chips with resonators that have an even higher Q-factor.

A research gap exists in a targeted drug delivery into the brain with an implant placed on the outer surface of the cerebral cortex. If an implant with spatial control that can release drugs to a target location can be developed, it will provide efficient treatment opportunities for a variety of brain disorders such as strokes. One of the questions in realizing this implant is how to activate the drug release mechanism. Light is a promising activation stimulus due to its spatial precision and flexibility in the optical path. This thesis is a feasibility study into carrying light inside such a brain implant using a photonic crystal waveguide. Such a device must be soft and maintain its functionality during the mechanical bending imposed on the implant by the geometry and movement of the brain. A flexible 2D photonic crystal is simulated using COMSOL Multiphysics with the goal of designing a waveguide that functions with infrared light. The dispersion diagram of the photonic crystal is plotted to design for a bandgap at the operating wavelength. The transmission through a linear waveguide is calculated for the deformed state of the implant in mechanical bending, which is modeled as a 2D strain. A metallo-photonic crystal with photoresist nanopillars coated with a gold thin film and embedded in a flexible PDMS matrix is selected as the prototype for fabrication. The nanopillar arrays that form the photonic crystal waveguide are printed using two-photon polymerization (2PP), deposited with gold then transferred into photosensitive PDMS by drop casting. For characterization, a tapered rib waveguide is designed for light coupling and an optical end-fire test setup is built for transmission measurements on the fabricated device.