We introduce a novel method to geometrically tune the tension in prestrained resonators by making Si 3 N 4 strings with a designed predisplacement. This enables us, for example, to study their dissipation mechanisms, which are strongly dependent on the stress. After release of the resonators from the substrate, their static displacement is extracted using scanning electron microscopy. The results match finite-element simulations, which allows a quantitative determination of the resulting stress. The in-and out-of-plane eigenmodes are sensed using on-chip Mach−Zehnder interferometers, and the resonance frequencies and quality factors are extracted. The geometrically controlled stress enables tuning not only of the frequencies but also of the damping rate. We develop a model that quantitatively captures the stress dependence of the dissipation in the same SiN film. We show that the predisplacement shape provides additional flexibility, including control over the frequency ratio and the quality factor for a targeted frequency.

Abstract. We consider the problem of numerical differentiation of a function f from approximate or noisy values of f on a discrete set of points; such discrete approximate data may result from a numerical calculation (such as a finite element or finite difference solution of a partial differential equation), from experimental measurements, or, generally, from an estimate of some sort. In some such cases it is useful to guarantee that orders of accuracy are not degraded: assuming the approximating values of the function are known with an accuracy of order O(h r ), where h is the mesh size, an accuracy of O(h r ) is desired in the value of the derivatives of f . Differentiation of interpolating polynomials does not achieve this goal since, as shown in this text, n-fold differentiation of an interpolating polynomial of any degree ≥ (r − 1) obtained from function values containing errors of order O(h r ) generally gives rise to derivative errors of order O(h r−n ); other existing differentiation algorithms suffer from similar degradations in the order of accuracy. In this paper we present a new algorithm, the LDC method (low degree Chebyshev), which, using noisy function values of a function f on a (possibly irregular) grid, produces approximate values of derivatives f (n) (n = 1, 2 . . . ) with limited loss in the order of accuracy. For example, for (possibly nonsmooth) O(h r ) errors in the values of an underlying infinitely differentiable function, the LDC loss in the order of accuracy is "vanishingly small": derivatives of smooth functions are approximated by the LDC algorithm with an accuracy of order O(h r ) for all r < r. The algorithm is very fast and simple; a variety of numerical results we present illustrate the theory and demonstrate the efficiency of the proposed methodology.

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Recent developments in quantum computing and the growing interest in optomechanics and quantum optics need platforms that enable rapid prototyping and scalability. This can be fulfilled by on-chip integration, as we present here. The different nanofabrication steps are explained, and our automated measurement setup is discussed. We present an opto-electromechanical device, the H-resonator, which enables optomechanical experiments such as electrostatic springs and nonlinearities and thermomechanical squeezing. Moreover, it also functions as an optomechanical phase shifter, an essential element for our integrated quantum optics efforts. Besides this, the equivalent of a beam splitter in photonics-the directional coupler-is shown. Its coupling ratio can be reliably controlled, as we show with experimental data. Several directional couplers combined can realize the CNOT operation with almost ideal fidelity.

The high voltage transmission network in South Africa contains a relatively high percentage of non-ceramic insulators. Techniques for assessing the condition of these insulators are under investigation.Such techniques include imaging techniques that take either an infra-red image o r an ultra-violet image of the insulator. Such images may indicate some changes to either the external (visible) components of the insulator o r to the internal (non-visible) components that may impact the long-term integrity of the insulator. This paper discusses the results of an investigation into these two imaging techniques applied to non-ceramic insulators.

Visualizing eigenmodes is crucial in understanding the behavior of state-of-the-art micromechanical devices. We demonstrate a method to optically map multiple modes of mechanical structures simultaneously. The fast and robust method, based on a modified phase-lock loop, is demonstrated on a silicon nitride membrane and shown to outperform three alternative approaches. Line traces and two-dimensional maps of different modes are acquired. The high quality data enables us to determine the weights of individual contributions in superpositions of degenerate modes.

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