The design of intrinsically flat two-dimensional optical components, i.e., metasurfaces, generally requires an extensive parameter search to target the appropriate scattering properties of their constituting building blocks. Such design methodologies neglect important near-field interaction effects, playing an essential role in limiting the device performance. Optimization of transmission, phase-addressing and broadband performances of metasurfaces require new numerical tools. Additionally, uncertainties and systematic fabrication errors should be analysed. These estimations, of critical importance in the case of large production of metaoptics components, are useful to further project their deployment in industrial applications. Here, we report on a computational methodology to optimize metasurface designs. We complement this computational methodology by quantifying the impact of fabrication uncertainties on the experimentally characterized components. This analysis provides general perspectives on the overall metaoptics performances, giving an idea of the expected average behavior of a large number of devices.

Abstract-In this paper, electrothermal field phenomena in electronic components are considered. This coupling is tackled by multiphysical field simulations using the Finite Integration Technique (FIT). In particular, the design of bonding wires with respect to thermal degradation is investigated. Instead of resolving the wires by the computational grid, lumped element representations are introduced as point-to-point connections in the spatially distributed model. Fabrication tolerances lead to uncertainties of the wires' parameters and influence the operation and reliability of the final product. Based on geometric measurements, the resulting variability of the wire temperatures is determined using the stochastic electrothermal field-circuit model.

View the article online for updates and enhancements. AbstractIn this paper, we study a high-order finite element approach to simulate an ultrahigh finesse FabryPérot superconducting open resonator for cavity quantum electrodynamics. Because of its high quality factor, finding a numerically converged value of the damping time requires an extremely high spatial resolution. Therefore, the use of high-order simulation techniques appears appropriate. This paper considers idealized mirrors (no surface roughness and perfect geometry, just to cite a few hypotheses), and shows that under these assumptions, a damping time much higher than what is available in experimental measurements could be achieved. In addition, this work shows that both high-order discretizations of the governing equations and high-order representations of the curved geometry are mandatory for the computation of the damping time of such cavities.

The stochastic Galerkin and stochastic collocation method are two state-of-the-art methods for solving partial differential equations (PDE) containing random coefficients. While the latter method, which is based on sampling, can straightforwardly be applied to nonlinear stochastic PDEs, this is nontrivial for the stochastic Galerkin method and approximations are required. In this paper, both methods are used for constructing high-order solutions of a nonlinear stochastic PDE representing the magnetic vector potential in a ferromagnetic rotating cylinder. This model can be used for designing solid-rotor induction machines in various machining tools. A precise design requires to take ferromagnetic saturation effects into account and uncertainty on the nonlinear magnetic material properties. A numerical comparison of the computational cost and accuracy of both methods is performed. The stochastic Galerkin method requires in general less stochastic unknowns than the stochastic collocation approach to reach a certain level of accuracy, however at a higher computational cost. AbstractThe stochastic Galerkin and stochastic collocation method are two state-of-the-art methods for solving partial differential equations (PDE) containing random coefficients. While the latter method, which is based on sampling, can straightforwardly be applied to nonlinear stochastic PDEs, this is nontrivial for the stochastic Galerkin method and approximations are required. In this paper, both methods are used for constructing high-order solutions of a nonlinear stochastic PDE representing the magnetic vector potential in a ferromagnetic rotating cylinder. This model can be used for designing solid-rotor induction machines in various machining tools. A precise design requires to take ferromagnetic saturation effects into account and uncertainty on the nonlinear magnetic material properties. A numerical comparison of the computational cost and accuracy of both methods is performed. The stochastic Galerkin method requires in general less stochastic unknowns than the stochastic collocation approach to reach a certain level of accuracy, however at a higher computational cost.

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