78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80)
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We present a Newton-like method to solve inverse problems and to quantify parameter uncertainties. We apply the method to parameter reconstruction in optical scatterometry, where we take into account a priori information and measurement uncertainties using a Bayesian approach. Further, we discuss the influence of numerical accuracy on the reconstruction result.
Gaining insights into the working principles of photocatalysts on an atomic scale is a challenging task. The obviously high complexity of the reaction mechanism involving photo-excited electrons and holes is one reason. Another complicating aspect is that the electromagnetic field, driving photocatalysis, is not homogeneous on a nanoscale level for particle based catalysts as it is influenced by the particle’s shape and size.
We present a simple model, inspired by the CO2 reduction on titania anatase, which addresses the impact of these heterogeneities on the photocatalytic kinetics by combining kinetic Monte Carlo with electromagnetic wave simulations. We find that average activity and especially efficiency might differ significantly between different particles. Moreover, we find sizable variation of the catalytic activity on a single facet of a nanocrystal. Besides this quantitative heterogeneity, the coverage situation in general changes laterally on this facet and we observe a concomitant change of the rate-determining steps.
This heterogeneity on all levels of photocatalytic activity is masked in experimental studies, where only the spatially averaged activity can be addressed. Microkinetic models based on experimental findings might therefore not represent the true micro- scopic behavior, and mechanistic conclusion drawn from these need to be handled with care.
Optical 3D simulations in many-query and real-time contexts require new solution strategies. We study an adaptive, error controlled reduced basis method for solving parametrized time-harmonic optical scattering problems. Application fields are, among others, design and optimization problems of nano-optical devices as well as inverse problems for parameter reconstructions occuring e. g. in optical metrology. The reduced basis method presented here relies on a finite element modeling of the scattering problem with parametrization of materials, geometries and sources.
Reconstruction of photonic crystal geometries using a reduced basis method for nonlinear outputs
(2016)
Maxwell solvers based on the hp-adaptive finite element method allow for accurate geometrical modeling and high numerical accuracy. These features are indispensable for the optimization of optical properties or reconstruction of parameters through inverse processes. High computational complexity prohibits the evaluation of the solution for many parameters. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem allowing to compute solutions for a parameter configuration orders of magnitude faster. The RBM allows to evaluate linear and nonlinear outputs of interest like Fourier transform or the enhancement of the electromagnetic field in milliseconds. We apply the RBM to compute light-scattering off two dimensional photonic crystal structures made of silicon and reconstruct geometrical parameters.
Rigorous optical simulations of 3-dimensional nano-photonic structures are an important tool in the analysis and optimization of scattering properties of nano-photonic devices or parameter reconstruction. To construct geometrically accurate models of complex structured nano-photonic devices the finite element method (FEM) is ideally suited due to its flexibility in the geometrical modeling and superior convergence properties. Reduced order models such as the reduced basis method (RBM) allow to construct self-adaptive, error-controlled, very low dimensional approximations for input-output relationships which can be evaluated orders of magnitude faster than the full model. This is advantageous in applications requiring the solution of Maxwell's equations for multiple parameters or a single parameter but in real time. We present a reduced basis method for 3D Maxwell's equations based on the finite element method which allows variations of geometric as well as material and frequency parameters. We demonstrate accuracy and efficiency of the method for a light scattering problem exhibiting a resonance in the electric field.