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Institute
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.
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 occurring e. g. in optical metrology. The reduced basis method pre-
sented 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.
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.
Simulations of optical processes and complex nanostructured devices have become omnipresent in recent years in several fields of current research and industrial applications, not limited to the field of photovoltaics. Devices or processes are optimized with respect to a certain objective where the underlying physical processes are described by partial differential equations. In photovoltaics and photonics electromagnetic fields are investigated which are governed by Maxwell’s equations.
In this thesis a reduced basis method for the solution of the parameter dependent electromagnetic scattering problem with arbitrary parameters is developed. The method is developed with the specific challenges arising in optical simulations of thin-film silicon solar cells in mind. These are large in domain size and have a complex three-dimensional structure, making optimization tasks infeasible if high-accuracy of the electromagnetic field solution is required. The application of the empirical interpolation methods allows to expand an arbitrary parameter dependence affinely. Thus not only geometries, but also material tensors and source fields can be parameterized. Additionally, the required non-linear post-processing steps of the electromagnetic field to derive energy fluxes or volume absorption are addressed. The reduced basis method allows to reduce the computational costs by orders of magnitude compared to efficient finite element solvers.
In addition, an efficient tailored domain decomposition algorithm is presented to model incoherent layers or illuminations in optical systems efficiently. This is of particular interest for solar cells in superstrate configuration where the absorber is illuminated through a glass substrate.
The developed methods are employed in application examples taken from collaborations with experimentalists active in the joint lab “BerOSE” (Berlin Joint Lab for Optical Simulations for Energy Research). The optical model of a thin-film silicon multi-junction with incoherent light-trapping is characterized in great detail. The computational gains through hybrid, hp adaptive finite elements are studied and the incoherent domain decomposition algorithm is applied to model
a more realistic light-trapping by the glass substrate.
The numerical examples of a hexagonal nano-hole array and multi-junction silicon solar cell with a tunable intermediate reflector layer show that the reduced basis method is well suited as a forward solver for modeling and optimization tasks arising in photovoltaics and photonics. Reduced models for illumination and geometric parameters are built providing up to five orders of magnitude savings in computational costs. Resonance phenomena present in the nano-hole array example are detected and the model adapts itself automatically.
The introduction of the near-field quantity of optical chirality has emerged in various numerical and few experimental studies of local chirality enhancement due to its relation to the excitation rate of chiral molecules. This time-even pseudoscalar has been dismissed as being a higher-order version of helicity. Nevertheless, we revisit the derivation of the underlying conservation law and define optical chirality in media similar to. We identify the mechanism of chirality conversion by either inhomogeneous or anisotropic space to complement the conservation of optical chirality.
The conservation law of optical chirality in arbitrary space enables the extension of the concept of polarization to the near-field where no distiniguished propagation direction of light is present. We show that the connection of electromagnetic energy and optical chirality provide the ability to define a circular polarization basis in time-harmonic near-field analysis.
In order to illustrate our theory, we present electromagnetic field simulations of simple as well as more complex nanostructures. Results using the well-known far-field polarization concept are readily reproduced and extended from the point of view of chirality conversion.