Semiconductor superlattice photodetectors

Superlattice photodetectors were investigated. A few major physical processes in the quantum-well heterostructures related to the photon detection and electron conduction mechanisms, the field effect on the wave functions and the energy levels of the electrons, and the optical absorption with and without the photon assistance were studied

A Hierarchical Solver for Time-Harmonic Maxwell\u27s Equations

Die Kombination von Transformationsoptik und Sweeping Preconditionern sowie ein hierarchischer Ansatz ermöglichen einen Vorkonditionierer für lineare Gleichungssysteme, die bei der Diskretisierung von Maxwell\u27s Gleichungen mit der Finite Elemente Methode entstehen. Das Verfahren wird beschrieben, numerische Beispiele präsentiert und unterschiedliche Anwendungen diskutiert. Das Dokument enthält auch den dokumentierten Code als Anhang

Iterative methods for scattering problems in isotropic or anisotropic elastic waveguides

International audienceWe consider the time-harmonic problem of the diffraction of an incident propagative mode by a localized defect, in an infinite straight isotropic elastic waveguide. We propose several iterative algorithms to compute an approximate solution of the problem, using a classical finite element discretization in a small area around the perturbation, and a modal expansion in unbounded straight parts of the guide. Each algorithm can be related to a so-called domain decomposition method, with or without an overlap between the domains. Specific transmission conditions are used, so that only the sparse finite element matrix has to be inverted, the modal expansion being obtained by a simple projection, using the Fraser bi-orthogonality relation. The benefit of using an overlap between the finite element domain and the modal domain is emphasized, in particular for the extension to the anisotropic case. The transparency of these new boundary conditions is checked for two- and three-dimensional anisotropic waveguides. Finally, in the isotropic case, numerical validation for two- and three-dimensional waveguides illustrates the efficiency of the new approach, compared to other existing methods, in terms of number of iterations and CPU time

Discontinuities in open photonic waveguides: Rigorous 3D modeling with the finite element method

In this paper, a general methodology to study rigorously discontinuities in open waveguides is presented. It relies on a full vector description given by Maxwell's equations in the framework of the finite element method. The discontinuities are not necessarily small perturbations of the initial waveguide and can be very general, such as plasmonic inclusions of arbitrary shapes. The leaky modes of the invariant structure are first computed and then injected as incident fields in the full structure with obstacles using a scattered field approach. The resulting scattered field is finally projected on the modes of the invariant structure making use of their bi-orthogonality. The energy balance is discussed. Finally, the modes of open waveguides periodically structured along the propagation direction are computed. The relevant complex propagation constants are compared to the transmission obtained for a finite number of identical cells. The relevance and complementarity of the two approaches are highlighted on a numerical example encountered in infrared sensing. Open source models allowing to retrieve most of the results of this paper are provided.Comment: The GetDP/Gmsh scripts allowing to retrieve the results are attache

Computer modelling of directional coupler based optical devices

This work is a study of the important parameters of synchronous and nonsynchronous, weakly and strongly coupled optical directional couplers, primarily using the finite element method. This method can be used to find accurate modal solutions of the isolated waveguides or the coupled waveguides with arbitrary shapes, index profiles, and anisotropies. Unlike the traditional coupled mode theory, the vector supermodes obtained by using the finite element method are orthogonal to each other, even when the guides are strongly coupled or when they are not identical. From an accurate knowledge of the propagation constants of the two supermodes, the coupling length of the system can also be calculated. However, the finite element method cannot provide directly the power-transfer efficiency or the cross-talk between the coupled waveguides. Calculations of the important coupling parameters can be achieved by introducing the coupled mode approach along with the accurate modal solutions obtained by using the finite element method. In this approach, the overlap integrals of the isolated modes and the coupling factors are calculated numerically and these values are subsequently used to find the power coupling efficiency from one waveguide to another. Recently, there have been several innovative approaches to improving the traditional coupled mode theory by enforcing orthogonality of the supermodes or by maintaining the power conservation criteria. In this work, some of these new coupled mode approaches have been implemented to study the coupling parameters along with the exploitation of the accurate modal solutions obtained using the finite element method. As an alternative, the least squares boundary residual method can be applied to find the excitation coefficients of the two supermodes by considering the butt-coupling between the input waveguide and the directional coupler section. In this approach, the continuity of the tangential electric and magnetic fields is achieved in a least squares sense at the junction discontinuity interface. Once the transmission coefficients of the two guided even- and odd- like supermodes are calculated, the power carried by the two guides along the axial direction can be easily evaluated. In this work, the power transfer from one optical waveguides to another by the use of the finite element based propagation model has also been studied. Simulation results are presented for a wide range of directional coupler based- devices including electro-optic switches and semiconductor filters. To show the advantages of the finite element-based approaches, the power transfer efficiency between coupled waveguides with two-dimensional confinement is also presented

Learned infinite elements for helioseismology

This thesis presents efficient techniques for integrating the information contained in the Dirichlet-to-Neumann (DtN) map of time-harmonic waves propagating in a stratified medium into finite element discretizations. This task arises in the context of domain decomposition methods, e.g. when reducing a problem posed on an unbounded domain to a bounded computational domain on which the problem can then be discretized. Our focus is on stratified media like the Sun, that allow for strong reflection of waves and for which suitable methods are lacking. We present learned infinite elements as a possible approach to deal with such media utilizing the assumption of a separable geometry. In this case, the DtN map is separable, however, it remains a non-local operator with a dense matrix representation, which renders its direct use computationally inefficient. Therefore, we approximate the DtN only indirectly by adding additional degrees of freedom to the linear system in such a way that the Schur complement w.r.t. the latter provides an optimal approximation of DtN and sparsity of the linear system is preserved. This optimality is ensured via the solution of a small minimization problem, which incorporates solutions of one-dimensional time-harmonic wave equations and allows for great flexibility w.r.t. properties of the medium. In the first half of the thesis we provide an error analysis of the proposed method in a generic framework which demonstrates that exponentially fast convergence rates can be expected. Numerical experiments for the Helmholtz equation and an in-depth study on modelling the solar atmosphere with learned infinite elements demonstrate the high accuracy and flexibility of the proposed method in practical applications. In the second half of the thesis, the potential of learned infinite elements in the context of sweeping preconditioners for the efficient iterative solution of large linear systems is investigated. Even though learned infinite elements are very suitable for separable media, they can only be used for tiny perturbations thereof since the corresponding DtN maps turn out to be extremely sensitive to perturbations in the presence of strong reflections.2021-12-2

Halfspace Matching: a Domain Decomposition Method for Scattering by 2D Open Waveguides

We study a scattering problem for the Helmholtz equation in 2D, which involves non-parallel open waveguides, by means of the halfspace matching method. This method has formerly been applied to periodic media and homogeneous anisotropic media, and we extend it to open waveguides. It allows the reformulation of the Helmholtz equation in an exterior domain to a set of equations for particular traces of the solution, reducing the overall dimension of the problem by 1, making it accessible for numerical discretisation. We show the well-posedness of the halfspace matching method for a model problem in the exterior of a triangular domain, assuming the presence of absorption. Furthermore, we introduce a numerical discretisation which allows the realisation of transparent boundary conditions by a system of coupled integral equations. To illustrate the practicality of this method, we study a number of optimisation examples involving junctions of open waveguides by means of material optimisation