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Simulation of microwave circuits and laser structures including PML by means of FIT
2004, Hebermehl, G., Schefter, J., Schlundt, R., Tischler, Th., Zscheile, H., Heinrich, W.
Field-oriented methods which describe the physical properties of microwave circuits and optical structures are an indispensable tool to avoid costly and time-consuming redesign cycles. Commonly the electromagnetic characteristics of the structures are described by the scattering matrix which is extracted from the orthogonal decomposition of the electric field. The electric field is the solution of an eigenvalue and a boundary value problem for Maxwell’s equations in the frequency domain. We discretize the equations with staggered orthogonal grids using the Finite Integration Technique (FIT). Maxwellian grid equations are formulated for staggered nonequidistant rectangular grids and for tetrahedral nets with corresponding dual Voronoi cells. The interesting modes of smallest attenuation are found solving a sequence of eigenvalue problems of modified matrices. To reduce the execution time for high-dimensional problems a coarse and a fine grid is used. The calculations are carried out, using two levels of parallelization. The discretized boundary value problem, a large-scale system of linear algebraic equations with different right-hand sides, is solved by a block Krylov subspace method with various preconditioning techniques. Special attention is paid to the Perfectly Matched Layer boundary condition (PML) which causes non physical modes and a significantly increased number of iterations in the iterative methods.
Efficient Current Injection Into Single Quantum Dots Through Oxide-Confined p-n-Diodes
2016, Kantner, Markus, Bandelow, Uwe, Koprucki, Thomas, Schulze, Jan-Hindrik, Strittmatter, Andre, Wunsche, Hans-Jurgen
Current injection into single quantum dots embedded in vertical p-n-diodes featuring oxide apertures is analyzed in the low-injection regime suitable for single-photon emitters. The experimental and theoretical evidence is found for a rapid lateral spreading of the carriers after passing the oxide aperture in the conventional p-i-n-design. By an alternative design employing p-doping up to the oxide aperture, the current spreading can be suppressed resulting in an enhanced current confinement and increased injection efficiencies, both, in the continuous wave and under pulsed excitation.
Boundary conditions for electrochemical interfaces
2017, Landstorfer, Manuel
Consistent boundary conditions for electrochemical interfaces, which cover double layer charging, pseudo-capacitive effects and transfer reactions, are of high demand in electrochemistry and adjacent disciplines. Mathematical modeling and optimization of electrochemical systems is a strongly emerging approach to reduce cost and increase efficiency of super-capacitors, batteries, fuel cells, and electro-catalysis. However, many mathematical models which are used to describe such systems lack a real predictive value. Origin of this shortcoming is the usage of oversimplified boundary conditions. In this work we derive the boundary conditions for some general electrode-electrolyte interface based on non-equilibrium thermodynamics for volumes and surfaces. The resulting equations are widely applicable and cover also tangential transport. The general framework is then applied to a specific material model which allows the deduction of a current-voltage relation and thus a comparison to experimental data. Some simplified 1D examples show the range of applicability of the new approach.
The Effect of Chirp on Pulse Compression at a Group Velocity Horizon
2016, Babushkin, Ihar, Amiranashvili, Shalva, Bree, Carsten, Morgner, Uwe, Steinmeyer, Gunter, Demircan, Ayhan
Group-velocity matched cross-phase modulation between a fundamental soliton and a dispersive wave packet has been previously suggested for optical switching applications similar to an optical transistor. Moreover, the nonlinear interaction in the resulting group-velocity horizon can be exploited for adiabatic compression of the soliton down into the few-cycle regime. Here, we study the delicate phase- and frequency-matching mechanism of soliton/dispersive wave interaction by controlling the input chirp of the dispersive wave. We demonstrate that such a modification of the dispersive wave can significantly alter the soliton dynamics. In particular, we show that it allows a decrease of the fiber length needed for the best compression and, to some extent, control of the trajectory of the soliton. The mechanism of such an influence is related to the modification of the phase-matching condition between the soliton and dispersive wave.
Toward mixed-element meshing based on restricted Voronoi diagrams
2014, Pellerin, J., Lévy, B., Caumon, G.
In this paper we propose a method to generate mixed-element meshes (tetrahedra, triangular prisms, square pyramids) for B-Rep models. The vertices, edges, facets, and cells of the final volumetric mesh are determined from the combinatorial analysis of the intersections between the model components and the Voronoi diagram of sites distributed to sample the model. Inside the volumetric regions, Delaunay tetrahedra dual of the Voronoi diagram are built. Where the intersections of the Voronoi cells with the model surfaces have a unique connected component, tetrahedra are modified to fit the input triangulated surfaces. Where these intersections are more complicated, a correspondence between the elements of the Voronoi diagram and the elements of the mixedelement mesh is used to build the final volumetric mesh. The method which was motivated by meshing challenges encountered in geological modeling is demonstrated on several 3D synthetic models of subsurface rock volumes.