Bastian Bandlow

Effective Modeling of Double Negative Metamaterial Macrostructures

This paper presents a numerical procedure applied to the modeling of double negative metamaterial (MTM) structures. At the unit-cell level, the properties of the MTM are described by the extracted isotropic constitutive parameters, dispersion diagrams, and higher order modes analysis. The information gathered at the unit-cell level is used to characterize and homogenize the MTM macrostructure. By comparison of the simulation results for the effective and detailed macrostructures models, the applicability of this approach is confirmed and the significant savings of numerical costs are pointed out.

Analysis of Single-Cell Modeling of Periodic Metamaterial Structures

We propose a comparison of two approaches to analyze the periodic arrays of left-handed metamaterials by field simulations in a single unit cell. First, a scattering matrix analysis in time domain is able to produce broadband results. The set of transfer functions between a small number of input and output ports of the unit cell is able to describe its macroscopic behavior, where, however, the appearance of higher order modes is systematically neglected. As a reference result with respect to this issue, an eigenvalue analysis with periodic boundary conditions provides one point of the dispersion relation of the array per simulation run. We show how these results can be transformed into each other, and present a quantitative analysis of the impact of higher order modes on the effective array properties.

An Improved Jacobi-Davidson Method for the Computation of Selected Eigenmodes in Waveguide Cross Sections

Numerical simulation of open structures requires the truncation of the computational domain and the definition of appropriate boundary conditions. However, any artificial boundary at finite distances causes additional undesired modes in the eigenanalysis of waveguides which must be excluded from the computed spectrum. We propose an extension of the Jacobi-Davidson method by introducing a special weighting function that enables a reliable suppression of undesired eigenmodes already during the solution process. Moreover, the number of iteration steps as well as the computation time can be drastically reduced by this process. We show the improvement of efficiency by means of an eigenmode computation in a photonic crystal fiber discretized by the finite integration technique.

Experimental Study of Subwavelength Waveguides Loaded by Electric and Magnetic Resonant Scatterer Arrays

The novel idea of the subwavelength waveguide transmission presented in this work relies on the insertion of electric and magnetic scatterer arrays in a rectangular waveguide. The transmission below waveguide cutoff takes place in the form of forward or backward waves, depending on the type and orientation of the inserted resonant elements. The design, fabrication and measurement of the loaded waveguides is described in this paper. The experimental results are compared with the numerical simulations and referred to the theoretical proposals known from the literature.

FIT & FLAME for sharp edges in electrostatics

We compare a modified edge correction of the Finite Integration Technique (FIT) with the Flexible Local Approximation MEthods (FLAME). The electrostatic field near a metallic edge is found numerically using both methods on Cartesian computational grids, and compared with the analytical solution. The accuracy and order of convergence are analyzed.

Computational analysis of whispering gallery modes in flat dielectric disks

Whispering gallery modes of a flat dielectric disk are studied by means of analytical and numerical computational methods based on the finite integration technique. The results are compared to a high accuracy measurement. The frequently used semi-analytical method of effective refractive index has certain weaknesses in finding accurate eigenfrequencies and quality factors.

Sensitivity approach for eigenmode characterization of structures with open boundary conditions

The computational models of open resonant nanophotonic structures include perfectly matched layers in order to realize a proper transition to free-space for the electromagnetic waves. As a consequence, the eigenvalue spectrum is spoilt by unwanted eigenmodes which are trapped within these layers. In the context of the finite integration technique we apply a computational inexpensive sensitivity analysis in order to identify those undesired eigenmodes.

Validation of ray optics capability to analyze the transfer behavior of bent optical slab waveguides

Integrated optical waveguides on PCB level are a promising technology to enhance data transfer rates. For minimal tolerance requirements these waveguides are multimodal, accordingly ray optical methods are used to analyze the transfer behavior. In this context the limits of ray optical methods are not well-known. It is the aim of this work to validate these methods by comparison with a wave analysis of bent dielectric slab waveguides. This analysis uses quasi-guided modes that are appropriate to simulate the optical power flow after passing a 90° bend. The fields of a Gaussian beam serve as reference source.

Metamaterial Loaded Waveguides for Miniaturized Filter Applications

The metamaterial loaded waveguides offer the possibility to obtain desired transmission characteristics below the cutoff frequency of the hollow waveguide. This property allows for the design and fabrication of narrowband and broadband miniaturized waveguide filters. The metamaterial inclusions are designed with CAD tools and fabricated in the form of resonant elements arrays loading the X-band rectangular waveguide. The experimental results are compared with the simulations validating the proposed design approach. Index Terms – Metamaterials, Waveguide Filters

Mode Selecting Eigensolvers for 3D Computational Models

For the computation of interior eigenpairs an educated initial guess on the eigenvalue is mandatory in general. The convergence behavior of eigensolvers can be improved by using a starting vector, which should be a reasonable approximation of the searched eigenvector. However, these two provisions do not lead necessarily to the searched eigenpair. We propose an extended selection strategy for the Ritz pairs occurring within the Jacobi-Davidson eigensolver algorithm and compare its performance with the Rayleigh quotient iteration. A complex unsymmetric standard eigenvalue problem resulting from a finite integration discretization of a dielectric disk in free-space serves for numerical experiments.