Roland Klose

Domain decomposition method for Maxwell’s equations: Scattering off periodic structures

Abstract We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). An adaptive strategy to determine optimal PML parameters is developed. Thus we can treat Wood anomalies appearing in periodic structures. We focus on the application to typical EUV lithography line masks. Light propagation within the multilayer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer.

JCMmode : An adaptive finite element solver for the computation of leaky modes

We present our simulation tool JCMmode for calculating propagating modes of an optical waveguide. As ansatz functions we use higher order, vectorial elements (Nedelec elements, edge elements). Further we construct transparent boundary conditions to deal with leaky modes even for problems with inhomogeneous exterior domains as for integrated hollow core Arrow waveguides. We have implemented an error estimator which steers the adaptive mesh refinement. This allows the precise computation of singularities near the metals corner of a Plasmon-Polariton waveguide even for irregular shaped metal films on a standard personal computer.

FEM modeling of 3D photonic crystals and photonic crystal waveguides

We present a finite-element simulation tool for calculating light fields in 3D nano-optical devices. This allows to solve challenging problems on a standard personal computer. We present solutions to eigenvalue problems, like Bloch-type eigenvalues in photonic crystals and photonic crystal waveguides, and to scattering problems, like the transmission through finite photonic crystals. The discretization is based on unstructured tetrahedral grids with an adaptive grid refinement controlled and steered by an error-estimator. As ansatz functions we use higher order, vectorial elements (Nedelec, edge elements). For a fast convergence of the solution we make use of advanced multi-grid algorithms adapted for the vectorial Maxwells equations.

Finite Element Simulation of Radiation Losses in Photonic Crystal Fibers

In our work we focus on the accurate computation of light propagation in finite size photonic crystal structures with the finite element method (FEM). We discuss how we utilize numerical concepts like high-order finite elements, transparent boundary conditions and goal-oriented error estimators for adaptive grid refinement in order to compute radiation leakage in photonic crystal fibers and waveguides. Due to the fast convergence of our method we can use it e.g. to optimize the design of photonic crystal structures with respect to geometrical parameters, to minimize radiation losses and to compute attenutation spectra for different geometries. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Adaptive FEM solver for the computation of electromagnetic eigenmodes in 3D photonic crystal structures

Photonic crystals (PhCs) are structures composed of different optical transparent materials with a spatially periodic arrangement of the refractive index [Joa95, Sak01]. Propagating light with a wavelength of the order of the periodicity length of the photonic crystal is significantly influenced by multiple interference effects. The most prominent effect is the opening of photonic bandgaps, in analogy to electronic bandgaps in semiconductor physics or atomic bandgaps in atom optics. Due to the fast progress in nano-fabrication technologies PhCs can be manufactured with high accuracy and with designed materials and geometrical properties. This allows for the miniaturization of optical components and a broad range of technological applications, like, e.g., in telecommunications [MBG04]. The properties of light propagating in PhCs are in general critically dependent on different system parameters, like the geometry of the device and the refractive indices of the present materials. Therefore, the design of photonic crystal devices calls for simulation tools with high accuracy, speed and reliability. In this paper we present a fast and flexible finite-element-solver for the calculation of Bloch-type eigenmodes of PhCs.

Numerical Investigation of Light Scattering off Split-Ring Resonators

It seems to be feasible in the near future to exploit the properties of left-handed metamaterials in the telecom or even in the optical regime. Recently, split ring-resonators (SRRs) have been realized experimentally in the near infrared (NIR) and optical regime.1, 2 In this contribution we numerically investigate light propagation through an array of metallic SRRs in the NIR and optical regime and compare our results to experimental results. We find numerical solutions to the time-harmonic Maxwells equations by using advanced finite-element-methods (FEM). The geometry of the problem is discretized with unstructured tetrahedral meshes. Higher order, vectorial elements (edge elements) are used as ansatz functions. Transparent boundary conditions (a modified PML method3) and periodic boundary conditions4 are implemented, which allow to treat light scattering problems off periodic structures. This simulation tool enables us to obtain transmission and reflection spectra of plane waves which are incident onto the SRR array under arbitrary angles of incidence, with arbitrary polarization, and with arbitrary wavelength-dependencies of the permittivity tensor. We compare the computed spectra to experimental results and investigate resonances of the system.

A multilevel method for the computation of eigenmodes in 3D photonic crystals

We present a multi-level finite-element-eigenmode-solver for the computation of Bloch-type modes in three-dimensional photonic crystals. We adapt the Dohler iteration method to cope with Maxwell-type eigenvalue problems of self-adjoint as well as non-selfadjoint type. Combined with an efficient multigrid method for preconditioning, we can experimentally verify linear complexity in terms of unknowns.

Finite element methods for optical device design

We discuss properties and performance of the finite element approach to the design of photonics components. The typical problem classes scattering and eigenvalue/resonance problems are considered. Special focus lies on the embedding of bounded components into the unbounded and possibly heterogeneous exterior.