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DFG Research Center MATHEON
Mathematics for key technologies

Design of nano-photonic devices - D9

nano-optics Konrad-Zuse-Zentrum Berlin

Head of the project: Frank Schmidt
Members of the project: Sven Burger
Therese Pollok
Achim Schädle
Lin Zschiedrich
Support: DFG Research Center MATHEON "Mathematics for Key Technologies"


Background.

Nano photonic structures offer the possibility to manipulate light on lengthscales of the order of its wavelength . This opens immense prospects for the miniaturization of optical components and other technological applications. The properties of such structures are generally critically dependent on the wavelength of the propagating light. Thus, for the design of many of their applications it is crucial to use simulation tools with high accuracy, speed, and reliability. The project has two main focuses:
Lens Gaussian beam focussed by a lens.

Scattering on unbounded domains with non-homogenous exterior.

Nano-photonic devices are most often 'infinite'. Consider for example the coupling of optical fibres with a photonic crystal (PhC). Thus we have to solve a scattering problem with an unbounded scatterer. The pole condition approach serves on one hand as a theoretical tool to establish existence and uniqueness of a solution. On the other hand it is used to obtain a solution numerically.
Using the slowly varying envelope approximation the Helmholtz equation reduces to the free time dependent Schrödinger equation, with the time axis the direction of propagation, cf. project D11.

For more information see the photonic devices project page of the Computational Nano-Optics group CNO.

MCR Coupling MCR Coupling
Resonant coupling of two horizontal waveguides by a square microcavity.

Eigensolutions of Maxwell's equations on unbounded domains.

For the analysis of unperturbed periodic crystals the main tool are band diagrams. To compute these, semi-infinite structures have to be modeled. The aim of this project is to treat the unbounded outer domain with the pole condition approach and to solve the interior problem with adaptive finite elements.

For the computatation of the eigenvalues and eigensolutions we work together with project C4 .

For more information see the photonic fields project page of the Computational Nano-Optics group CNO.

Defect Mode Defect mode in photonic crystal.

Research program.

We address the following two areas of optical chip design:

  • time-harmonic scattering of optical beams on arbitray objects
  • field propagation along waveguides,
with a focus in both topics on the analytical and algortihmical aspects of simulation tools. Together with our partners in industry we develop codes for the fast and reliable design of real-life optical chips. The development of the code is based on "Kaskade". In project A1 our code is used and developed further to solve optimal control problems.

Cooperations.

  • Internal cooperations
    • We performed tests of the eigenvalue-solver SHIRA developed in project C4 on problems of photonic crystal bandstructure calculation.
    • With project C10 we exchange ideas and techniques for modelling nano-structured materials.
    • With D8 the coupling of active components to 3D electric fields is investigated.
    • D14: Computation of dispersion and diffraction properties of photonic crystals.
    • Project D15 applies the tools developed in our project.
  • External Cooperations with other research institutes and industry
    • M. Gander (Universite Genéve, Switzerland): We cooperate on Schwarz waveform relaxation algorithms and optimized Schwarz methods.
    • T. Hohage, L. Nannen (Universität Göttingen), W. Koch (DLR Göttingen): Development of the pole conditio.
    • Ch. Lubich (Universität Tübingen), C. Palencia (Universidad Valladolid, Spain), M. López-Fernández (Universidad Carlos III Madrid, Spain): We work on fast convolution algorithms, that can be used to evaluate exact transparent boundary conditions and on numerical inverse Laplace transform.
    • X. Antoine (U Nancy, France), A. Arnold (TU Wien, Austria), C. Besse (INRIA Futurs, Lille, France) and M. Ehrhardt (WIAS, Berlin): Joint review paper on TBCs for the Schödinger equation
    • M. Wegener and S. Linden (CFN Karlsruhe): Simulation of metamaterials
    • H. Heidrich (HHI, Berlin): The application of metamaterials in integrated optics is investigated.
    • O. Hess (University Surrey, England): Design of integrated optical devices
    • D. Davidov (University Jerusalem, Israel): Quasi crystals that are constructed from Penrose tilings are currently investigated.
    • B. Bodermann (PTB, Braunschweig), F. Scholz (PTB, Berlin): Quantitative microscopy
    • A. Erdmann (FHI für Integrierte Systeme und Bauelementetechnologie, Erlangen): Photo-lithography processes
    • JCMwave GmbH, Putzbrunn: The research codes developed in the project provided the basis for a reimplementaion in JCMgeo and JCMsolve.
    • Ch. Nölscher (Qimonda AG, Dresden): Simulation of photomasks
    • U. Dersch (Advanced Mask and Technology Center (AMTC), Dresden): Scatterometry for EUV masks
    • A. Kühlmann (Cadence Design Systems, Inc, San Jose): Model order reduction for lithography mask simulation

Literature.

For an up to date list of publications and further information see the following page .
This file was last modified 26.02.2009