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Multiscale FEM for Photonic Crystal Structures
| Project Leader: | Prof. Dr. Ch. Schwab, Prof. Dr. D. Kressner |
| Researchers: |
Holger Brandsmeier (Seminar for Applied Mathematics, ETH Zurich) Dr. Kersten Schmidt (INRIA Paris-Rocquencourt) |
Description
Photonic Crystals (PhC) are dielectric materials used in optical signal processing to mold the flow of light. PhCs can guide an electromagnetic wave around bends, slow its group velocity and reflect or transmit the wave depending on its frequency. From a mathematical perspective PhCs are challenging, as they are described by a locally periodic dielectricity. This high variation makes numerical simulations of realistic PhC
structures with many replications of the periodic pattern infeasible with standard discretization techniques such as FDTD or h-, p- and hp-FEM. On the other hand the solutions for a globally periodic PhC can be computed numerically and are known to be the Bloch- (and Floquet-) modes.
The project aims at developing a Multiscale FEM based on the microscopic Bloch modes and macroscopic piecewise polynomials to efficiently simulate large PhC structures.
Research Reports
- H. Brandsmeier, K. Schmidt, Ch. Schwab, A multiscale hp-FEM for 2D photonic crystal band, SAM Report 2010/12
http://www.sam.math.ethz.ch/reports/2010/12
Contacts
Prof. Christoph Schwab
Prof. Daniel Kressner
Holger Brandsmeier
Dr. Kersten Schmidt
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