Complex electromagnetic responses from simple geometries

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Sähkötekniikan korkeakoulu | Doctoral thesis (article-based)
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Date
2011
Major/Subject
Mcode
Degree programme
Language
en
Pages
134
Series
Aalto University publication series. Doctoral dissertations, 106/2011
Abstract
The electromagnetic properties of a material arise from its intrinsic microstructure, which may often be very complex. However, materials are usually characterized more simply using macroscopic material parameters, electric permittivity and magnetic permeability. This thesis considers the principles of material modeling from the electromagnetics point of view. The analysis is mostly based on electrostatics. The aim of the thesis is to enhance the understanding of the interaction between matter and the electromagnetic fields, and further, the relation between matter and geometry. The contents of the thesis can be divided into three parts. The first part discusses the concepts of polarization and polarizability and considers the electric reponses of particles with different geometries. Polarizabilities of a three-dimensional hemisphere and a two-dimensional half-disk are solved. The second part studies negative material parameters. The emphasis lies on negative permittivity. Interfaces between permittivities of opposite signs are found supporting surface plasmons, or electrostatic resonances. The occurrence of these resonances is especially studied for a hemisphere and a half-disk. Moreover, it is showed that sharp edges with negative permittivity may support unphysically singular field modes, which in numerical simulations can result in non-convergent solutions. The most efficient way to overcome this problem in computational modeling is to slightly round all sharp corners. The third part focuses on homogenization of composite media. Effective material parameters modeling the response of a thin dielectric composite slab are retrieved. Computational homogenization techniques and their limitations are studied. The results indicate that for a successful homogenization, the unit cells of the slab must remain very small compared with the wavelength. Also, the boundary layers of the slab show higher effective permittivity than the corresponding bulk medium.
Description
Supervising professor
Sihvola, Ari
Thesis advisor
Wallen, Henrik
Keywords
permittivity, polarizability, negative material parameters, surface plasmon resonances, metamaterials, tech, homogenization, tech, composite media, tech
Other note
Parts
  • [Publication 1]: H. Kettunen, H. Wallén and A. Sihvola. Polarizability of a dielectric hemisphere. Journal of Applied Physics, vol. 102, no. 4, 044105:1-7, August 2007. (incl. Erratum: J. Appl. Phys., vol. 102, no. 11, 119902, 2007). © 2007 American Institute of Physics (AIP). By permission.
  • [Publication 2]: H. Kettunen, H. Wallén and A. Sihvola. Electrostatic resonances of a negative-permittivity hemisphere. Journal of Applied Physics, vol. 103, no. 9, 094112:1-8, May 2008. © 2008 American Institute of Physics (AIP). By permission.
  • [Publication 3]: H. Kettunen, H. Wallén and A. Sihvola. Electrostatic response of a half-disk. Journal of Electrostatics, vol. 67, no. 6, pp. 890-897, November 2009. © 2009 Elsevier. By permission.
  • [Publication 4]: H. Wallén, H. Kettunen and A. Sihvola. Surface modes of negative-parameter interfaces and the importance of rounding sharp corners. Metamaterials, vol. 2, no. 2-3, pp. 113-121, September 2008. © 2008 Elsevier. By permission.
  • [Publication 5]: H. Kettunen, J. Qi, H. Wallén and A. Sihvola. Homogenization of thin dielectric composite slabs: techniques and limitations. The Applied Computational Electromagnetics Society Journal, vol. 26, no. 3, pp. 179-187, March 2011. © 2011 Applied Computational Electromagnetics Society (ACES). By permission.
  • [Publication 6]: J. Qi, H. Kettunen, H. Wallén and A. Sihvola. Quasi-dynamic homogenization of geometrically simple dielectric composites. The Applied Computational Electromagnetics Society Journal, vol. 25, no. 12, pp. 1036-1045, December 2010. © 2010 Applied Computational Electromagnetics Society (ACES). By permission.
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