The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.

Computational Methods for Finite Thickness Photonic Crystals

Karri Varis

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Electrical and Communications Engineering for public examination and debate in Auditorium S4 at Helsinki University of Technology (Espoo, Finland) on the 2nd of December, 2005, at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-7938-X)   [398 KB]
Dissertation is also available in print (ISBN 951-22-7937-1)


We develop a computational algorithm for finite thickness photonic crystals and apply it to photonic crystal slabs and artificial opals. The algorithm is not limited to solving only photonic crystals but can be applied to any electromagnetic problem, which is periodic in a plane and has a finite thickness in the perpendicular direction. An application in cylindrical coordinates is also presented. The method is based on the diagonalized form of Maxwell's equations, in which one spatial direction is distinguished and isolated. We show that this formulation is especially suitable for problems, which are periodic along two and non-periodic along the third axis. The fields are expanded in a combination of several bases, planewaves in the transversal plane, finite differences and eigenvectors in the perpendicular direction. The method is applied to both eigenmode and excitation problems. Furthermore, we develop an efficient scheme for computing the reflection of arbitrarily shaped and polarised beams from the surface of a periodic media. A great emphasis is laid on accuracy and efficiency. The resulting equations are solved using iterative techniques together with problem adapted, operator level preconditioners. Finally, we compare the computations to measurement results obtained from artificial opals.

This thesis consists of an overview and of the following 4 publications:

  1. K. Varis, A. R. Baghai-Wadji, A 2D Pseudo-Spectral Approach of Photonic Crystal Slabs, ACES Journal, 20, 107-118 (2005). © 2005 Applied Computational Electromagnetics Society (ACES). By permission.
  2. K. Varis, A. R. Baghai-Wadji, A Novel 3D Pseudo-Spectral Analysis of Photonic Crystal Slabs, ACES Journal, 19, 101-111 (2004). © 2004 Applied Computational Electromagnetics Society (ACES). By permission.
  3. K. Varis, A. R. Baghai-Wadji, Pseudo-Spectral Analysis of Radially-Diagonalized Maxwell's Equations in Cylindrical Co-Ordinates, Optics Express, 11, 3048-3062 (2003). © 2003 Optical Society of America (OSA). By permission.
  4. K. Varis, M. Mattila, S. Arpiainen, J. Ahopelto, F. Jonsson, C. M. Sotomayor Torres, M. Egen, R. Zentel, Reflection of Focused Beams from Opal Photonic Crystals, Optics Express, 13, 2653-2667 (2005). © 2005 Optical Society of America (OSA). By permission.

Keywords: photonic crystals, computational electromagnetics, synthetic opals

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© 2005 Helsinki University of Technology

Last update 2011-05-26