University of Twente Student Theses


Accurate Modeling of Light : Propagation inside Photonic Crystals of Increasing Geometric Complexity

Gietema, J.G. (2018) Accurate Modeling of Light : Propagation inside Photonic Crystals of Increasing Geometric Complexity.

Abstract:Photonic crystals are an important class of metamaterials, which are typified by spatially periodic variations of the refractive index commensurate with the wavelength of light. Using a careful selection of the properties, geometry, and topology of the dielectric materials inside the photonic crystal it is possible to manipulate the optical properties of photonic crystals. In particular, 2D and 3D photonic crystals can develop a complete photonic band gap: a range of frequencies where light is forbidden to exist due to interference. Such a gap opens novel routes to manipulate light: by introducing defects in photonic crystals light is trapped, called Anderson localization after Nobel laureate Philip Anderson. With line or point defects one can realize waveguides and cavities that can be applied as narrow band filters, splitters, or channel-drop filters in on-chip optical circuits. For an overview, see [JO08]. In this project, we will develop novel numerical techniques to compute light in a photonic crystal. Recently, a mixed discontinuous Galerkin finite element method for the solution of the Maxwell equations in infinite periodic photonic crystals has been developed, [LU17, DE17]. We will use this DGFEM code DGMax to compute the behaviour of light in a series of photonic crystals of increasing geometric complexity. The main purpose of these computations is to test and validate the numerical method and investigate its potential in accurately and efficiently computing light in photonic crystals. [JO08] J.D. Joannopoulos, S.G. Johnson, J.N. Winn, R.D. Meade, Photonic crystals. Molding the flow of light, 2nd edition, Princeton, 2008. [LU17] Z. Lu, A. Cesmelioglu, J. J. W. Van der Vegt, and Y. Xu, Discontinuous Galerkin Approximations for Computing Electromagnetic Bloch Modes in Photonic Crystals, J. Sci. Comput. 70(2), 922-964 (2017). [DA17] D. Devashish, D. Devashish, 3D Periodic photonic nanostructures with disrupted symmetries, Phd Thesis, University of Twente (2017).
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:02 science and culture in general
Programme:Applied Mathematics MSc (60348)
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