Journal article
Bloch modes and evanescent modes of photonic crystals: Weak form solutions based on accurate interface triangulation
Crystals, Vol.5(1), pp.14-44
2015
Abstract
We propose a new approach to calculate the complex photonic band structure, both purely dispersive and evanescent Bloch modes of a finite range, of arbitrary three-dimensional photonic crystals. Our method, based on a well-established plane wave expansion and the weak form solution of Maxwell’s equations, computes the Fourier components of periodic structures composed of distinct homogeneous material domains from a triangulated mesh representation of the inter-material interfaces; this allows substantially more accurate representations of the geometry of complex photonic crystals than the conventional representation by a cubic voxel grid. Our method works for general two-phase composite materials, consisting of bi-anisotropic materials with tensor-valued dielectric and magnetic permittivities " and and coupling matrices . We demonstrate for the Bragg mirror and a simple cubic crystal closely related to the Kelvin foam that relatively small numbers of Fourier components are sufficient to yield good convergence of the eigenvalues, making this method viable, despite its computational complexity. As an application, we use the single gyroid crystal to demonstrate that the consideration of both conventional and evanescent Bloch modes is necessary to predict the key features of the reflectance spectrum by analysis of the band structure, in particular for light incident along the cubic [111] direction.
Details
- Title
- Bloch modes and evanescent modes of photonic crystals: Weak form solutions based on accurate interface triangulation
- Authors/Creators
- M. Saba (Author/Creator)G.E. Schröder-Turk (Author/Creator)
- Publication Details
- Crystals, Vol.5(1), pp.14-44
- Publisher
- MDPI
- Identifiers
- 991005544668107891
- Copyright
- 2015 by the authors
- Murdoch Affiliation
- Murdoch University
- Language
- English
- Resource Type
- Journal article
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InCites Highlights
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- Collaboration types
- Domestic collaboration
- International collaboration
- Citation topics
- 5 Physics
- 5.38 Optical Electronics & Engineering
- 5.38.991 Photonic Crystals
- Web Of Science research areas
- Crystallography
- Materials Science, Multidisciplinary
- ESI research areas
- Materials Science