The homogenisation of Maxwell's equations with applications to photonic crystals and localised waveforms on metafilms

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Title: The homogenisation of Maxwell's equations with applications to photonic crystals and localised waveforms on metafilms
Authors: Maling, BJ
Colquitt, DJ
Craster, RV
Item Type: Working Paper
Abstract: An asymptotic theory is developed to generate equations that model the global behaviour of electromagnetic waves in periodic photonic structures when the wavelength is not necessarily long relative to the periodic cell dimensions; potentially highly-oscillatory short-scale detail is encapsulated through integrated quantities. The theory we develop is then applied to two topical examples, the first being the case of aligned dielectric cylinders, which has great importance in the modelling of photonic crystal fibres. We then consider the propagation of waves in a structured metafilm, here chosen to be a planar array of dielectric spheres. At certain frequencies strongly directional dynamic anisotropy is observed, and the asymptotic theory is shown to capture the effect, giving highly accurate qualitative and quantitative results as well as providing interpretation for the underlying change from elliptic to hyperbolic behaviour.
Issue Date: 7-Jun-2015
URI: http://hdl.handle.net/10044/1/39766
Copyright Statement: © The Author(s) 2015
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/J009636/1
EP/DCT/DC/P49839
EP/L024926/1
Keywords: math-ph
math.MP
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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