Dynamic homogenisation of Maxwell’s equations with applications to photonic crystals and localised waveforms on gratings

Maling, BJ, Colquitt, DJ ORCID: 0000-0001-5637-1626 and Craster, RV (2016) Dynamic homogenisation of Maxwell’s equations with applications to photonic crystals and localised waveforms on gratings. Wave Motion.

Text 1-s2.0-S016521251630138X-main.pdf - Published version Download (1MB)

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.

Item Type:	Article
Uncontrolled Keywords:	math.MP, math-ph, math-ph
Depositing User:	Symplectic Admin
Date Deposited:	23 Aug 2017 07:45
Last Modified:	19 Jan 2023 06:57
DOI:	10.1016/j.wavemoti.2016.11.003
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3009093