@article{Maling:2016:10.1016/j.wavemoti.2016.11.003,
author = {Maling, B and Colquitt, D and Craster, RV},
doi = {10.1016/j.wavemoti.2016.11.003},
journal = {Wave Motion},
pages = {35--49},
title = {Dynamic homogenisation of Maxwell’s equations with applications to photonic crystals and localised waveforms on gratings},
url = {http://dx.doi.org/10.1016/j.wavemoti.2016.11.003},
volume = {69},
year = {2016}
}

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TY  - JOUR
AB  - A two-scale asymptotic theory is developed to generate continuum equations that model the macroscopic be-haviour  of  electromagnetic  waves  in  periodic  photonic  structures  when  the  wavelength  is  not  necessarily  longrelative to the periodic cell dimensions;  potentially highly-oscillatory short-scale detail is encapsulated throughintegrated quantities.  The resulting equations include tensors that represent effective refractive indices near bandedge frequencies along all principal axes directions, and these govern scalar functions providing long-scale mod-ulation of short-scale Bloch eigenstates,  which can be used to predict the propagation of waves at frequenciesoutside of the long wavelength regime; these results are outside of the remit of typical homogenisation schemes.The theory we develop is applied to two topical examples, the first being the case of aligned dielectric cylin-ders, which has great importance in modelling photonic crystal fibres.  Results of the asymptotic theory are veri-fied against numerical simulations by comparing photonic band diagrams and evanescent decay rates for guidedmodes.  The second example is the propagation of electromagnetic waves localised within a planar array of di-electric spheres; at certain frequencies strongly directional propagation is observed, commonly described as dy-namic anisotropy.  Computationally this is a challenging three-dimensional calculation, which we perform, andthen demonstrate that the asymptotic theory captures the effect, giving highly accurate qualitative and quantitativecomparisons as well as providing interpretation for the underlying change from elliptic to hyperbolic behaviour.
AU  - Maling,B
AU  - Colquitt,D
AU  - Craster,RV
DO  - 10.1016/j.wavemoti.2016.11.003
EP  - 49
PY  - 2016///
SN  - 0165-2125
SP  - 35
TI  - Dynamic homogenisation of Maxwell’s equations with applications to photonic crystals and localised waveforms on gratings
T2  - Wave Motion
UR  - http://dx.doi.org/10.1016/j.wavemoti.2016.11.003
UR  - http://hdl.handle.net/10044/1/42548
VL  - 69
ER  - 

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