@article{Schnitzer:2017:10.1137/16M107222X,
author = {Schnitzer, O and Craster, RV},
doi = {10.1137/16M107222X},
journal = {SIAM Journal on Applied Mathematics},
pages = {2119--2135},
title = {Bloch waves in an arbitrary two-dimensional lattice of subwavelength  Dirichlet scatterers},
url = {http://dx.doi.org/10.1137/16M107222X},
volume = {77},
year = {2017}
}

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TY  - JOUR
AB  - We study waves governed by the planar Helmholtz equation, propagating in aninfinite lattice of subwavelength Dirichlet scatterers, the periodicity beingcomparable to the wavelength. Applying the method of matched asymptoticexpansions, the scatterers are effectively replaced by asymptotic pointconstraints. The resulting coarse-grained Bloch-wave dispersion problem issolved by a generalised Fourier series, whose singular asymptotics in thevicinities of scatterers yield the dispersion relation governing modes that arestrongly perturbed from plane-wave solutions existing in the absence of thescatterers; there are also empty-lattice waves that are only weakly perturbed.Characterising the latter is useful in interpreting and potentially designingthe dispersion diagrams of such lattices. The method presented, that simplifiesand expands on Krynkin & McIver [Waves Random Complex, 19 347 2009], could beapplied in the future to study more sophisticated designs entailing resonantsubwavelength elements distributed over a lattice with periodicity on the orderof the operating wavelength.
AU  - Schnitzer,O
AU  - Craster,RV
DO  - 10.1137/16M107222X
EP  - 2135
PY  - 2017///
SN  - 0036-1399
SP  - 2119
TI  - Bloch waves in an arbitrary two-dimensional lattice of subwavelength  Dirichlet scatterers
T2  - SIAM Journal on Applied Mathematics
UR  - http://dx.doi.org/10.1137/16M107222X
UR  - http://arxiv.org/abs/1604.07792v1
UR  - http://hdl.handle.net/10044/1/52571
VL  - 77
ER  - 

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