Asymptotic network models of subwavelength metamaterials formed by closely packed photonic and phononic crystals

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Title: Asymptotic network models of subwavelength metamaterials formed by closely packed photonic and phononic crystals
Authors: Vanel, AL
Schnitzer, O
Craster, RV
Item Type: Journal Article
Abstract: We demonstrate that photonic and phononic crystals consisting of closely spaced inclusions constitute a versatile class of subwavelength metamaterials. Intuitively, the voids and narrow gaps that characterise the crystal form an interconnected network of Helmholtz-like resonators. We use this intuition to argue that these continuous photonic (phononic) crystals are in fact asymptotically equivalent, at low frequencies, to discrete capacitor-inductor (mass-spring) networks whose lumped parameters we derive explicitly. The crystals are tantamount to metamaterials as their entire acoustic branch, or branches when the discrete analogue is polyatomic, is squeezed into a subwavelength regime where the ratio of wavelength to period scales like the ratio of period to gap width raised to the power $1/4$ ; at yet larger wavelengths we accordingly find a comparably large effective refractive index. The fully analytical dispersion relations predicted by the discrete models yield dispersion curves that agree with those from finite-element simulations of the continuous crystals. The insight gained from the network approach is used to show that, surprisingly, the continuum created by a closely packed hexagonal lattice of cylinders is represented by a discrete honeycomb lattice. The analogy is utilised to show that the hexagonal continuum lattice has a Dirac-point degeneracy that is lifted in a controlled manner by specifying the area of a symmetry-breaking defect.
Issue Date: 28-Nov-2017
Date of Acceptance: 10-Nov-2017
ISSN: 1286-4854
Publisher: European Physical Society
Journal / Book Title: Europhysics Letters: a letters journal exploring the frontiers of physics
Volume: 119
Copyright Statement: ©2017 IOP Publishing Ltd.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Funder's Grant Number: EP/L024926/1
Keywords: Science & Technology
Physical Sciences
Physics, Multidisciplinary
01 Mathematical Sciences
02 Physical Sciences
Fluids & Plasmas
Publication Status: Published
Article Number: 64002
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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