@article{Vanel:2017:119/64002,
author = {Vanel, AL and Schnitzer, O and Craster, RV},
doi = {119/64002},
journal = {Europhysics Letters: a letters journal exploring the frontiers of physics},
title = {Asymptotic network models of subwavelength metamaterials formed by closely packed photonic and phononic crystals},
url = {http://dx.doi.org/10.1209/0295-5075/119/64002},
volume = {119},
year = {2017}
}

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TY  - JOUR
AB  - 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.
AU  - Vanel,AL
AU  - Schnitzer,O
AU  - Craster,RV
DO  - 119/64002
PY  - 2017///
SN  - 1286-4854
TI  - Asymptotic network models of subwavelength metamaterials formed by closely packed photonic and phononic crystals
T2  - Europhysics Letters: a letters journal exploring the frontiers of physics
UR  - http://dx.doi.org/10.1209/0295-5075/119/64002
UR  - http://hdl.handle.net/10044/1/53423
VL  - 119
ER  - 

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