In this section
@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}
}
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 -