Complex waves on periodic arrays of lossy and lossless permeable spheres: 1. Theory

Shore, Robert A.; Yaghjian, Arthur D.

doi:10.1029/2011rs004859

Cited by 24 publications

(45 citation statements)

References 37 publications

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“…In practice, we fix the direction of propagation along one of the principal axes of the 3D lattice (in the following we assume k kx) and find numerically, for each angular frequency ω, modes with complex wavenumber propagating inside the periodic array with the electric or magnetic field polarized both in the transverse (along y or z) and in the longitudinal (along x) directions. We want to stress that the analysis of complex wavenumber is not trivial and only a few studies are devoted to that, such as [23,35,36]. This is a further motivation for our present work.…”

Section: Modes Supported By the Metamaterials Arraymentioning

confidence: 99%

Artificial magnetism at terahertz frequencies from three-dimensional lattices of TiO_2 microspheres accounting for spatial dispersion and magnetoelectric coupling

et al. 2014

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We employ the generalized Lorentz-Lorenz method to investigate how both magnetoelectric coupling and spatial dispersion influence the artificial magnetic capabilities at terahertz frequencies of the representative case of a metamaterial consisting of a three-dimensional (3D) lattice of TiO 2 microspheres. The complex wavenumber dispersion relations pertaining to modes supported by the array, traveling along one of the principal axes of the array with electric or magnetic field polarized transversely and longitudinally (with respect to the mode traveling direction), are studied and thoroughly characterized. One mode with transverse polarization is dominant at any given frequency for the analyzed dimensions, proving that the 3D lattice can be treated as a homogeneous medium with defined electromagnetic material parameters. We show, however, that bianisotropy is a direct consequence of magnetoelectric coupling, and the dyadic expressions of both effective and equivalent material parameters are derived. In particular, we analyze the effect of spatial dispersion on the effective parameters relative to a composite material made by a 3D lattice of TiO 2 microspheres with filling fraction around 30% and near the first Mie magnetic dipolar resonance. Finally, we homogenize the metamaterial in terms of equivalent index and impedance, and by comparison with full-wave simulations, we explain the presence of the unphysical antiresonance permittivity behavior observed in previous work.

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Section: Modes Supported By the Metamaterials Arraymentioning

confidence: 99%

Artificial magnetism at terahertz frequencies from three-dimensional lattices of TiO_2 microspheres accounting for spatial dispersion and magnetoelectric coupling

et al. 2014

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“…In that approximation guided waves in arrays of magnetodielectric spheres were first considered by Shore and Yaghjian [66,67] who derived the dispersion relation and computed the dispersion curves for dipolar waves. Recently a more tractable form of the dispersion equations was presented by the same authors [68] with the use of the polilogarithmic functions. The dipolar waves in arrays of Si dielectric nanospheres were thoroughly analyzed in [21].…”

Section: Light Guiding Above the Light Linementioning

confidence: 99%

“…The dispersion curves were computed by solving the dispersion equations f d,m (k, β) = 0, where k is the vacuum wave number k = ω/c, and β is the Bloch wave number, while the subscripts d, m designate either dipole [21,68], or multipole [24] dispersion relations. For brevity we do not present the exact dispersion relations f d,m (k, β) = 0.…”

Section: Light Guiding Above the Light Linementioning

confidence: 99%

Light Trapping above the Light Cone in One-Dimensional Arrays of Dielectric Spheres

2017

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Abstract:We demonstrate bound states in the radiation continuum (BSC) in a linear periodic array of dielectric spheres in air above the light cone. We classify the BSCs by orbital angular momentum m = 0, ±1, ±2 according to the rotational symmetry of the array, Bloch wave vector β directed along the array according to the translational symmetry, and polarization. The most simple symmetry protected BSCs have m = 0, β = 0 and occur in a wide range of the radius of the spheres and dielectric constant. More sophisticated BSCs with m = 0, β = 0 exist only for a selected radius of spheres at fixed dielectric constant. We also find robust Bloch BSCs with β = 0, m = 0. All BSCs reside within the first but below the other diffraction continua. We show that the BSCs can be easily detected by bright features in scattering of different plane waves by the array as dependent on type of the BSC. The symmetry protected TE/TM BSCs can be traced by collapsing Fano resonance in cross-sections of normally incident TE/TM plane waves. When plane wave with circular polarization with frequency tuned to the bound states with OAM illuminates the array the spin angular momentum of the incident wave transfers into the orbital angular momentum of the BSC. This, in turn, gives rise to giant vortical power currents rotating around the array. Incident wave with linear polarization with frequency tuned to the Bloch bound state in the continuum induces giant laminar power currents. At last, the plane wave with linear polarization incident under tilt relative to the axis of array excites Poynting currents spiralling around the array. It is demonstrated numerically that quasi-bound leaky modes of the array can propagate both stationary waves and light pulses to a distance of 60 wavelengths at the frequencies close to the bound states in the radiation continuum. A semi-analytical estimate for decay rates of the guided waves is found to match the numerical data to a good accuracy.

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“…3(b) and Ref. [30] for the case of the particles with same permittivity and permeability). Since Purcell factors are proportional to the density of photonic states, very large values of PF cannot be achieved in the chain of core-shell nanoparticles with fully spectrally overlapping MD and ED resonances.…”

Section: Yagi-uda Core-shell Nanoantennasmentioning

confidence: 99%

“…The analytical dipole model for a one-dimensional array of identical particles is formulated as follows [34][35][36][37] :…”

Section: Appendix A: Theoretical Modelmentioning

confidence: 99%

Dynamically reconfigurable metal-semiconductor Yagi-Uda nanoantenna

et al. 2017

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We propose a novel type of tunable Yagi-Uda nanoantenna composed of metal-dielectric (AgGe) core-shell nanoparticles. We show that, due to the combination of two types of resonances in each nanoparticle, such hybrid Yagi-Uda nanoantenna can operate in two different regimes. Besides the conventional nonresonant operation regime at low frequencies, characterized by highly directive emission in the forward direction, there is another one at higher frequencies caused by hybrid magneto-electric response of the core-shell nanoparticles. This regime is based on the excitation of the van Hove singularity, and emission in this regime is accompanied by high values of directivity and Purcell factor within the same narrow frequency range. Our analysis reveals the possibility of flexible dynamical tuning of the hybrid nanoantenna emission pattern via electron-hole plasma excitation by 100 femtosecond pump pulse with relatively low peak intensities ∼200 MW/cm 2 .

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Complex waves on periodic arrays of lossy and lossless permeable spheres: 1. Theory

Cited by 24 publications

References 37 publications

Artificial magnetism at terahertz frequencies from three-dimensional lattices of TiO_2 microspheres accounting for spatial dispersion and magnetoelectric coupling

Artificial magnetism at terahertz frequencies from three-dimensional lattices of TiO_2 microspheres accounting for spatial dispersion and magnetoelectric coupling

Light Trapping above the Light Cone in One-Dimensional Arrays of Dielectric Spheres

Dynamically reconfigurable metal-semiconductor Yagi-Uda nanoantenna

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