Nonlocal electrodynamics of homogenized metal-dielectric photonic crystals

Abstract

The nonlocal effective permittivity tensor for photonic crystals (PCs), having dielectric and metallic inclusions in the unit cell, is calculated and analyzed within the homogenization theory based on the Fourier formalism and the form-factor division approach. A method allowing us to extract the effective bianisotropic metamaterial parameters (permeability and chirality) from the wave vector dependence of the nonlocal effective dielectric response is proposed. Both the original nonlocal dielectric response parameters and the new bianisotropic metamaterial ones reproduce the photonic band structure of the artificial crystal far beyond the long wavelength limit and for a wide class of metal-dielectric structures. To calculate the optical spectra (reflection and transmission) of finite-size PC, the nonlocal homogenization approach is extended with the method of expansion into photonic bulk-modes (Bloch waves). The application of the developed theory is illustrated with well-known forms of metallic inclusions (slabs, thin wires, split-ring resonators) and experimentally confirmed with novel designs based on metallic crosses.

A Superspace Formalism for the Electromagnetism of Generic Nonlocal Continuous Metamaterials: Principal Structures and Applications

“…The idea of exploiting nonlocality to design and develop a new generation of metamaterials (MTMs) exhibiting novel EM behaviour has also received a revival in recent years, though the basic concept in itself is not completely new, going back to at least [4] and possibly earlier. Recent examples of research focused in explicating nonlocal behaviour to harness the associated new physics include spatial dispersion in photonic crystals [69], wire media [70]- [73], semiconductor nanoparticles [74]- [77], optically nonlinear liquids [78], hyperbolic metamaterials [79], layered dielectric-metal structures [80], [81] and thin films [82], plasma-based metamaterials [83]- [85], quantum wells [86], soliton interactions with matter [87]- [92], superconducting films [93] and circuits [94], plasmonic devices and structures [95]- [97], nanocubes [98], cloaking [99], Chern metamaterials [100] and superconductors [101], dispersion management profiles [22], [102], biomedical applications in materials [103], and nonlocal uniaxial metamaterials [104].…”

On the Topology of Nonlocal Field Theories of Material Continua

“…2) A Simple Explanation of How Nonlocality Emerges in Excitonic Semiconductor: They key to the origin of nonlocality is the scenario when the excitation photon has an energy ω that is greater than the minimum exciton energy (131). In the case where ω > ω e ,…”

On the Topology of Nonlocal Field Theories of Material Continua

“…7) Novel Systems and Devices with New Electromagnetic Behaviour: The idea of exploiting nonlocality to design and develop a new generation of metamaterials (MTMs) exhibiting novel EM behaviour has also received a revival in recent years [31], [46], [130], though the basic concept in itself is not completely new, going back to at least the 1980s and possibly earlier [16] . Recent examples of research focused in explicating nonlocal behaviour to harness the associated new physics include spatial dispersion in photonic crystals [131], wire media [132]- [135], semiconductor nanoparticles [136]- [139], optically nonlinear liquids [140], hyperbolic metamaterials [141], layered dielectric-metal structures [142], [143] and thin films [144], plasma-based metamaterials [145]- [147], quantum wells [148], soliton interactions with matter [149]- [154], superconducting films [155] and circuits [156], plasmonic devices and structures [157]- [159], nanocubes [160], cloaking [161], Chern metamaterials [162] and superconductors [163], 31 Cf. Sec.…”