Effective-medium theory of surfaces and metasurfaces containing two-dimensional binary inclusions

Abstract

The paper extends one-body effective-medium theory to incorporate the correct second-order interactions in a two-dimensional Maxwell-Garnett theory. The two-body inclusion problem is solved using the averaged dipole moments that are induced by the scattering electromagnetic field on the medium/inclusion system. By incorporating the appropriate polarizability factor in the solutions, conventional right-handed media with binary embeddings are analyzed while a different form for the polarizability term allows the study of the effective properties of a metasurface. In both cases, it is shown that the two-body coefficient to second order in the low area fraction of inclusions is exact, while the corresponding results of the Maxwell-Garnett and Bruggeman theories are incorrect. This is especially true in the superconducting and holes limits, respectively. In the study of metasurfaces, the requirement for electromagnetic screening of the inclusions as well as the requirement needed to achieve the Fröhlich condition are stated. Negative permittivity and permeability are presented for strong-scattering showing negative resonances for a given frequency spectrum. It is shown that these resonances disappear when we derive the weak-scattering limit. The possibility of obtaining doubly negative effective permittivity and permeability is discussed by using an appropriate polarization for the applied electromagnetic field propagating in the metasurface. Finally, the potential difference and hence voltage and capacitance between binary inclusions is determined for surfaces/metasurfaces which allows, in the case of metasurfaces, the behavior of split-ring-type resonators to be investigated.

Alignment‐Free Three‐Dimensional Optical Metamaterials

“…Each panel shows a resonant peak, corresponding to the metasurface resonance, for which increased coupling to higher‐order harmonics is found due to the stronger wave interaction with the metasurface. By increasing the period, the resonance becomes sharper and the coupling coefficient peak grows, which is reflected in a decrease in the decay rate for all higher‐order Floquet modes . Monitoring the fields farther away from the surface, i.e., for increased d , the peak decays exponentially, as expected.…”

Macroscopic optical response and photonic bands

“…Novel effects have been obtained, for example, negative refraction, inverse Doppler effect, optical invisibility cloaking and optical magnetism, etc [14][15][16][17]. 4 Effective medium theories [18][19][20][21][22][23][24][25][26] have been proposed for describing inhomogeneous systems, such as diluted colloidal suspensions in the quasistatic or long-wavelength limit, in terms of a homogeneous macroscopic response. Further developments on homogenization of composites have been proposed [27][28][29][30][31][32][33][34][35] and their limits of validity have been discussed [2,36,37].…”

Mixing rules and the Casimir force between composite systems

“…Examples for which this is an important issue include magnetodielectric photonic crystals [31], metamaterials [32], and surfaces and metasurfaces [33]. Composite materials are also important in colloid chemistry, and there has been recent interest in the optical [34] and structural properties of such materials as a result of advances in the preparation of colloidal crystals and clusters [35], and in the preparation of DNA-linked gold nanoparticle superlattice materials [36].…”