Effective medium theory for anisotropic metamaterials

Abstract

We present an effective medium theory that can predict the effective permittivity and permeability of a geometrically anisotropic two-dimensional metamaterial composed with a rectangular array of elliptical cylinders. It is possible to obtain a closed-form analytical solution for the anisotropic effective medium parameters if the aspect ratio of the lattice and the eccentricity of elliptical cylinder satisfy certain conditions. The derived effective medium theory can recover the well-known Maxwell-Garnett results in the quasi-static regime. More importantly, it is valid beyond the long-wavelength limit, where the wavelength in the host medium is comparable to the size of the lattice so that previous anisotropic effective medium theories fail. The validity of the derived effective medium theory is verified by band structure calculations. A real sample of a recent theoretically proposed anisotropic medium with near-zero index to control flux is achieved from the derived effective medium theory and control of electromagnetic waves in the sample is clearly demonstrated. The accuracy of the theory is further systematically studied as material and geometric parameter varies, and we find the derived effective medium theory applies over a large range in the parameter space. Such applicability greatly broadens the applicable realm of the effective medium theory and opens many vistas in the design of structures with desired anisotropic material characteristics.

Paper draft. An updated formal version is under review

References in corpus (4)

• Optical Hyperlens: Far-field imaging beyond the diffraction limit
• Epsilon-Near-Zero (ENZ) Metamaterials and Electromagnetic Sources: Tailoring the Radiation Phase Pattern
• Realization of an all-dielectric zero-index optical metamaterial
• Semi-Dirac dispersion relation in photonic crystals

Cited by in corpus (9)

• Topology optimization of anisotropic elastic metamaterial with broadband double-negative index
• Hyperbolic Metamaterials: From Dispersion Manipulation to Application
• Metamaterials: $\text{supra}$-classical dynamic homogenization
• Anomalous diffraction in hyperbolic materials
• Polaritonic cylinders as multifunctional metamaterials: Single scattering and effective medium description
• Closed-form expressions for effective constitutive parameters and electro/magneto-strictive tensors for bi-anisotropic metamaterials and their use in optical force density calculations
• Clausius-Mossotti Relation Revisited: Media with Electric and Magnetic Response
• Diamonds in Klein geometry
• Dispersion Characteristics of a Glide-Symmetric Square Patch Metamaterial with Giant Anisotropy