Analytic Materials
arXiv:1610.06059 · doi:10.1098/rspa.2016.0613
Abstract
The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer . If takes its maximum value then we have a complete analytic material. Otherwise it is incomplete analytic material of rank . For two-dimensional materials further progress can be made in the identification of analytic materials by using the well-known fact that a rotation applied to a divergence free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.
28 pages, 1 figure
References in corpus (39)
- Optical Cloaking with Non-Magnetic Metamaterials
- Achieving transparency with plasmonic coatings
- Optical Hyperlens: Far-field imaging beyond the diffraction limit
- Strong spatial dispersion in wire media in the very large wavelength limit
- Experiments on transformation thermodynamics: Molding the flow of heat
- General Relativity in Electrical Engineering
- A complementary media invisibility cloak that can cloak objects at a distance outside the cloaking shell
- Acoustic cloaking theory
- On the feasibility of pentamode mechanical metamaterials
- Cloaking of Matter Waves
- Achieving control of in-plane elastic waves
- Notes on Conformal Invisibility Devices
- PT Metamaterials via Complex-Coordinate Transformation Optics
- On three-dimensional dilational elastic metamaterials
- Active Exterior Cloaking
- Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots
- New metamaterials with macroscopic behavior outside that of continuum elastodynamics
- Broadband Exterior Cloaking
- Transformation elastodynamics and cloaking for flexural waves
- A Rigorous Analysis of Plane-transformed Invisibility Cloaks
- Isotropic transformation optics: approximate acoustic and quantum cloaking
- Solutions in folded geometries, and associated cloaking due to anomalous resonance
- Anomalous localized resonance using a folded geometry in three dimensions
- On the possible effective elasticity tensors of 2-dimensional and 3-dimensional printed materials
- Schrodinger's Hat: Electromagnetic, acoustic and quantum amplifiers via transformation optics
- Controlling elastic wave with isotropic transformation materials
- Finite wavelength cloaking by plasmonic resonance
- Wave propagation in complex coordinates
- Source amplitudes for active exterior cloaking
- Transformation elastodynamics and active exterior acoustic cloaking
- Opaque perfect lenses
- Active elastodynamic cloaking
- Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors
- Exterior cloaking with active sources in two dimensional acoustics
- Mathematical analysis of the two dimensional active exterior cloaking in the quasistatic regime
- Complete characterization and synthesis of the response function of elastodynamic networks
- Plane-Wave Solutions to Frequency-Domain and Time-Domain Scattering from Magnetodielectric Slabs
- The searchlight effect in hyperbolic materials
- Hybrid electromagnetic circuits