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Publication# Parity-Time Symmetric Nonlocal Metamaterials for Focusing and Image Processing

Abstract

Parity-Time (PT) symmetry refers to the invariance of a physical system upon reflection of space and time. An intriguing property of PT-symmetric quantum systems is the fact that they can have entirely real eigenvalue spectra, despite being non-Hermitian. Although the application of these concepts in quantum mechanics remains speculative, in classical optics non-Hermitian PT-symmetric systems can be readily realized with spatially balanced gain and loss. These systems have been shown to exhibit exotic responses, e.g., unidirectional invisibility, or anomalous scattering. Recently, negative refraction and planar focusing have been achieved by pairing a perfectly coherent absorbing metasurface with its time-reversed counterpart, i.e., a coherently lasing metasurface. Here, we generalize this idea to any pair of PT-symmetric structures, characterized by their scattering matrix, to put forward a realistic venue to PT-symmetric metamaterials for imaging. This approach allows us to design realistic structures based, e.g., on multilayered slabs, which implement the necessary nonlocality and spatial dispersion to achieve ideal all-angle negative refraction and planar focusing. We will also discuss how these concepts may realize arbitrary magnifying, focusing and image processing systems.

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Related concepts (34)

Refractive index

In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, n1 sin θ1 = n2 sin θ2, where θ1 and θ2 are the angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices n1 and n2.

Hermitian matrix

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j: or in matrix form: Hermitian matrices can be understood as the complex extension of real symmetric matrices.

Negative refraction

Negative refraction is the electromagnetic phenomenon where light rays become refracted at an interface that is opposite to their more commonly observed positive refractive properties. Negative refraction can be obtained by using a metamaterial which has been designed to achieve a negative value for (electric) permittivity (ε) and (magnetic) permeability (μ); in such cases the material can be assigned a negative refractive index. Such materials are sometimes called "double negative" materials.

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