Abstract
We derive a general theory for imaging by a flat lens without optical axis. We show that the condition for imaging requires a material having elliptic dispersion relations with negative group refraction. This medium is characterized by two intrinsic parameters sigma and kappa. Imaging can be achieved with both negative and positive wave vector refraction if sigma is a positive constant. The Veselago-Pendry lens is a special case with sigma = 1 and kappa = 0. A general law of refraction for anisotropic media is revealed. Realizations of the imaging conditions using anisotropic media and inhomogeneous media, particularly photonic crystals, are discussed. Numerical examples of imaging and requirements for sub-wavelength imaging are also presented.
Highlights
We derive a general theory for imaging by a flat lens without optical axis
We present a general theory of imaging by a flat lens without optical axis, resulting in a proposal for a new material which is translationally invariant along the surface and has anisotropic refractive index n(θ)
The ENGRM is defined by two parameters: the anisotropy parameter σ which is a measure of the ellipse eccentricity, and a phase factor κ which determines the center of the ellipse
Summary
We derive a general theory for imaging by a flat lens without optical axis. We show that the condition for imaging requires a material having elliptic dispersion relations with negative group refraction. In 1968 Veselago [7] pointed out that for a material with refractive index n = −1 a flat surface would focus light. A decade later, Silin [8] discussed a more general case and obtained the lens equation of a flat slab with negative elliptic dispersion.
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