Abstract

We study the influences of the graded index on Pendry’s perfect lens. A perfect lens, in its idealized case, is a slab of material with both the electric permittivity $\epsilon$ and the magnetic permeability $\mu$ being -1. In the graded-index lens discussed here the $\epsilon$, as well as $\mu$, gradually changes from -1 in the main body of the slab to $+1$ in the vacuum. During this process of changing, the $\epsilon$ will inevitably touch the zero value, which introduces singularities in the corresponding wave equations. We analytically discuss the imaging properties of the graded-index lens by use of confluent hypergeometric Kummer functions and discover that the limit of resolution of the lens has a logarithmic dependence on the graded-index regions. This logarithmic dependence implies that the hyper resolution of a “perfect” lens can only be obtained if the negative-to-positive transition layers are exponentially thin compared with the wavelength as well as the thickness of the lens. Similar effects in a metal slab lens are also discovered.

© 2016 Optical Society of America

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