title: Optical waves in a gradient negative-index lens of a half-infinite length.
abstract: Materials with negative permittivity and permeability can overcome the diffraction limit, thereby making the sub-wavelength imaging possible. In this study, we analyze the effects of gradient index on a half-infinite perfect lens. We assume that the sharp interface between the vacuum and the negative-index material is replaced by a smooth transition profile such that the index gradually changing from positive to negative. Interestingly, we find that if the graded index profile is modeled by a tanh function, we can have closed-form analytical solutions for this problem, which is a distinct advantage as numerical solutions are not accurate for evanescent waves with large transverse wave vectors. By analyzing the analytical formulas we confirm that a nonzero total absorption can occur even for a near-zero absorption coefficient in the steady-state limit and the image plane contains multiple sub-wavelength images of an object.
authors.affiliation: School of physics, Peking University and Department of Physics, The Hong Kong University of Science and Technology.
authors.forename: Yi S
authors.initials: YS
authors.lastname: Ding
authors.forename: C T
authors.initials: CT
authors.lastname: Chan
authors.forename: R P
authors.initials: RP
authors.lastname: Wang