Frequency Dispersion Limits Resolution in Veselago Lens

D.1 Introduction

In 1968, Veselago introduced the concept of a material having simultaneous negative values of epsilon and mu. He discussed a number of properties of such media, such as negative refraction, left-handed wave solutions, and a flat lens configuration, among other features (Veselago, 1968). Veselago pointed out that any medium with negative mu or epsilon would have to be frequency dispersive in order for the field energy to be positive. Many years later, Pendry considered a flat slab lens made from material with the relative values of both epsilon and mu equal to −1 (Pendry, 2000). He showed that a propagating plane wave incident upon this lens would be perfectly matched at the interface; that is, the reflection coefficient would be zero and the transmission coefficient through the slab would equal 1 whenever the relative values of epsilon and mu were both equal to −1. In the case of an incident evanescent wave, the reflection and transmission coefficients become infinite when the index of refraction becomes equal to −1, so the standard method of solving for the reflected and transmitted waves cannot be used. In order to overcome this difficulty, Pendry began with relative values of epsilon and mu different from −1 and expressed the solution as a series of multiple reflected waves within the slab. This series is a geometric series that was summed ...