Negative index materials: at the frontier of macroscopic electromagnetism

The notions of negative refraction and negative index, introduced by V. Veselago more than 50 years ago, have appeared beyond the frontiers of macroscopic electromagnetism and purely formal during 30 years, until the work of J. Pendry in the late 1990s. Since then, the negative index materials and the metamaterials displayed extraordinary properties and spectacular effects which have tested the domain of validity of macroscopic electromagnetism. In this article, several of these properties and phenomena are reviewed. First, mechanisms underlying the negative index and negative refraction are briefly presented. Then, it is shown that the frame of the time-harmonic Maxwell's equations cannot describe the behavior of electromagnetic waves in the situations of the perfect flat lens and corner reflector due to the presence of essential spectrum at the perfect-1 index frequency. More generally, it is shown that simple corner structures filled with frequency dispersive permittivity have a whole interval of essential spectrum associated with an analog of "black hole" phenomenon. Finally, arguments are provided to support that, in passive media, the imaginary part of the magnetic permeability can take positive and negative values. These arguments are notably based on the exact expression, for all frequency and wave vector, of the spatially-dispersive effective permittivity tensor of a multilayered structure.