Negative refraction in indefinite media

Initial experiments on wedge samples composed of isotropic metamaterials with simultaneously negative permittivity and permeability have indicated that electromagnetic radiation can be negatively refracted. In more recently reported experiments Phys. Rev. Lett. 90, 1074011 (2003), indefinite metamaterial samples, for which the permittivity and permeability tensors are negative along only certain of the principal axes of the metamaterial, have also been used to demonstrate negative refraction. We present here a detailed analysis of the refraction and reflection behavior of electromagnetic waves at an interface between an indefinite medium and vacuum. We conclude that certain classes of indefinite media have identical refractive properties as isotropic negative index materials. However, there are limits to this correspondence, and other complicating phenomena may occur when indefinite media are substituted for isotropic negative index materials. We illustrate the results of our analysis with finite-element-based numerical simulations on planar slabs and wedges of negative index and indefinite media.