Lorentz covariance of the canonical perfect lens

The electromagnetic properties of classical vacuum (i.e., empty space) are characterized by its permittivity ǫ0 = 8.854 × 10 −12 F m and permeability μ0 = 4π × 10 −7 H m. In contrast, anti–vacuum has permittivity −ǫ0 and permeability −μ0 [1]. The perfect lens, as conceptualized by Pendry [2], consists of a slab of anti–vacuum sandwiched by two slabs of vacuum. While this perfect lens is an idealization which can never be fully realized in practice [3], the concept of the perfect lens has spawned much theoretical and experimental work within the past few years on negative refraction and metamaterials. Indeed, interest in this area continues to escalate, with negatively refracting metamaterials having now entered the visible frequency regime [4]. Aside from metamaterials, negative refraction occurs in biological scenarios [5], and there is the possibility of negative refraction arising in special [6] and general [7] relativistic scenarios. A fundamental characteristic of vacuum is that its constitutive parameters are invariant under a Lorentz transformation. A straightforward derivation reveals that the constitutive parameters of anti–vacuum are also invariant under a Lorentz transformation. Therefore, the vacuum/anti– vacuum/vacuum perfect lens is Lorentz covariant. A canonical formulation for the perfect lens has also been developed, wherein the two constituent materials are linear, homogeneous, orthorhombic materials [3, 8]. In this Letter, we address the question: is this canonical perfect lens invariant under a Lorentz transformation?