Linear and Nonlinear Metamaterials and Transformation Optics

Albert Einstein said once: “OEe important thing is not to stop questioning.” Indeed, it is the scientižc curiosity of a Russian physicist, Victor Veselago, in 1968 that led to the emergence of an entirely new area of modern optics: the optics of metamaterials [1-3]. In optics, interactions between light waves and materials are usually characterized by two parameters-dielectric permittivity ε and magnetic permeability µ-that explicitly enter Maxwell’s equations, or by their product, the index of refraction, dežned as n = ± εµ. In common transparent optical materials, the index of refraction and dielectric permittivity are positive numbers that are greater or equal to 1 and µ ≈ 1. OEe refractive index can be modižed to some degree by altering the chemical composition of the material or using electrical, thermal, or nonlinear e^~ects. Nevertheless, the refractive index is typically greater than one (air) and less than four (silicon). Veselago investigated in detail the question of whether or not ε and µ can simultaneously take negative values, leading to a negative index of refraction. It is noteworthy that the discussions of backward waves and negative index of refraction date back to the beginning of the twentieth century (see, e.g., [4]); nowadays, we can generalize Veselago’s question and ask whether one could engineer ε and µ (or n) to take any value beyond the limits imposed by nature. Meta in Greek means “beyond, " so the ultimate goal of metamaterials research is to create materials with properties and functionalities that have not been found in nature.