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Concept
Negative refraction
Summary
Negative refraction is the electromagnetic phenomenon where light rays become refracted at an interface that is opposite to their more commonly observed positive refractive properties. Negative refraction can be obtained by using a metamaterial which has been designed to achieve a negative value for (electric) permittivity (ε) and (magnetic) permeability (μ); in such cases the material can be assigned a negative refractive index. Such materials are sometimes called "double negative" materials.
Negative refraction occurs at interfaces between materials at which one has an ordinary positive phase velocity (i.e., a positive refractive index), and the other has the more exotic negative phase velocity (a negative refractive index).
Negative phase velocity (NPV) is a property of light propagation in a medium. There are different definitions of NPV; the most common is Victor Veselago's original proposal of opposition of the wave vector and (Abraham) the Poynting vector. Other definitions include the opposition of wave vector to group velocity, and energy to velocity. "Phase velocity" is used conventionally, as phase velocity has the same sign as the wave vector.
A typical criterion used to determine Veselago's NPV is that the dot product of the Poynting vector and wave vector is negative (i.e., that ), but this definition is not covariant. While this restriction is not practically significant, the criterion has been generalized into a covariant form. Veselago NPV media are also called "left-handed (meta)materials", as the components of plane waves passing through (electric field, magnetic field, and wave vector) follow the left-hand rule instead of the right-hand rule. The terms "left-handed" and "right-handed" are generally avoided as they are also used to refer to chiral media.
One can choose to avoid directly considering the Poynting vector and wave vector of a propagating light field, and instead directly consider the response of the materials. Assuming the material is achiral, one can consider what values of permittivity (ε) and permeability (μ) result in negative phase velocity (NPV).
Official source
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