In
optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...
, negative refraction is the
electromagnetic
In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...
phenomenon where light
rays become
refracted
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenome ...
at an
interface that is opposite to their more commonly observed positive refractive properties. Negative refraction can be obtained by using a
metamaterial
A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is a type of material engineered to have a property, typically rarely observed in naturally occu ...
which has been designed to achieve a negative value for electric
permittivity
In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...
() and magnetic
permeability (); in such cases the material can be assigned a negative
refractive index
In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...
. Such materials are sometimes called "double negative" materials.
Negative refraction occurs at interfaces between materials at which one has an ordinary positive
phase velocity
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, t ...
(i.e., a positive refractive index), and the other has the more exotic negative phase velocity (a negative refractive index).
Negative phase velocity
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
In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength) ...
and (Abraham) the
Poynting vector
In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or '' power flow'' of an electromagnetic field. The SI unit of the Poynting vector is the wat ...
. Other definitions include the opposition of
wave vector
In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength) ...
to
group velocity
The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the ''modulation'' or ''envelope (waves), envelope'' of the wave—propagates through space.
For example, if a stone is thro ...
, 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
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a Scalar (mathematics), scalar as a result". It is also used for other symmetric bilinear forms, for example in a pseudo-Euclidean space. N ...
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
In mathematics and physics, the right-hand rule is a Convention (norm), convention and a mnemonic, utilized to define the orientation (vector space), orientation of Cartesian coordinate system, axes in three-dimensional space and to determine the ...
. The terms "left-handed" and "right-handed" are generally avoided as they are also used to refer to
chiral
Chirality () is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek language, Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is dist ...
media.
Negative refractive index
One can choose to avoid directly considering the
Poynting vector
In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or '' power flow'' of an electromagnetic field. The SI unit of the Poynting vector is the wat ...
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). Since both ε and μ are generally complex, their imaginary parts do not have to be negative for a passive (i.e.
lossy
In information technology, lossy compression or irreversible compression is the class of data compression methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to reduce data size ...
) material to display negative refraction. In these materials, the criterion for negative phase velocity is derived by Depine and Lakhtakia to be
:
where
are the real valued parts of ε and μ, respectively. For active materials, the criterion is different.
NPV occurrence does not necessarily imply negative refraction (negative refractive index). Typically, the
refractive index
In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...
is determined using
:
,
where by convention the positive square root is chosen for
. However, in NPV materials, the negative square root is chosen to mimic the fact that the wave vector and phase velocity are also reversed. The refractive index is a derived quantity that describes how the wavevector is related to the optical frequency and propagation direction of the light; thus, the sign of
must be chosen to match the physical situation.
In chiral materials
The refractive index
also depends on the chirality parameter
, resulting in distinct values for left and right circularly polarized waves, given by
:
.
A negative refractive index occurs for one polarization if
>
; in this case,
and/or
do not need to be negative. A negative refractive index due to chirality was predicted by Pendry and Tretyakov ''et al.'', and first observed simultaneously and independently by Plum ''et al.'' and Zhang ''et al.'' in 2009.
Refraction
The consequence of negative refraction is light rays are refracted on the same side of the
normal on entering the material, as indicated in the diagram, and by a general form of
Snell's law
Snell's law (also known as the Snell–Descartes law, the ibn-Sahl law, and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing th ...
. When refraction occurs with no accompanying reflection it is termed total refraction.
See also
*
Acoustic metamaterials
*
Metamaterial
A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is a type of material engineered to have a property, typically rarely observed in naturally occu ...
*
Negative index metamaterials
*
Metamaterial antennas
*
Multiple-prism dispersion theory
The first description of multiple-prism arrays, and multiple-prism dispersion, was given by Isaac Newton in his book '' Opticks,'' also introducing prisms as beam expanders. Prism pair expanders were introduced by David Brewster in 1813. A modern ...
*
N-slit interferometric equation
Quantum mechanics was first applied to optics, and interference in particular, by Paul Dirac. Richard Feynman, in his Lectures on Physics, uses Dirac's notation to describe thought experiments on double-slit interference of electrons. Feynman's ...
*
Perfect lens
*
Photonic metamaterials
*
Photonic crystal
*
Seismic metamaterials
*
Split-ring resonator
*
Tunable metamaterials
Electromagnetic interactions
*
Bloch's theorem
*
Casimir effect
In quantum field theory, the Casimir effect (or Casimir force) is a physical force (physics), force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of a field (physics), field. The term Casim ...
*
Dielectric
In electromagnetism, a dielectric (or dielectric medium) is an Insulator (electricity), electrical insulator that can be Polarisability, polarised by an applied electric field. When a dielectric material is placed in an electric field, electric ...
*
Electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...
*
EM radiation
*
Electron mobility
In solid-state physics, the electron mobility characterizes how quickly an electron can move through a metal or semiconductor when pushed or pulled by an electric field. There is an analogous quantity for Electron hole, holes, called hole mobilit ...
*
Permeability (electromagnetism)
In electromagnetism, permeability is the measure of magnetization produced in a material in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter Mu (letter), ''μ''. It is the ratio of t ...
*
Permittivity
In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more ...
*
Wavenumber
In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of ...
*
Photo-Dember
*
Impedance
References
{{reflist, 2
Photonics
Physical phenomena
Metamaterials
Articles containing video clips