Optical conductivity is the property of a material which gives the relationship between the induced

current Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...

density in the material and the magnitude of the inducing

electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...

for arbitrary

frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...

. This

linear response function A linear response function describes the input-output relationship of a signal transducer such as a radio turning electromagnetic waves into music or a neuron turning synaptic input into a response. Because of its many applications in information ...

is a generalization of the

electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allow ...

, which is usually considered in the static limit, i.e., for time-independent or slowly varying electric fields. While the static electrical conductivity is vanishingly small in insulators (such as

diamond Diamond is a Allotropes of carbon, solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the Chemical stability, chemically stable form of car ...

porcelain Porcelain () is a ceramic material made by heating substances, generally including materials such as kaolinite, in a kiln to temperatures between . The strength and translucence of porcelain, relative to other types of pottery, arises mainl ...

), the optical conductivity always remains finite in some frequency intervals (above the optical gap in the case of insulators). The total optical weight can be inferred from sum rules. The optical conductivity is closely related to the

dielectric function In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in r ...

, the generalization of the

dielectric constant The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulat ...

to arbitrary frequencies.

High Frequency Limit

In the simplest cases, this property can be considered as a complex valued scalar function of frequency only. This formulation applies in the limit of long wavelengths, coarse grained structure, and cubic material symmetry. In this approximation, the electric current density

\mathbf

(a three-dimensional vector), the scalar optical conductivity

\sigma

and the electric field vector

\mathbf

are linked by the equation: :

\mathbf(\omega) = \sigma(\omega) \mathbf(\omega)

For comparison, the dielectric function

\varepsilon

relates the

electrical displacement In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as in ...

to the electric field: :

\mathbf(\omega) = \varepsilon(\omega) \mathbf(\omega)

In SI units, this implies the following connection between the two linear response functions: :

\varepsilon(\omega) = \varepsilon_0 + \frac

, where

\varepsilon_0

is the

vacuum permittivity Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric consta ...

and

i

denotes the

imaginary unit The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition an ...

Measurement

The optical conductivity is most often measured in optical frequency ranges via the

reflectivity The reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electronic ...

of polished samples under normal incidence (in combination with a Kramers–Kronig analysis) or using variable incidence angles. For samples that can be prepared in thin slices, higher precision is obtainable using optical transmission experiments. To fully determine the electronic properties of the material of interest, such measurements are combined with other techniques that work in different frequency ranges, e.g., in the static limit or at

microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...

frequencies.

References

External links

Lecture notes Optical Properties of Solids
by E. Y. Tsymbal Scattering, absorption and radiative transfer (optics) Fiber-optic communications {{Technology-stub