{{Short description|Property of a material}} {{Multiple issues| {{Original research|date=May 2021}} {{More citations needed|date=May 2021}} }} '''Optical conductivity''' is the property of a material which gives the relationship between the induced current density in the material and the magnitude of the inducing electric field for arbitrary frequencies.<ref>{{cite book |url=https://books.google.com/books?id=nLJFc_gDexcC&pg=PA299 |title=Handbook of High -Temperature Superconductivity: Theory and Experiment |author1=J. Robert Schrieffer |author2=J.S. Brooks |page=299 |year=2007 |isbn=9780387687346 |publisher=Springer Publishing}}</ref> This linear response function is a generalization of the electrical conductivity, 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 or porcelain), 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, the generalization of the dielectric constant 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 <math>\mathbf{J}</math> (a three-dimensional vector), the scalar optical conductivity <math>\sigma</math> and the electric field vector <math>\mathbf{E}</math> are linked by the equation:
:<math>\mathbf{J}(\omega) = \sigma(\omega) \mathbf{E}(\omega)</math><ref>{{cite book |url=https://books.google.com/books?id=GEa9BAAAQBAJ&pg=PA64 |page=64 |title=Optical Properties of Bismuth-Based Topological Insulators |author=Paola Di Pietro |year=2013 |isbn=9783319019918 |publisher=Springer International Publishing}}</ref>
For comparison, the permittivity <math>\varepsilon</math> relates the electrical displacement to the electric field:
:<math>\mathbf{D}(\omega) = \varepsilon(\omega) \mathbf{E}(\omega)</math><ref>{{cite book |url=https://books.google.com/books?id=KJB2DwAAQBAJ&pg=PA70 |page=70 |title=Graphene Photonics |author1=Jia-Ming Liu |author2=I-Tan Lin |year=2018 |isbn=9781108476683 |publisher=Cambridge University Press}}</ref>
In SI units, this implies the following connection between the two linear response functions:<ref> {{cite book |last=Fox |first=Mark |date=2010 |title=Optical Properties of Solids |edition=2 |url=https://isbnsearch.org/isbn/9780199573370 |publisher=Cambridge University Press |page=183 |isbn=9780199573370 |oclc=870994520 }} </ref>
:<math>\varepsilon(\omega) = 1 + \frac{i \sigma(\omega)}{\varepsilon_0 \omega}</math>,
where <math>\varepsilon_0</math> is the vacuum permittivity and <math>i</math> denotes the imaginary unit.
== Measurement ==
The optical conductivity is most often measured in optical frequency ranges via the reflectivity of polished samples under normal incidence (in combination with a Kramers–Kronig analysis) or using variable incidence angles.<ref>{{cite book |url=https://books.google.com/books?id=a9s4Wrl-014C&pg=PA66 |title=Handbook of Advanced Electronic and Photonic Materials and Devices, Ten-Volume Set |editor=Hari Singh Nalwa |year=2000 |page=66 |publisher=Elsevier Science|isbn=9780125137454 }}</ref> 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 frequencies.
== References == {{reflist}}
==External links== *[http://physics.unl.edu/~tsymbal/teaching/SSP-927/Section%2013_Optical_Properties_of_Solids.pdf Lecture notes Optical Properties of Solids] by E. Y. Tsymbal
Category:Scattering, absorption and radiative transfer (optics) Category:Fiber-optic communications
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