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Nonlinear Optics

  • Chapter
Superlattices and Other Heterostructures

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 110))

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Abstract

Many nonlinear phenomena can be conveniently described phenomenologically by expanding the electric polarization P in powers of the light-wave electric field

$$\begin{array}{*{20}{c}} {{P_a}{\text{ = }}\chi _{a\beta }^{(1)}(\omega ){E_\beta }(\omega ,k){\text{ exp (ik }}\cdot{\text{ x - i}}\omega t{\text{)}}} \\ {{\text{ + }}\chi _{a\beta \gamma {\text{ }}}^{(2)}({\omega _1}{\text{, }}{\omega _2}){\text{ }}{{\text{E}}_\beta }{\text{ (}}{\omega _1}{\text{, }}{{\text{k}}_1}{\text{) }}{{\text{E}}_\gamma }{\text{ (}}{\omega _2}{\text{, }}{{\text{k}}_2}{\text{)}}} \\ {{\text{ x exp}}[{\text{i}}({{\text{k}}_1}{\text{ + }}{{\text{k}}_2}){\text{ }}\cdot{\text{ x - i (}}{\omega _1}{\text{ + }}{{\text{k}}_2}{\text{)}}} \\ {{\text{ + }}\chi _{a\beta \gamma \delta }^{(3)}{\text{ (}}{\omega _1}{\text{, }}{\omega _2}{\text{, }}{\omega _3}{\text{) }}{{\text{E}}_\beta }{\text{ (}}{\omega _1}{\text{, }}{{\text{k}}_1}{\text{) }}{{\text{E}}_\gamma }{\text{ (}}{\omega _2}{\text{, }}{{\text{k}}_2}{\text{) }}{{\text{E}}_\delta }{\text{ (}}{\omega _3}{\text{, }}{{\text{k}}_3}{\text{)}}} \\ {{\text{ x exp}}[{\text{i}}({{\text{k}}_1}{\text{ + }}{{\text{k}}_2}{\text{ + }}{{\text{k}}_3}{\text{) }}\cdot{\text{ x - i(}}{\omega _1}{\text{ + }}{\omega _2}{\text{ + }}{\omega _3}){\text{t}}]{\text{.}}} \end{array}$$
((10.1))

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  1. A.F. Ioffe Physico-Technical Institute, Politechnicheskaya 26, St. Petersburg, 194021, Russia

    Professor Eougenious L. Ivchenko & Professor Grigory E. Pikus

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Ivchenko, E.L., Pikus, G.E. (1997). Nonlinear Optics. In: Superlattices and Other Heterostructures. Springer Series in Solid-State Sciences, vol 110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60650-2_10

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