Materials for third-order nonlinear optics
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ion The application of an electric field to an atom induces polarization and an associated dipole moment. In an oscillating electric field, the electrons in a molecule also oscillate in response to the field. A plot of the induced dipole moment (polarization), μ induced, in a molecule as a function of the applied field will be linear if the molecule has a linear restoring force for the electrons around the nuclei. At the molecular level, an equation for this relationship is given by: μ induced = α E ,
(1)
where E is the electric field, and α is the linear polarizability. At the material level, one can write an analogous equation for the polarization density, which is related to the electric field by the constant referred to as the first-order susceptibility χ(1)—this is also related to the dielectric constant, and therefore, is the square of the refractive index of a material.1 Not all materials respond linearly to an oscillating electric field. In some cases, there is a significant deviation from linearity in a plot of the induced dipole moment as a function of the electric field (especially at high field strengths), which can be described by expressing dipole moment as a Taylor series
expansion as a function of the field (shown below to third order in the field): μ induced = α E + β/2 E 2 + γ/6 E 3 + ... .
(2)
Beyond the first term, α E, the terms scale with higher powers of the field, for example, quadratically (β) and cubically (γ) with the electric field; these terms are referred to as “nonlinear polarization” terms. Both β and γ (χ(2)), second-order susceptibility, and χ(3), third-order susceptibility, for bulk materials, respectively) give rise to interesting effects that can be used, for example, for optical switching and for generation of new frequencies using lasers. In order to generate these effects and others efficiently, we are interested in understanding how to design molecules and materials that optimize molecular nonlinearity and bulk nonlinear susceptibility. In this article, we limit the discussion to effects that scale as the third-power of the electric field (E3),1–16 referred to as thirdorder nonlinear optical effects. The term that relates E3 to the induced polarization on the molecular level is the “second-hyperpolarizability” (or “third-order polarizability”) (γ), and on the bulk materials level is the “third-order susceptibility” (χ(3)).
Seth R. Marder, Georgia Institute of Technology, USA; [email protected] DOI: 10.1557/mrs.2015.310
© 2016 Materials Research Society
MRS BULLETIN • VOLUME 41 • JANUARY 2016 • www.mrs.org/bulletin
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MATERIALS FOR THIRD-ORDER NONLINEAR OPTICS
There is both a real1,6,10–15 and an imaginary part of χ(3).2–4,7–9 materials can be realized precisely in three dimensions by The real part, Re(χ(3)) is the “nonlinear refractive index,” which 2PA-induced processes.3,5,9 Although 3D printing holds promdescribes how the refractive index of a material changes in ise in additive manufacturing, 2PA allows for 3D microfabrithe presence of an electric field, for exampl
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