Tables for
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 1.7, p. 183

Section Linear susceptibility

B. Boulangera* and J. Zyssb

aInstitut Néel CNRS Université Joseph Fourier, 25 rue des Martyrs, BP 166, 38042 Grenoble Cedex 9, France, and bLaboratoire de Photonique Quantique et Moléculaire, Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan, France
Correspondence e-mail: Linear susceptibility

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By substitution of ([link] in ([link],[\eqalignno{{\bf P}^{(1)}(t)&=\varepsilon_o\textstyle \int \limits_{-\infty}^{+\infty}{\rm d}\omega\textstyle \int \limits_{-\infty}^{+\infty}{\rm d}\tau\,\,R^{(1)}(\tau)\cdot{\bf E}(\omega)\exp[-i\omega(t-\tau)]&\cr {\bf P}^{(1)}(t)&=\varepsilon_o\textstyle \int \limits_{-\infty}^{+\infty}{\rm d}\omega\,\,\chi^{(1)}(-\omega_{\sigma}\semi\omega){\bf E}(\omega)\exp(-i\omega_{\sigma}t),&\cr&&(}]where[\chi^{(1)}(-\omega_{\sigma}\semi\omega)=\textstyle \int \limits_{-\infty}^{+\infty}{\rm d}\tau\,\,R^{(1)}(\tau)\exp(i\omega\tau).]

In these equations, [\omega_{\sigma}=\omega] to satisfy the energy conservation condition that will be generalized in the following. In order to ensure convergence of χ(1), ω has to be taken in the upper half plane of the complex plane. The reality of R(1) implies that [\chi^{(1)}(-\omega_{\sigma};\omega)^*= \chi^{(1)}(\omega_{\sigma}^*;-\omega^*)].

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