International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2013 |
International Tables for Crystallography (2013). Vol. D, ch. 1.7, p. 182
Section 1.7.2.1.1.1. Linear response^{a}Institut Néel CNRS Université Joseph Fourier, 25 rue des Martyrs, BP 166, 38042 Grenoble Cedex 9, France, and ^{b}Laboratoire de Photonique Quantique et Moléculaire, Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan, France |
Let us first consider the first-order linear response in (1.7.2.1) and (1.7.2.2): the most general possible linear relation between P(t) and E(t) iswhere T^{(1)} is a rank-two tensor, or in Cartesian index notationApplying the time-invariance assumption to (1.7.2.4) leads tohence or, setting and ,where R^{(1)} is a rank-two tensor referred to as the linear polarization response function, which depends only on the time difference . Substitution in (1.7.2.5) leads toR^{(1)} can be viewed as the tensorial analogue of the linear impulse function in electric circuit theory. The causality principle imposes that R^{(1)}(τ) should vanish for so that P^{(1)}(t) at time t will depend only on polarizing field values before t. R^{(1)}, P^{(1)} and E are real functions of time.