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, pp. 183184
Section 1.7.2.1.4.1. Classical convention^{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 
Insertion of (1.7.2.26) in (1.7.2.25) together with permutation symmetry provideswhere the summation over ω stands for all distinguishable permutation of , K being a numerical factor given bywhere p is the number of distinct permutations of , n is the order of the nonlinear process, m is the number of d.c. fields (e.g. corresponding to ) within the n frequencies and when , otherwise . For example, in the absence of a d.c. field and when the ω_{i}'s are different, .
The K factor allows the avoidance of discontinuous jumps in magnitude of the elements when some frequencies are equal or tend to zero, which is not the case for the other conventions (Shen, 1984).
The induced nonlinear polarization is often expressed in terms of a tensor d^{(n)} by replacing χ^{(n)} in (1.7.2.29) byTable 1.7.2.1 summarizes the most common classical nonlinear phenomena, following the notations defined above. Then, according to Table 1.7.2.1, the nth harmonic generation induced nonlinear polarization is writtenThe are the components of the total electric field E(ω).

References
Shen, Y. R. (1984). The principles of nonlinear optics. New York: Wiley.