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. 185
Section 1.7.2.2.1.2. Manley–Rowe relations^{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 |
An important consequence of overall permutation symmetry is the Manley–Rowe power relations, which account for energy exchange between electromagnetic waves in a purely reactive (e.g. non-dissipative) medium. Calling W_{i} the power input at frequency ω_{i} into a unit volume of a dielectric polarizable medium,where the averaging is performed over a cycle andThe following expressions can be derived straightforwardly:Introducing the quadratic induced polarization P^{(2)}, Manley–Rowe relations for sum-frequency generation stateSince , (1.7.2.40) leads to an energy conservation condition, namely , which expresses that the power generated at ω_{3} is equal to the sum of the powers lost at ω_{1} and ω_{2}.
A quantum mechanical interpretation of these expressions in terms of photon fusion or splitting can be given, remembering that is precisely the number of photons generated or annihilated per unit volume in unit time in the course of the nonlinear interactions.