SFG () with undepletion at  and

Boulanger, B.; Zyss, J.

doi:10.1107/97809553602060000634

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

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International Tables for Crystallography (2006). Vol. D. ch. 1.7, p. 208

Section 1.7.3.3.4.1. SFG ( $[\omega_1+\omega_2=\omega_3]$ ) with undepletion at $[\omega_1]$ and $[\omega_2]$

B. Boulanger^a ^* and J. Zyss^b

^a Laboratoire de Spectrométrie Physique, Université Joseph Fourier, 140 avenue de la Physique, BP 87, 38 402 Saint-Martin-d'Hères, France, and ^bLaboratoire de Photonique Quantique et Moléculaire, Ecole Normale Supérieure de Cachan, 61 Avenue du Président Wilson, 94235 Cachan, France
Correspondence e-mail: benoitb@satie-bourgogne.fr

1.7.3.3.4.1. SFG ( $[\omega_1+\omega_2=\omega_3]$ ) with undepletion at $[\omega_1]$ and $[\omega_2]$

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The resolution of system (1.7.3.22) with $[E_1(X,Y,0)\ne 0]$ , $[E_2(X,Y,0)\ne 0]$ , $[\partial E_1(X,Y,Z)/\partial Z=\partial E_2(X,Y,Z)/\partial Z=0]$ and [E_3(X,Y,0)= 0] , followed by integration over [(X,Y)] , leads to $[\eqalignno{P^{\omega_1}(L)&=(T^{\omega_1})^2P^{\omega_1}(0)&(1.7.3.81)\cr P^{\omega_2}(L)&=(T^{\omega_2})^2P^{\omega_2}(0)&(1.7.3.82)\cr P^{\omega_3}(L)&=BP^{\omega_1}(0)P^{\omega_2}(0){L^2\over w_o^2}\sin c^2{\Delta k\cdot L\over 2}&(1.7.3.83)}%fd1.7.3.83]$ with $[B_{\rm SFG}={72\pi\over\varepsilon_oc}{2N-1\over N}{d_{\rm eff}^2\over\lambda_\omega^2}{T^{\omega_3}T^{\omega_1}T^{\omega_2}\over n^{\omega_3}n^{\omega_1}n^{\omega_2}}\quad({\rm W}^{-1})]$ in the same units as equation (1.7.3.70).