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

International Tables for Crystallography (2013). Vol. D, ch. 1.7, p. 210

Section 1.7.3.3.3.3. Direct THG ([\omega+\omega+\omega=3\omega])

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:  benoit.boulanger@grenoble.cnrs.fr

1.7.3.3.3.3. Direct THG ([\omega+\omega+\omega=3\omega])

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As for the cascading process, we consider a flat plane wave which propagates in a direction without walk-off. The integration of equations (1.7.3.24)[link] over the crystal length L, with [E_4^{3\omega}(X,Y,0)=0] and in the undepleted pump approximation, leads to[\eqalignno{E_4^{3\omega}(X,Y,L)&=jK^{3\omega}_4[\varepsilon_o\chi^{(3)}_{\rm eff}]E_1^{\omega}(X,Y,0)E_2^{\omega}(X,Y,0)E_3^{\omega}(X,Y,0)&\cr&\quad\times L\sin c[(\Delta k\cdot L)/2]\exp(-j\Delta kL/2).&\cr&&(1.7.3.79)}]

According to (1.7.3.36)[link] and (1.7.3.38)[link], the integration of (1.7.3.79)[link] over the cross section, which is the same for the four beams, leads to[\eta_{\rm THG}(L)={P^{3\omega}(L)\over P^\omega(0)}=B_{\rm THG}[P^\omega(0)]^2{L^2\over w_o^4}\sin c^2[(\Delta k\cdot L)/2]]with[B_{\rm THG}={576\over \varepsilon_o^2c^2}{d_{\rm eff}^2\over\lambda_\omega^2}{T_4^{3\omega}(T_1^\omega)^2T_2^\omega\over n_4^{3\omega}(n_1^\omega)^2n_2^\omega}\quad({\rm m}^{2}\;{\rm W}^{-2}),\eqno(1.7.3.80)]where [d_{\rm eff}=(1/4)\chi_{\rm eff}^{(3)}] is in m2 V−2 and λω is in m. The statistical factor is assumed to be equal to 1, which corresponds to a longitudinal single-mode laser.

The different types of phase matching and the associated relations and configurations of polarization are given in Table 1.7.3.2[link] by considering the SFG case with [\omega_1=\omega_2=\omega_3=\omega_4/3].








































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