Abstract

To describe inducing of non-zero macroscopic second-order susceptibility in a centro-symmetric media such as the glass we suppose that a pump wave excites electrons from certain "donor" states in the middle of the v-SiO₂forbidden gap to defect states near the conduction band edge and the conformation of each defect changes significantly owing to pseudo-Jahn-Teller effect with a certain number of electrons placed in the proper state of the defect. Our cluster calculation performed by MNDO method proves the pseudo-effect to occur in Ge and Al atom substituted for the Si one and in =Ge-O-Ge= diatomic center with a certain defect state occupied by two electrons or by one election, respectively. The relaxed conformation of the defects is stable since their spontaneous decay is forbidden. We suppose that a phase transition occurs owing to cooperative pseudo-Jahn-Teller effect in the system of defects created in the glass by the pump wave, that it is described by a vector order parameter $\overrightarrow{\eta }$ and that it is caused by small relaxation of each of the defects with non-zero polarizability b^ω. Under these assumptions macroscopic second-order susceptibility is proved to be ${\chi }_{\text{ijk}}^{(2)}={\chi }^{(2)}\left({\eta }_{\text{i}}{\delta }_{\text{jk}}+{\eta }_{\text{j}}{\delta }_{\text{ik}}+{\eta }_{\text{k}}{\delta }_{\text{ij}}\right)$ where ${\chi }^{(2)}\equiv n{b}^{\omega }\delta R/R,\delta R/R$ being mean relative atomic displacement in relaxed defect, n being defects concentration. Bloembergen's relations [1] are valid for ${\chi }_{\text{ijk}}^{(2)}$since ${\chi }_{\text{xxy}}^{(2)}={\chi }_{\text{xyx}}^{(2)}={\chi }_{\text{yxx}}^{(2)}={\chi }^{{(2)}^{\prime }}{\eta }_{\text{y}},{\chi }_{\text{yyy}}^{(2)}=3{\chi }^{(2)}{\eta }_y$. So the results of [2] are explained by our theory and therefore those do not prove the SH generation to be caused by strong electrostatic field induced in the glass by the pump wave, as supposed in [2]. Our computer simulation of the defects results in δR/R ~ 0.1. The defect polarizability may be estimated as b^ω~ (νd)³(ηω)^-2with d being mean value of dipole matrix element in the defect, ν being number of the defect states. Since νd ~ le, one finds for wavelength ~ 1 μm: νd ~ 5·10^-18CGS and b^ω~ 10^-28CGS . Assuming the mene order parameter to be η ~ 0.1 one obtains χ⁽²⁾~ 10^-30CGS ~ 10^-12CGS for n ~ 10¹⁸cm^-3in good agreement with experimental data (see review in [3]).

© 1991 Optical Society of America