Spatial profile reconstruction of individual componentsof the nonlinear susceptibility tensors $\hat\chi^{(3)}(z,\omega',\omega',-\omega,\omega)$ and $\hat\chi^{(3)}(z,2\omega\pm\omega',\pm\omega',\omega,\omega)$ of a one-dimensionally inhomogeneous medium

We have proved for the first time and proposed an algorithm of unique spatial profile reconstruction of the components $\chi^{(3)}_{yyyy}$ of complex tensors $\hat\chi^{(3)}(z,\omega',\omega',-\omega,\omega)$ and $\hat\chi^{(3)}(z,2\omega\pm\omega',\pm\omega',\omega,\omega)$, describing four-photon interaction of light waves in a one-dimensionally inhomogeneous plate, whose medium has a symmetry plane $m_y$ that is perpendicular to its surface. For the media with an additional symmetry axis $2_z,4_z,6_z$ or $\infty_z$ that is perpendicular to the plate surface, the proposed method can be used to reconstruct about one-fifth of all independent components of the above tensors.