Determining the coordinate dependence of some components of the cubic susceptibility tensor $\hat\chi^{(3)}(z,\omega,-\omega,\omega,\omega)$ of a one-dimensionally inhomogeneous absorbing plate at an arbitrary frequency dispersion

The possibility of unique reconstruction of the spatial profile of the cubic nonlinear susceptibility tensor component $\hat\chi_{yyyy}^{(3)}(z,\omega,-\omega,\omega,\omega)$ of a one-dimensionally inhomogeneous plate whose medium has a symmetry plane $m_y$ perpendicular to its surface is proved for the first time and the unique reconstruction algorithm is proposed. The amplitude complex coefficients of reflection and transmission (measured in some range of angles of incidence) as well as of conversion of an $s$-polarised plane signal monochromatic wave into two waves propagating on both sides of the plate make it possible to reconstruct the profile. These two waves result from nonlinear interaction of a signal wave with an intense plane wave incident normally on the plate. All the waves under consideration have the same frequency $\omega$, and so its variation helps study the frequency dispersion of the cubic nonlinear susceptibility tensor component $\hat\chi_{yyyy}^{(3)}(z,\omega,-\omega,\omega,\omega)$. For media with additional symmetry axes $2_z$, $4_z$, $6_z$, or $\infty_z$ that are perpendicular to the plate surface, the proposed method can be used to reconstruct the profile and to examine the frequency dispersion of about one third of all independent complex components of the tensor $\hat\chi^{(3)}$.