Third harmonic generation of the elliptically polarized radiation in an isotropic medium in the approximation of reciprocal action of propagating waves

In the plane-wave approximation, the collinear generation of the third harmonic, arising due to the third-order susceptibility of a non-absorbing isotropic medium, when the incident fundamental-frequency radiation is elliptically polarized, is numerically investigated, and the difference between the solution of the self-consistent system of equations in the slowly varying envelope approximation for propagating waves and the results obtained in the popular approximation of immutability of the parameters of the fundamental wave during its propagation is analyzed. It is shown that the intensity of the third harmonic in local maxima, in the experimentally realized range of radiation and medium parameters, can differ from the values obtained using the approximate description no more than ten percent. However, its polarization in some regions of the medium can significantly differ from the degree of ellipticity of the fundamental-frequency wave and be practically circular.