No abstract

The vectors used in the solution of the problem of second-harmonic generation in the surface layer of a dielectric spheroidal particle are explicitly expressed in terms of the basis vectors of the spherical, cylindrical, and Cartesian coordinate systems. Three-dimensional directivity patterns characterizing the spatial distribution of the generated radiation in the far-field region and its polarization are constructed. It is found that for a small size of a spheroidal particle, the directivity pattern due to each of the non-chiral components of the nonlinear dielectric susceptibility tensor has its own individual shape. A proportional increase in the linear dimensions of the particle leads to separation of several directions of predominant radiation with a high directivity in the directivity pattern. If the exciting radiation has a linear polarization, then the generated radiation due to one (any) of the independent components of the tensor is also linearly polarized. Mathematical properties characterizing the spatial distribution of the generated radiation in the far-field region and properties associated with the change of problem parameters are found for the functions used in the solution. A relationship between the symmetries of the directivity patterns of doubled-frequency radiation and the indicated properties is revealed. The conditions under which the generation of radiation does not occur and the conditions under which the generated radiation has a linear polarization are found. The above conditions are related to the features of the spatial distribution of the generated radiation and its polarization, illustrated in the directivity patterns. Methods for estimating the independent components of the nonlinear dielectric susceptibility tensor using these conditions are proposed. Keywords: second-harmonic generation, spheroidal dielectric particle, symmetry of the spatial distribution of radiation, conditions for the absence of generation, conditions for the generation of linearly polarized radiation.

The problem of second-harmonic generation by a plane elliptically polarized electromagnetic wave in a thin optically nonlinear surface layer of a dielectric particle shaped as an ellipsoid of revolution is solved. The generalized Rayleigh-Gans-Debye approximation is used for an analytical description with taking into account the difference in refractive indices of the medium corresponding to the frequencies of the exciting and generated radiation. The limiting forms of functions are obtained, with the use of which the electric field strength of the generated radiation is expressed. The order of dependence of these functions on the linear dimensions is found, when the lengths of the semiaxes of the particle are small compared to the wavelength of the exciting radiation and their ratio remains constant. It was found that the power density of the generated radiation in this case is determined to a greater extent by the chiral components of the nonlinear dielectric susceptibility tensor and is proportional to the fourth power of the length of the semiaxis of the particle, if the shape of the spheroidal particle differs significantly from the spherical one. The solution of this problem, obtained by other authors, is supplemented for the possibility of applying to the description of generation in the surface layer of a dielectric particle not only in the form of a prolate, but also in the form of an oblate spheroid. Corrections of inaccuracies and misprints made in similar works by other authors are proposed. The relationships between the formulas used in these works are found, taking into account the corrections and the formulas used in this work. Keywords: second-harmonic generation, dielectric spheroidal particle, generalized Rayleigh-Gans-Debye model, small particle approximation, chiral component.

Explicit forms of the power density and the total radiation power of the second-harmonic generation in a thin spherical layer of a small radius are determined. The conditions for a maximal total power of the second harmonic and the direction of observation of the maximum intensity of the second harmonic are found analytically for special cases of the second-order dielectric susceptibility tensor. A numerical maximization of the energy characteristics of the second-harmonic generated radiation is carried out using one and two coherent sources with the same ellipticity of radiation. The advantage of using several coherent sources compared to a single source of initial radiation is shown.