No abstract

More than 50 different combinations are given for parameters of the problem of second harmonic generation by a plane electromagnetic elliptically polarized wave from a thin optical layer on the surface of cylindrical particle, in which the generation from the lateral surface cannot be observed. Also, 18 combinations of parameters are found, in which generation from the end surfaces of the cylindrical particle is not observed. More than 30 problem parameter combinations are given, in which linearly polarized second harmonic radiation is generated from the side surface (or from the end surfaces). The combinations of problem parameters are indicated, at which generation from the entire surface of the cylindrical particle cannot be observed, and also parameter combinations at which the generation has linear polarization. A method is proposed for determining the anisotropy coefficients on the base of the properties above.

Mathematical properties of functions characterizing symmetries of spatial distribution of second harmonic–sum frequency radiation are determined. The conditions at which there occurs no generation and the conditions at which the polarization of the generated radiation is linear are found. The revealed properties are systematized by their manifestations in the directivity patterns of the generated radiation. Methods based on these properties for determining the components of the nonlinear dielectric susceptibility tensor are proposed. The relationship is described between the revealed properties as well as conditions and previously found similar properties and conditions for the phenomena of second–harmonic generation and sum–frequency generation.

The solution to the problem of second harmonic–sum frequency generation by two coherent plane electromagnetic waves with elliptical polarizations and equal frequencies in a thin spherical layer is analyzed graphically. Asymmetries are introduced that quantitatively describe the shape of three-dimensional directivity patterns (spatial distribution of the power density of second harmonic–sum frequency radiation). Three-dimensional directivity patterns and asymmetries are analyzed for various combinations of the parameters: ratio of the complex amplitudes of the incident waves, angle between the wave vectors of the incident waves (the opening angle), ellipticities, orientations of polarization ellipses, spherical particle size. It is found that, at small particle sizes, each anisotropy type corresponds to its own individual directivity pattern. It is revealed that, for one of the anisotropy types, the shape of the directivity pattern almost does not change for nearly all possible ranges of the above parameters.