Second harmonic–sum frequency generation in a thin spherical layer. II. Analysis of directivity patterns

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.