Analysis of energy characteristics of the second-harmonic generation in long cylindrical dielectric particles

The explicit forms of the power density, the total radiation power of the second-harmonic generation in a long thin cylindrical layer of a small radius, and the conditions for their maximum are found. The spatial distribution of the generated radiation is examined for special cases of the nonlinear dielectric susceptibility tensor. A numerical maximization of the intensity of the second-harmonic is carried out for the range of the particle base radius from nanometers to micrometers. The distribution of the generated radiation from a linear structure of cylindrical particles is determined. The conditions at which the generated radiation is maximal and the conditions at which there occurs no generation are found.