Second-harmonic generation from a thin cylindrical layer: I. Analytical solution

In the Rayleigh–Gans–Debye approximation an analytical solution is obtained for the problem of second harmonic generation by a plane electromagnetic wave with elliptical polarization from a thin optically nonlinear layer on the surface of a cylindrical dielectric particle of finite size placed in a dielectric. The result is presented in tensor and vector forms in general case, in which the nonlinear dielectric susceptibility tensor has four independent components (one chiral and three non-chiral). For the first time it is shown that at generation from the end plane surfaces of a cylindrical particle the contribution of chiral components differs in phase from that of non-chiral components. It is also found that for small linear dimensions of the cylindrical particle (height and radius of the base), the radiation due to the chiral component of the second-order nonlinear dielectric susceptibility tensor makes a dominant contribution to the second harmonic generation from a non-linear cylindrical layer (end and side surfaces).