On possibility of enhanced second harmonic generation in chiral smectics under diffraction of the fundamental wave

Abstract

In the paper of M.Copic and I.Drevensek-Olenik (Liq.Cryst; 22, 233 (1996)) it was shown that independently on the dielectric tensor frequency dispersion in chiral smectic liquid crystal an enhancement of the nonlinear second harmonic generation (SHG) can be reached for a special configuration of the fundamental wave, namely in the form of two counterpropagating waves. In the present presentation we attract attention to the fact that independently on the dielectric tensor frequency dispersion in chiral smectic liquid crystal an enhancement of SHG can also be reached for a plane fundamental wave if it is subjected to diffraction at the chiral smectic periodical structure. This possibility may be realised for the fundamental wave propagating at an angle to the helical axis for the first order diffraction scattering in the smectic. The phase-matching conditions of SHG are found under diffraction scattering both the fundamental wave and the wave of doubled frequency. The conditions corresponding to the SHG phase-matching at the edge of selective reflection band for the doubled frequency, i.e. at realisation of the SHG enhancement effect, are found. The analytically obtained results are illustrated by numerical calculations. Unusual dependence of the SHG intensity on the sample thickness is revealed.