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

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 dispersi on 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 t he present presentation we attract attention to the fact that independently on the dielectric tensor frequency dispersion in chiral smectic liquid cry stal an enhancement of SHG can also be reached for a plane fundamental wave if it is subjected to diffraction at the chiral smectic periodical structu re. This possibility may be realised for the fundamental wave propagating a t an angle to the helical axis for the first order diffraction scattering i n the smectic. The phase-matching conditions of SHG are found under diffrac tion scattering both the fundamental wave and the wave of doubled frequency . The conditions corresponding to the SHG phase-matching at the edge of sel ective reflection band for the doubled frequency, i.e. at realisation of th e SHG enhancement effect, are found. The analytically obtained results are illustrated by numerical calculations. Unusual dependence of the SHG intens ity on the sample thickness is revealed.