THEORY OF 2ND-HARMONIC GENERATION IN PERIODIC FERROELECTRIC MATERIALS

Second harmonic generation is investigated in SmC liquid crystals as an example of periodic ferroelectric materials. The electric field is expanded in a Fourier series having the same periodicity as the ferroe lectric material. If the nonlinear dielectric susceptibility is ignore d, the Fourier components, or the amplitudes of the electric field in various modes, satisfy a five term vector recursion relation and the s olutions are obtained by iteration for small tilt angles. The exact li near solutions are obtained for normal incidence and become identical with those for a cholesteric liquid crystal if the tilt angle becomes 90 degrees. In the lowest order approximation, it is shown that the se cond harmonic field is given by a product of the linear solution multi plied by the leading term of the Fourier series which is calculated us ing the slowly varying envelope approximation.