Theory of Second Harmonic Generation in Periodic Ferroelectric Materials

Abstract

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 ferroelectric material. If the nonlinear dielectric susceptibility is ignored, the Fourier components, or the amplitudes of the electric field in various modes, satisfy a five term vector recursion relation and the solutions are obtained by iteration for small tilt angles. The exact linear solutions are obtained for normal incidence and become identical with those for a cholesteric liquid crystal if the tilt angle becomes 90°. In the lowest order approximation, it is shown that the second harmonic field is given by a product of the linear solution multiplied by the leading term of the Fourier series which is calculated using the slowly varying envelope approximation.