A General Approach to Perturbation Theoretic Calculations of Nonlinear Susceptibility Coefficient Tensors for Ferroelectric Materials

Perturbation analysis in which the time variation of an electric field is treated as inducing a weakly nonlinear response that is expressed as a Taylor series expansion is a standard technique for deriving the nonlinear susceptibility coefficients that relate the electric field to the polarization. In this paper a generalized method is used to generate the coefficients and Fourier analysis is employed in order to treat any time dependent electric field as a superposition of single frequency waves. It is then shown how this method can be applied to the calculation of nonlinear susceptibility coefficients in bulk ferroelectric materials in such a way that preserves the tensorial nature of the coefficients, appropriate for crystalline materials. An advantage of this general approach is that it is useful for the development of computer modelling packages involving nonlinear calculations.