An Analytic Theory of Dielectric and Optic Nonlinear Effects of Ferroelectrics

An analytical theory of dielectric and optic non-linear effects of ferroelectrics is presented in this paper. The theory includes the intrinsic relations between the ferroelectricity (P-E), dielectric nonlinear (ε-E) and optic nonlinear (△n-E) in ferroelectric materials. An analytic equation for dielectric and optic nonlinear effects of ferroelectrics is obtained, and then the simple polynomial functions of P(E), ε(E) and △n(E) are used to describe the mechanism of dielectric and optic nonlinearity. From the experimental hysteresis loop, e.g., ε-E and △n-E curves in ferroelectric materials, the boundary conditions and original conditions are obtained, and the related coefficients are also determined in the terms of P
m
, P
s
, P
r
, E
A
E
c
, and E
D
. Moreover, this analytic theory is verified by the data from Ba
0.9
Sr
0.1
TiO
3
and PLT/PZT films.