ABSTRACT
In terms of third-order susceptibility tensor x(3)(-ro,ro,ro,-ro) of the medium, the nonlinear refractive indices for a linearly polarized wave and a circularly polarized wave in an isotropic material are
n2(LP) = (121t/no)X(3\ 111(-ro,ro,ro,-ro) and
Whereas in a cubic material the linear refractive index is isotropic, n2 is not. If 8 is the angle made by the electric field vector with the [100] axis for a wave propagating along, say, [001], the effective value ofx(3) is given by
where
The nonlinear refractive index is not a unique quantity for a given material because several physical mechanisms contribute to the polarization that is cubic in the applied optical elect-
ric field. These physical mechanisms require a material response that can take place on various time scales. The mechanisms that contribute most strongly to n2 , and their characteristic time scales (in parentheses) are bound electrons (lo-15 s), optically created free carriers (> IQ-12 s ), Raman-active optical phonons (1 o-12 s ), electrostriction (> 1 o-9 s ), and thermal excitation ( ~ 1 o-9 s ).
