J. Chen et al., NONLINEAR LOCAL-FIELD CORRECTIONS TO THE OPTICAL 2ND-HARMONIC SUSCEPTIBILITY OF INSULATING CRYSTALS, Physical review. B, Condensed matter, 56(4), 1997, pp. 1787-1799
There are two kinds of local-field corrections to the optical second-h
armonic susceptibility in insulating crystals: those linear and those
nonlinear In the macroscopic electric field originating from the linea
rly and nonlinearly induced microscopic charge densities, respectively
. An algebraic relation is established between these two local-field c
orrections, which obviates the need to calculate the nonlinearly induc
ed density. There is a hierarchy of local-field corrections consisting
of first-, second-, and third-order corrections containing one, two,
and three matrix elements of the linear local field, respectively. Our
calculations show that the first-order local-field correction gives t
he leading correction. We demonstrate that the first-order correction
from the previously neglected nonlinear local fields is exactly one ha
lf of the linear-local-field correction in the static limit. The newly
computed total local-field corrections range from -21% to +30% for th
e 15 semiconductors and insulators studied. The expression recently ob
tained for the second-harmonic susceptibility using the (2n+1) theorem
[A. Dal Corso et al., Phys. Rev. B 53, 15 638 (1996)] is shown to be
equivalent to the expression we obtained using a sum-over-states metho
d.