
314 Second Harmonic Generation Imaging
SHG is well known to occur only in a material that is noncentrosymmetric. For a material that is
centrosymmetric (i.e., possesses inversion symmetry), each element of the second-order nonlinear sus-
ceptibility
χ
(2)
must vanish and no SHG can be induced. is can be explained by changing the sign of
the electric eld
E t( ) applied for the second-order nonlinear polarization, which is given by
P t E t( ) = ( )
(2)
0
(2) 2
ε χ .
(14.4)
If the sign of the electric eld is changed, the sign of the induced polarization also has to be changed
because the medium is assumed to possess inversion symmetry, and Equat ...