In a very handwaving qualitative way a classical explanation goes like this: Quadratic nonlinearity requires that the crystal have noncentrosymmetric symmetry. Only a few crystal classes are not centrosymmetric. The lack of inversion symmetry means that the crystal has a non-zero polarization. Adding defects, particularly, polar ones, will tend to reduce the polarization of the crystal and thus the magnitude of the nonlinearity. Yariv in Quantum Electronics (Section 16.3, 2nd edition) has a discussion of the origin of nonlinear optical coefficients.
Thanks Sir Kenneth L. Schepler for reply my question. I want to ask another question for further understanding. If Halogens especially Fluorine introduce to the inorganic crystals show opposite effect than OH ans H2O . Will The reason be reverse for Fluorine? As fluorine and other halogens enhance the Nonlinearity of inorganic crystals. What is reason behind it?
In general way if you would you like to know how effect the different dopants on the nonlinear properties of material. first thing we have to know the crystal structure and then after a dopants how they are changing the crystal symmetry. Another thing is non linearity depends on the individual molecules intrinsic characteristics.
more details can be get in R W boyd nonlinear optics book
I am not aware of halogens enhancing 2nd order nonlinearity in inorganic crystals. Do you have papers that report this? I agree with A S V Rao that we have to know the crystal structure and then how dopants change the crystal symmetry.