具有反演对称中心的硅单晶在电场作用下体内的反演对称中心消失,因而理论上应产生偶数阶非线性极化率。从理论上根据矢量与张量的作用,利用χ(2)eff=χ(3)·E这一关系和张量变换理论系统地阐述了硅材料在内建电场或外加电场的作用下,具体在方向分别沿[111]、[110]和[001]的电场作用下,得到的等效二阶极化率张量χ(2)eff分别与C3v、C2v和C4v点群的二阶极化率张量具有相同的形式,说明在物理性质方面,硅的对称性由Oh群在相应方向电场作用下分别被降低为C3v、C2v和C4v群,因此应该具有相应对称性晶体的二阶非线性光学性质;提出了电场E沿任意方向时硅的等效二阶极化率张量χ(2)eff的计算方法,对研究硅材料和其他具有反演对称中心材料的场致二阶非线性光学性质实验具有指导意义。

Electric field applied to silicon, which is a kind of centrosymmetric materials, induces effective even-order nonlinear susceptibilities for silicon due to the vanishing of its inversion symmetry. The tensors of effective second-order susceptibilities of silicon are systematically studied according to the theories of χ(2)eff=χ(3)·E and tensor transformation when the directions of the applied electric fields or the built-in fields in the bulk of silicon crystal are along the crystal orientations of [111], [110] and [001], respectively. The results show that the forms of effective second-order susceptibilities agree with those of point groups of C3v, C2v and C4v, respectively, which indicates that silicon single crystal should belong to C3v, C2v or C4v group instead of Oh group under corresponding electric field, and thus, it should possess second-order nonlinear optical properties corresponding to related symmetric crystal. Also, a general deduction of χ(2)eff for silicon under an arbitrary applied electric field E is proposed, which can provide theoretical fundamentals for electric field-induced second-order nonlinear optical experiments of silicon and for those of other centrosymmetric materials.