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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(eχf2f)=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(eχf2f)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e(χf2f)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。
The inversion symmetry center disappears in the silicon monocrystal with inversion symmetry center under the action of electric field, so theoretically even-order non-linear polarizations should be generated. In theory, according to the function of vector and tensor, the relationship between e xf2f = χ (3) .E and tensor transformation theory is used to systematically expound the effect of silicon material under the effect of built-in electric field or applied electric field, The second-order polarizability tensor (eχf2f) obtained under the electric field of [111], [110] and [001] respectively has the same characteristic as the second-order polarizability tensor of C3v, C2v and C4v The same form shows that in terms of physical properties, the symmetry of silicon is reduced to the groups of C3v, C2v and C4v respectively by the Oh group under the electric field of the corresponding direction, and therefore should have the second-order nonlinear optical properties of the corresponding symmetric crystal; The calculation of the equivalent second-order polarizability e (χf2f) of silicon in any direction of the electric field E is helpful to the study of field-induced second-order nonlinear optical properties of silicon materials and other materials with inverted symmetry centers significance.