The DC electric field induced second-order nonlinear susceptibility of silicon crystals

Abstract

Silicon crystal is a kind of centrosymmetric materials, which has no second-order optical effects at dipole approximation. However, the inversion symmetry of silicon crystals will be broken by the built-in field or the DC electric field applied to it. We theoretically studied the response of the third-order susceptibility to the electric field and deduced the effective second-order susceptibility tensors when the electric fields applied to silicon are along the [111], [110] and [001] directions, respectively. The results show that the forms of the effective second-order susceptibilities of Si are consistent with those of C_3V, C_2V and C_4V symmetry groups of crystals which indicate that silicon crystals should belong to C_3V, C_2Vand C_4V symmetry groups instead of O_h symmetry group, respectively. So silicon crystals will exhibit some second-order nonlinear optical properties corresponding to related symmetric crystals under the corresponding incident electric fields. This research method of the electric field-induced second-order nonlinear optical processes can also be used to other centrosymmetric materials.