极化效应作用下长方体各向同性电光晶体中光束相移的解析计算

Analytical Calculation of Beam Phase-shift in Cuboid Isotropic Electro-optic Crystal With Polarization Effect

电光晶体中光束相移的计算对光学电场传感器的研究至关重要,但空间电场作用下晶体极化效应对光束相移的影响尚未得到深入理解。该文提出极化效应作用下长方体各向同性电光晶体中光束相移的计算方法,定义电场变换张量以描述极化效应作用下晶体内部电场与空间电场之间的关联关系,推导出引入电场变换张量的光束相移公式。该方法同时考虑空间电场作用下电光晶体和环境介质的极化效应,可用于计算具有任意三维尺寸和介电特性的长方体各向同性电光晶体中的光束相移。结果表明:电光晶体与环境介质的介电常数之比是关键因素,该比例的增加会引起光束相移的非线性衰减;晶体三维尺寸的变化均会对光束相移产生显著影响;光束在晶体中的传播路径也是影响光束相移的重要因素。最后,以BGO晶体为例开展实验,验证相移公式的有效性。该文研究可为电光晶体中光束相移的计算评估以及光学电场传感器的优化设计提供理论依据。

The calculation of beam phase-shift in electro-optic(E-O)crystal is a key in the research of optical electric field sensors,but the influence of polarization effect of crystal on phase-shift under the action of the spatial electric field has not been deeply understood.In this paper,the calculation method of the beam phase-shift in cuboid isotropic E-O crystal with the polarization effect was proposed,an electric field transformation tensor was defined to describe the correlation between the internal electric field of crystal and the space electric field,and the phase-shift formula which introduces the electric field transformation tensor was deduced.This method considered both the polarization effects of E-O crystal and environmental medium,and can be used to calculate the beam phase-shift in the cuboid isotropic E-O crystal with any three-dimensional sizes and dielectric constants.The calculation results show that the dielectric constant ratio of crystal to environmental medium is the key factor,and an increase of this ratio will cause a nonlinear attenuation of beam phase-shift;three-dimensional sizes of the crystal all have significant effects on the phase-shift;the beam path in crystal is also an important factor affecting the phase-shift.Finally,an experiment was carried out with BGO crystal to verify the phase-shift formula.This paper can provide a theoretical basis for the calculation of the beam phase-shift in E-O crystal and the optimal design of the optical electric field sensors.