Abstract:
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.