本征广义琼斯矩阵方法

Eigen generalized Jones matrix method

为了描述完全偏振光在非线性晶体中传播时的偏振态及相位变化,本文基于Ortega-Quijano等人在推导非线性晶体的广义琼斯矩阵时采用的微分广义琼斯矩阵方法,提出了本征广义琼斯矩阵方法。与微分广义琼斯矩阵方法相比,本征广义琼斯矩阵方法使用了更精确的数学技巧,在描述光在非线性晶体中传播的物理过程上更为严谨。解决了微分广义琼斯矩阵不能计算斜入射光或者光轴与实验室坐标不重合时光的偏振变化的问题。首先,根据折射率椭球方程和光的入射方向,计算出非线性晶体中本征光的传播方向和折射率。然后,给出了本征光的本征广义琼斯矩阵。最后,计算了本征光的偏振态和相位变化。本文使用本征广义琼斯矩阵对带有一个奇点的涡旋光在KDP晶体中的传播情况进行模拟计算,计算结果表明,本征广义琼斯矩阵方法能够描述任意入射角度、任意光轴方向的完全偏振光在非线性晶体中的传播过程。

A differential generalized Jones matrix method(dGJM)was recently introduced by Ortega-Quijano and colleagues to derive the GJM for modelling uniaxial and biaxial crystals with arbitrary orientations in laboratory coordinate systems.Later,we propose an eigen generalized Jones matrix method to simulate the phase and polarization of fully polarized light propagating in an anisotropic crystal when the optical axis orientations and light directions are both arbitrary.In our method,we use physics that are equivalent in principle to those of Ortega-Quijano,but we use a modified mathematical technique.We introduce the eigen generalized Jones matrix in the intrinsic coordinate system to precisely calculate the phase and polarization of the light,which overcomes the limitations of the differential generalized Jones matrix method.The simulation results indicate that our method can be used to calculate the polarization distribution,regardless of how the light beam and optical axis positioned,or whether the light beam has a vortex.