Electrically controlled polarization rotator based on liquid crystal optical waveguide
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摘要: 为了更准确地分析基于液晶光波导的电控偏振旋转器的偏振转换长度和偏振转换效率，研究了向列相液晶场致重新取向的渐变特性。首先，根据液晶磁场耦合方程组得出的本征值方程构建偏振转换长度与外加电压的对应关系。然后通过对电场传输方程进行横向有限差分离散得到了交替方向隐式束传播法迭代方程组的显式表达，用于求解液晶光波导中的传播场，进而计算偏振转换效率。最后，通过仿真实验求解了本征模式以及传播场，进而分析液晶指向矢的渐变特性对偏振转换长度和偏振转换效率的影响。结果表明，液晶指向矢的渐变对偏振转换长度的影响可以忽略，但其得出的最大偏振转换效率相较于液晶重新取向均匀的求解结果低大约20%。这一结果将为基于液晶光波导的电控偏振旋转器的实际开发提供理论参考。Abstract: In this study, the gradient characteristic of field-induced reorientation of nematic liquid crystal was investigated to accurately analyze the Polarization Conversion Length (PCL) and Polarization Conversion Efficiency (PCE) of an electronically controlled polarization rotator based on a liquid crystal optical waveguide. Firstly, according to the eigenvalue equation obtained from the liquid crystal magnetic field coupling equations, the corresponding relationship between PCL and the applied voltage was constructed. Then, the explicit expression of the iterative equations of the Alternating Direction Implicit Beam Propagation Method (ADI-BPM) was obtained by transverse finite-difference discretization of the electric field transmission equation, which was used to solve the propagation field in the liquid crystal optical waveguide and calculate the PCE. Finally, the eigenmode and propagation field were solved through a simulation experiment, and then the effects of the gradient characteristics of the liquid crystal director on PCL and PCE were analyzed. The results show that the effect of the gradient of the liquid crystal director on the PCL can be ignored, but the maximum PCE is about 20% lower than that of the uniform reorientation of the liquid crystal. This result will provide a certain theoretical reference for the practical development of an electronically controlled polarization rotator based on a liquid crystal optical waveguide.
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Key words:
- liquid crystal /
- optical waveguide /
- polarization rotator /
- electric tuning
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图 1 (a)液晶光波导横截面示意图；(b)液晶分子偏转示意图
Figure 1. (a) Schematic diagram of the cross-section of liquid crystal optical waveguide; (b) deflection diagram of liquid crystal molecular
图 2 有限差分法中使用的网格节点示意图。(p, q) 表示中心节点，其余节点为距离其最近的8个节点。
${\Delta }x$ ，${\Delta }y$ 分别表示x和y方向上的网格间距Figure 2. Diagram of mesh nodes used in the finite difference method. (p, q) represent the central node, and the other nodes are the 8 nodes closest to the central node.
${\Delta }x$ and${\Delta }y$ are the mesh spacing in the x and y direction, respectively
图 3 不同外加电压下
$ {\varepsilon _{xx}} $ ，$ {\varepsilon _{yy}} $ ，$ {\varepsilon _{xy}} $ （或$ {\varepsilon _{yx}} $ ）随y的一维渐变曲线Figure 3. One-dimensional gradual change curves of
$ {\varepsilon _{xx}} $ ,$ {\varepsilon _{yy}} $ ,$ {\varepsilon _{xy}} $ (or$ {\varepsilon _{yx}} $ ) with y at different applied voltages
图 4 PCL分别在渐变和均匀两种介电张量下随外加电压变化的曲线
Figure 4. PCL varying with applied voltage under gradient and uniform dielectric tensors, respectively
图 5 初始和输出位置处的电场分布。(a)~(b)初始激励；(c)~(f) 外加电压为1.26倍阈值时输出端的传播场分布；(g)~(j) 外加电压为2.1倍阈值时输出端的传播场分布
Figure 5. Electric field distribution at initial and output positions. (a)−(b) Initial excitation; (c)−(f) propagation field distribution at the output when the applied voltage is 1.26 times the threshold; (g)−(j) propagation field distribution at the output when the applied voltage is 2.1 times the threshold
图 6 外加电压为1.26倍阈值时X截面(a)~(d)和Y截面(e)~(h)的传播场分布
Figure 6. When the applied voltage is 1.26 times the threshold, the propagation field distribution of X section (a)−(d) and Y section (e)−(h)
图 7 外加电压为2.1倍阈值时X截面(a)~(d)和Y截面(e)~(h)的传播场分布
Figure 7. When the applied voltage is 2.1 times the threshold, the propagation field distribution of X section (a)−(d) and Y section (e)−(h)
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