非对称锚定面内开关液晶平板光波导的色散方程

Dispersion equation of asymmetric anchored in-plane switching liquid crystal slab optical waveguide

为了准确计算液晶光波导中的模式,推导出了非对称锚定面内开关平板液晶光波导中横电模式的色散方程。进行了模式的求解,并与仅适用于均匀各向同性材料的传统色散方程得出的结果进行了比较。结果显示,传统色散方程得出的每一个模式的有效折射率都比本文方程的求解结果更大,且该偏差随模式阶数的增加而变得更加严重。在本文的例子中,基模、阶模、2阶模对应的最大偏差分别占液晶双折射的7.8%,17.8%,26.3%,这表明液晶指向矢的渐变特性对有效折射率解有不容忽视的影响。因此,相较于传统色散方程的不足,本文提出的色散方程能更有效地分析液晶光波导中的模式。最后,通过与已有的数值结果进行比较验证了本文提出的色散方程的有效性与准确性。

To calculate the modes in liquid crystal optical waveguides,we derive the dispersion equation of transverse electric(TE)mode in the asymmetrical anchoring in-plane switching nematic liquid crystal(IPS-NLC)slab optical waveguide by using the analytical thinking of the WKB method.The mode is solved and compared with the results obtained from the traditional dispersion equation.The results show that the effective refractive index of each mode obtained by the traditional dispersion equation is always greater than that calculated by our equation.The deviation between the effective refractive index is not only related to the applied voltage but also becomes more severe with the increase of the mode order.In the current example,the maximum deviations corresponding to the fundamental,first-order,and second-order modes account for 7.8%,17.8%,and 26.3%of the liquid crystal’s birefringence,respectively.This result indicates that the gradient characteristic of the liquid crystal’s director has a non-negligible effect on calculating the effective refractive index.Consequently,the dispersion equation proposed by us can analyze the modes in the IPS-NLC optical waveguide more effectively than the traditional dispersion equation.Finally,the accuracy of the dispersion equation presented in this study is verified by comparing ours with the existing numerical results.