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

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.