中文摘要：

液晶对微波的调制取决于外加电压作用下液晶分子的取向，而基板的锚泊对液晶取向有重要影响，必然导致微波调制的变化.本文研究了无手性掺杂的弱锚泊90°扭曲向列相液晶的微波调制特性.基于液晶弹性理论和变分原理得到了液晶盒系统的平衡态方程和边界条件，采用差分迭代方法数值模拟了不同锚定强度大小和不同预倾角下单位长度相移随电压的变化.结果表明：1）预倾角对微波相移的影响与施加电压有关.当液晶盒施加电压为0.5—1.6 V之间时，随预倾角增大，单位长度微波相移及其与强锚泊0°预倾角90°扭曲液晶相移差均增大，且相移差达到最大时的电压值也随倾角增大而减小；1.6—3.0 V之间，单位长度微波相移及相移差随预倾角增大而减小；1.6 V附近及3.0 V之后，相移基本没有变化.2）表面锚定强度大小对微波相移的影响非常大.随锚定强度减小，单位长度微波相移及相移差均会增大，微波相移的可调范围也增大，且增加越来越明显.此研究为液晶微波调制器件的设计提供了理论依据。

英文摘要：

The microwave modulation induced by liquid crystals is determined by the orientation of liquid crystal molecules under an external applied voltage. The anchoring of substrate has an important effect on the liquid crystal orientation, which results in the change of microwave modulation. In this paper, the microwave modulation property of 90° twisted nematic liquid crystals with weak anchoring without chiral dopant is studied. Based on the elastic theory of liquid crystals and the variational theory, the equations of equilibrium state and the boundary condition are given, and the variations of phase-shift per unit-length with voltage for different anchoring energy coe-cients and pre-tilt angles are also simulated using the finite-difference iterative method. Results are as follows： （1） The influence of pre-tilt angle on microwave phase-shift is related to the applied voltage. When the voltage applied to the liquid crystal cell is from 0.5 to 1.6 V, with increasing pre-tilt angle, the microwave phase-shift per unit-length and the phase-shift difference relative to the strong anchoring 90° twisted nematic liquid crystal with pre-tilt angle 0° will all increase, and the applied voltage for the maximum phase-shift difference decreases. When the applied voltages are from 1.6 to 3.0 V, the microwave phase-shift per unit-length and the phase-shift difference all decrease with increasing pre-tilt angle. When the applied voltages are near 1.6 V or larger than 3.0 V, the phase-shift per unit-length has little change. （2） The anchoring energy strength has a great influence on microwave phase-shift. As the anchoring strength decreases, the microwave phase shift per unit-length and the phase-shift difference will increase, also the tunable range of microwave phase-shift increases more and more obviously. This research provides a theoretical foundation for the design of the liquid crystal modulator.