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 coefficients 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.
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