A liquid crystal (LC) microlens with a new type of electrode pattern is designed. The both bottom and top ITO electrodes of LC microlens are placed face to face, and are separated by glass spacer with the thickness in micron scale, and then LC materials are injected into the cell constructed by them. Because of the two electrodes directly and closely facing the LC layer injected, the design can largely decrease the driving signal voltage for LC lens. The bottom electrode is designed with one round hole pattern. The top electrode is four circle patterns. The diameters of round hole and circle are 500μm and 160μm, respectively. Each circle pattern electrode can be used to focus incident light into different region over the focal plane of LC lens. When the four circle electrodes are driven by different signal at the same time, the focus can be moved off-axis over the focal plane of LC lens, and thus the voltage amplitude can be varied in the range from 0V<sub>rms</sub> to 20V<sub>rms</sub>. So, we realize a LC microlens with tunable-focus over the focal plane of LC lens driven by low-amplitude voltage signal.
In this paper, a three-dimensional (3-D) relaxation method is used to model the dynamic response behavior of liquid crystal (LC) directors in LC micro-optics structures with complex patterned electrodes. The method is based on Frank- Oseen continuum elastic theory by using a vectorial representation. This method can deal with liquid crystal structures with arbitrary patterned electrodes, and it is quite computational stability. Different numerical results obtained according the method are as follows: (1) the nematic LC structures with complex patterned electrodes applied by a constant voltage signal, and (2) the nematic LC structures with different thickness of LC layer, and (3) the nematic LC structures with different signal voltage. The typical results include the distribution of LC directors in LC layers, the distribution of electric potential in LC layers, and the distribution of phase retardation. The results show that the method can be used to effectively predict the formation of disclination lines, which has a strong impact on the performance of LC micro-optics structures.