Light-focusing phenomena of field-tuned micro-lens made of polymer-stabilized blue phase liquid crystals

The analytical distribution of the electric field in a micro-lens made of polymer-stabilized blue phase liquid crystals (PS-BPLCs) between two electrodes has been derived, and ray bending and focusing for the o (ordinary) and e (extraordinary) rays caused by the field-induced extended Kerr effect on the PS-BPLC have also been calculated. Those calculations show that the focal lengths of most o rays are longer than those of e rays. The o and e rays result in a focal length of 11.6 cm at a Kerr constant of 2.3768 nm/V2 close to the experimental data, and the calculated focal spot diameter is about 80.0 μm. If the Kerr constant is decreased to 2.14 nm/V2, we can obtain a focal length of 13.1 cm, the same as the experimental data. This reduction in the Kerr constant is reasonable because it is still within the experimental error. In summary, our calculations reveal an efficient and accurate way to discuss the focusing phenomena in the PS-BPLC micro-lens.