Liquid crystal lens with biased-electrode based on generalized Snell’s law

LI Zhao; ZHANG Baolong; LI Dan; LIU Yongkun; WANG Hao

doi:10.37188/CJLCD.2026-0056

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Liquid crystal lens with biased-electrode based on generalized Snell’s law

Device Physics and Device Preparation | 更新时间：2026-09-12

- Liquid crystal lens with biased-electrode based on generalized Snell’s law
- Chinese Journal of Liquid Crystals and Displays Vol. 41, Issue 5, Pages: 649-658(2026)
- 作者机构：
  
  天津科技大学电子信息与自动化学院，天津 300457
- 作者简介：
- 基金信息：
- DOI：10.37188/CJLCD.2026-0056
  CLC： O753.2;O436
- CSTR：32172.14.CJLCD.2026-0056
- Received：30 March 2026，
  
  Revised：2026-04-15，
  
  Published：05 May 2026
- 稿件说明：
移动端阅览
LI Zhao, ZHANG Baolong, LI Dan, et al. Liquid crystal lens with biased-electrode based on generalized Snell’s law[J]. Chinese Journal of Liquid Crystals and Displays, 2026, 41(5): 649-658.
DOI：

LI Zhao, ZHANG Baolong, LI Dan, et al. Liquid crystal lens with biased-electrode based on generalized Snell’s law[J]. Chinese Journal of Liquid Crystals and Displays, 2026, 41(5): 649-658. DOI： 10.37188/CJLCD.2026-0056. CSTR： 32172.14.CJLCD.2026-0056.

摘要

复合介电层液晶透镜通过加长电极的方式增强中心电场强度，使得边缘折射率分布偏离理想抛物线模型。通常须约束有效孔径来改善聚焦效果，从而导致透镜通光量损失。为了优化全孔径范围内的折射率分布，本文基于广义斯涅尔定律提出了一种具有偏置电极结构的液晶透镜。该透镜通过在边缘电极之间引入内环偏置电极与中心偏置电极，实现了对液晶层内梯度电场的有效调控。仿真结果表明，在低驱动电压（

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=2 V）下，优化后透镜的折射率分布与理想抛物线模型高度吻合。通过Zemax光学性能分析，该透镜在可见光波段下可以实现85.73%的通光效率，较复合介电层液晶透镜提升约38.89%。同时，公差分析表明，将光刻套刻引起的电极横向偏移控制在0.5 μm以内，透镜仍能保持良好的光束汇聚质量，该结论为实际器件制备的工艺公差分配提供了依据。

Abstract

In liquid crystal（LC） lenses with composite dielectric layers， electrode extension is used to enhance the central electric field. However， this extension often makes the peripheral refractive index of the lens deviate from the ideal parabolic model. Consequently， the effective aperture is constricted to improve focusing quality， resulting in a loss of optical throughput. To optimize the refractive index distribution across the entire aperture， a biased-electrode LC lens based on the generalized Snell’s law is proposed. An inner-ring and a central biased electrode are added between the peripheral electrode. The structure effectively modulates the gradient electric field in the LC layer. Simulation results demonstrate that at

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=2 V， the refractive index profile of the lens closely matches the ideal parabolic model. Optical simulations in Zemax demonstrate that the proposed lens achieves a light transmission of 85.73% across the visible spectrum. This design improves the transmission by 38.89% compared to the conventional LC lens with composite dielectric layers. Meanwhile， tolerance analysis reveals that the lens maintains excellent beam focusing quality when the lateral offset of the lithography-aligned bias electrode is kept within 0.5 μm. This conclusion provides a basis for process tolerance allocation in practical device fabrication.

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references

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