Liquid crystal (LC) lenses have attracted widespread attention in modern optics due to their tunable focal lengths and adaptability in a range of cutting-edge applications, including virtual reality (VR), augmented reality (AR), and machine vision systems. These lenses exploit the unique electro-optical properties of liquid crystals to achieve variable optical characteristics. However, conventional LC lenses often face limitations due to the necessity of operating within the linear response region of LC materials. This constraint not only restricts the achievable focal power but also limits the effective utilization of birefringence, which is critical for optimizing lens performance. In this paper, we aim to address these inherent limitations by proposing an innovative circular LC lens design that enables a parabolic phase distribution even under nonlinear voltage driving. This approach provides greater flexibility and efficiency in light modulation, leading to enhanced optical performance across a wider range of operating conditions. By overcoming the constraints of linear behavior, our design maximizes the potential of liquid crystal materials and paves the way for advanced optical systems. Ultimately, this paper highlights the potential of nonlinear dynamics in LC lens technology and demonstrates their value for future adaptive optics applications.

We develop a hybrid approach combining electrode structure optimization and nonlinear voltage driving. Concentric circular electrodes with envelope functions are designed to generate voltage distributions suitable for the nonlinear response region of the liquid crystal material (HTG116900-100, Δn=0.206). These electrodes are fabricated using photolithography, and the liquid crystal cells are assembled with a 20-micron thick LC layer. Interferometric measurements (Fig. 7) are conducted to capture the phase profiles under varying voltages, allowing analysis of LC’s optical characteristics and phase behavior. Zernike polynomial fitting (Figs. 9 and 11) is applied for phase distribution and wavefront analysis. Image quality is evaluated by measuring the root mean square contrast (RMS contrast) and birefringence utilization rates (Table 3). RMS contrast reflects image clarity and contrast of the image, while birefringence utilization rate reflects the effective use of the material’s optical anisotropy. These metrics provide crucial insight into the practical performance and future optimization of the proposed LC lens design. This integrated approach enables improved optical behavior under nonlinear driving conditions, enhancing the competitiveness of LC lenses in advanced optical systems.

The proposed design achieves parabolic phase profiles in both linear and nonlinear response regions. Key results include: 1) enhanced birefringence utilization. The birefringence utilization rate increases from 33.3% to 66.2% for positive lenses and from 32.1% to 67.6% for negative lenses, corresponding to improvements of 98.93% and 110.4%, respectively (Fig. 11). 2) Nonlinear voltage compatibility. With the optimized envelope function of the concentric electrodes (Fig. 4), the lens maintains a parabolic phase distribution even at voltages beyond the linear threshold (V=4.5Vrms), with R-Square values above 0.99 for phase fitting (Table 2). 3) Imaging performance. Resolution tests using ISO 1233 charts demonstrate accurate focusing at the designed voltages (Figs. 13 and 14), supported by RMS contrast values peaking at 0.2550 (Table 3).

In this paper, we present an innovative design for a circular LC lens that extends the operating voltage range into the nonlinear response region while maintaining a parabolic phase distribution. By optimizing the electrode structure and driving method, the proposed design significantly enhances both focal power and birefringence utilization, addressing long-standing limitations in LC lens technology. The improved electrode configuration enables effective control of the liquid crystal materials across a wider voltage range, thus expanding the application potential of LC lenses in dynamic imaging systems. This design not only improves image quality but also flexibly meets optical requirements under various operating conditions, offering new opportunities for the development of compact and high-performance optical devices. Moreover, the results demonstrate that the optimized driving method allows more efficient utilization of the birefringence properties of the LC material, leading to further improvements in optical performance. This is particularly critical for multifunctional optical systems that require fast response and wide dynamic range. Future research will focus on the scalability of this LC lens design, aiming to support mass production and explore its integration into multifunctional optical platforms. In combination with other optical technologies, this approach may further enhance LC lens performance and facilitate the widespread adoption of LC technology in emerging fields, such as wearable devices, intelligent imaging systems, and miniaturized optical instruments.