A liquid crystal droplet lens driven by the dielectrophoresis (DEP) force was demonstrated. The liquid crystal droplet lens was deformed by the DEP forces under non-uniform AC electric fields. Focal length, hysteresis and electrode design were studied. The focal length varied from 1.6mm to 2.6mm in the range of 0-200V at 1 kHz for electrode spacing of 50μm; that is, the tuning ratio of the focal length was about 60% in maximum. The hysteresis of contact angle was found to be less than 3° and it vanished after 1 minute at the rest state. As the electrode spacing over 200μm, the tuning ratios of the focal length dropped below 5%. The liquid crystal droplet lens that had numerical aperture of about 0.5 consumed power of about 0.1mW. Its response time was measured to be about 220ms.
©2006 Optical Society of America
Variable focus lenses are commonly used in optical systems. Focal length is conventionally adjusted by mechanical actuation of lens sets using geared motors or piezoelectric actuators. Mechanical tuning suffers from higher power consumption and miniaturization difficulties when it is used for portable applications that require small form factors. Alternative variable lenses, including gradient-index-changed lens [1–3] and shape-changed lens [4–7], were proposed to eliminate the problems associated with miniaturized mechanical focus systems. The gradient-index-changed lens adjusts its focal length by electrically redistributing individual liquid crystal molecules within the lens where the liquid crystal molecules are sealed in between two Indium Tin Oxide (ITO) glasses. Both the optical power (1/f) and the numerical aperture (NA) are two primary constraints for applications of the gradient-index-changed lens. The shape-changed lens, also known as liquid lens, adjusts its focal length by electrically transforming the surface profile of a liquid droplet. The surface profile that depends on the contact angle of the droplet can be changed by the electrowetting effect. Salt is commonly added to water in order to increase water conductivity for the electrowetting mechanism and to widen operation temperature of water. Electrolysis, Joule heating, microbubbles and evaporation were also found to hinder optical performance and operation conditions of the water-based liquid lens.  The electrolysis of the salty water could be minimized based on electrowetting on dielectric (EWOD) technique that places an insulating layer on the electrodes. The insulating layer reduces the Joule heating effect and the microbubbles; however, it leads to higher operation voltages.  Further, high saturated vapor pressure of the salty water (i.e. 5 torr) requires expensive hermetic packaging (i.e. typically metal-glass package) to seal the water inside the lens for long term operation.
In this paper, we proposed an alternative shape-changed lens, a DEP-driven liquid crystal droplet lens. Liquid crystals have been extensively used in optical applications, such as Liquid Crystal Display (LCD), Liquid-Crystal-On-Silicon (LCOS), optical shutter, etc. Fundamental properties of liquid crystal have been investigated for many decades and they are still improved by a large number of scientists. Both microbubbles and electrolysis in water do not occur to liquid crystal. Liquid crystal also has much lower electrical conductivity of 10-10 Ω.m-1 than salty water by eight orders, extensively reducing Joule heating effect and power consumption. Further, liquid crystal has lower saturated vapor pressure of below 10-6 torr than water by about six orders, easing packaging requirements. Liquid crystals are able to be designed for the desired operation temperature if required in the future. The liquid crystalline refractive index of 1.6 in average (i.e. 1.5-1.7) is larger than water, enabling better optical performance. Liquid crystal is expected to have better performance in many aspects than water in the application of tunable liquid lens; however, it may suffer from birefringence due to its optical anisotropy. The image of a liquid crystal droplet lens might be blurred due to double focal lengths when the birefringence of liquid crystals exists. To eliminate the birefringence, liquid crystals used had better to be in the isotropic phase. Thus, the operation temperature must be higher than the transition temperature TNI between the nematic phase and the isotropic phase.
2. Driving mechanism
Liquid crystal itself is high dielectric medium; thus, it could be potentially actuated by DEP forces. Given ϵ//=16.5 and σ=5×10-12 (Ω.m)-1 for liquid crystal MDA2625 (Merck), the factor σ/(ωϵbϵ0) is calculated to be 5×10-6 at the operation frequency of 1 kHz. By definition of dielectric material of σ/(ωϵbϵ0)<<1, liquid crystal behaves as a dielectric medium. Using the DEP mechanism we demonstrated to adjust the focal length of a liquid crystal droplet lens. Figure 1(a) and 1(b) illustrate the operation schematics of the liquid crystal droplet lens. Non-uniform electric fields that were generated by concentric electrodes yield DEP forces [10–11] exerted on the droplet. The ITO electrodes of 50μm in width and 50μm in spacing were fabricated on an ITO glass wafer, followed by Teflon® coating. Teflon® functions as a hydrophobic layer, increasing the contact angle of the liquid crystal droplet. The DEP mechanism used to deform the droplet can be described using the Kelvin polarization volume force density as
where ϵ// and ϵ0 are the permittivities of liquid crystal and free space, respectively. E denotes the electric field intensity.
3. Experimental results
Figure 2 shows the interference images of the liquid crystal droplet lens in the nematic phase and in the isotropic phase, respectively. The images were obtained using a transmissive optical microscope with crossed polarizers. Figure 2(a) implies the birefringence effect of the droplet lens at the temperature of 20°C. Such birefringence issue disappeared as the operation temperature exceeded TNI of 23.5°C since the liquid crystal transited from the nematic phase to the isotropic phase [refer to Fig. 2(b)]. Figure 3 shows the transmission spectrum of the 700μm thick liquid crystal used in the two phases. The liquid crystal has the spectral transmission in average of 54% and 78% in nematic phase and in isotropic phase, respectively.
Figure 4(a) shows the images of the letter “F” given different focal lengths of a 2μL liquid crystal droplet lens in the isotropic phase. The images were captured by a CCD sensor on a microscope. The image appeared to be on focus at the voltage of 150V. The images blurred when the voltages were tuned to be away from 150V. As the voltages decrease to 100V or even lower, the liquid crystal droplet lens has shorter focal length. Figure 5 shows the droplet profile under different voltages applied. The droplet profiles were measured and fitted using a semi-automatic contact angle meter (OCA20, Data-physics). At the rest state, the droplet lens was 1.76mm in diameter and 0.65mm in height. The droplet lens began to deform at the voltages of over 40V. At 200V, the droplet lens transformed to have diameter of 2.1mm and height of 0.5mm. The lens functions in between a spherical lens and a parabolic lens. The conic constants were calculated to be -0.04 and -0.15 at the rest state and at 200V, respectively. Figure 6 shows the focal lengths and their corresponding contact angles at various applied voltages. When the voltages increased from zero to 200V at 1 kHz, the focal length increased from 1.6mm to 2.6mm and the contact angle decreased from 65° to 41°. Hysteresis of the contact angle was found to be about 3° when the voltages applied switched from 200V to the rest state. Such hysteresis vanished after 1 minute at the rest state.
Figure 7 shows the tuning ratio of the focal length Δf/f0 and the variation of the contact angle Δθ in the range of 0-200V where f0 is the focal length of liquid crystal droplet lens at the rest state. The maximum tuning ratio of the focal length was about 60% given the electrode spacing of 50μm; this tuning ratio corresponds to the contact angle change of 24°. As the electrode spacing over 200μm, the tuning ratios of the focal length dropped below 5% (i.e. the contact angle change of less than 3°.) The droplet deformation was induced by the DEP force, according to Eq. (1), which is proportional to the gradient of the electric field intensity squared. The electric field intensity is inversely proportional to the electrode spacing to some extent. Hence, the larger DEP forces can be induced by the narrower electrode spacings.
Liquid crystal droplet was demonstrated as the dielectric liquid lens driven by DEP forces. Conventional liquid crystals are not used for this purpose. Therefore, new liquid crystals with low TNI are required to be developed. The applied voltages could be reduced by narrowing the concentric electrode spacings or by redesigning the electrodes. The lens has spherical aberration and distortion at its edge.
Numerical aperture (NA) of the liquid crystal droplet lens was calculated to be about 0.5, 0.4 at the rest state and at 200V, respectively. High numerical aperture results from large refractive index of the liquid crystal. The response time from 200V to the rest state was measured to be about 220ms. Actuation of the liquid crystal droplet lens was determined to consume electric power of about 0.1mW. Both microbubbles and evaporation were not observed in the lens after continuous one week operation.
Table 1 shows performance comparison of DEP-driven liquid crystal droplet lenses proposed and electrowetting-driven water-based liquid lenses. Compared to the water-based liquid lenses, the liquid crystal droplet lenses have comparable performances in the aspects of numerical aperture, power consumption, tuning ratio of focal length and negligible evaporation. Such advantages permit the liquid crystal droplets lenses as a potentially better alternative for miniaturized tunable focus lenses in the near future. Both response time and hysteresis are still required to be improved.
References and links
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