Large aperture liquid crystal lens array using a ... - OSA Publishing

Vol. 26, No. 7 | 2 Apr 2018 | OPTICS EXPRESS 9254

Large aperture liquid crystal lens array using a composited alignment layer HU DOU,1 FAN CHU,1 YU-QIANG GUO,2 LI-LAN TIAN,1 QIONG-HUA WANG,1,* AND YU-BAO SUN2 1

School of Electronic and Information Engineering, Sichuan University, Chengdu, 610065, China Department of Applied Physics, Hebei University of Technology, Tianjin, 300401, China *[email protected] 2

Abstract: A liquid crystal (LC) lens array with high light control power and a large aperture using a composited alignment layer is proposed. In our design, the alignment layer is not only used for getting a uniform arrangement of LC molecule, but also for getting a lens-like refractive index distribution in the LC layer when a voltage is applied. Through simple technology processes, a tunable focal length LC lens array with a millimeter scale diameter can be achieved. Furthermore, the maximum phase difference of the proposed LC lens array can achieve 105.38π. So, the proposed LC lens array has a high light control power. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (230.3720) Liquid-crystal devices; (220.1140) Alignment; (110.2760) Gradient-index lenses.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

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#323025 Journal © 2018

https://doi.org/10.1364/OE.26.009254 Received 13 Feb 2018; revised 22 Mar 2018; accepted 22 Mar 2018; published 29 Mar 2018


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1. Introduction As an important optical device, the liquid crystal (LC) lens has become increasingly attractive. It has the potential to replace the conventional glass lens because of its excellent characteristics, such as lightweight, small size, low power consumption and tunable focal length without moving mechanical parts [1–10]. Compared with the conventional glass lens array applied in the autostereoscopic display, the LC lens array has drawn more attentions because of its characteristic photoelectric properties: a switchable function of 2D/3D display and 2D/3D coexist can be realized. In an autostereoscopic display composed of a lens array and a 2D display, an LC lens should cover multiple pixels of the 2D display. So, the diameters of the lens should in the millimeter range for matching most of the 2D display [11-12]. But compared with the LC micro-lenses, it is hard to generate a parabolic refractive index distribution in the LC layer in a long range. Thus, the structure of the large aperture LC lenses with the diameter in the millimeter range are complicated [13–16]. Although a number of researches about large aperture LC lenses have been reported, the manufacturing process of a single LC lens is intricate enough, and few of them can be used to manufacture lens arrays. A hole patterned electrode with dielectric slab has been used for fabricating LC lens array [4, 17]. It has a convenient fabrication process, but the thick dielectric slab causes some vertical electric field in the center of the hole, which decreases the adjusting range of the focal


length and increases the applied voltage. Moreover, the diameter of the LC lens is not large enough, if the diameter of the lens is increased to the millimeter level. The thickness of the dielectric slab must be increased to ensure a parabolic refractive index distribution, but the applied voltage is increased, and the range of the tunable focal length is reduced. The LC lenses that comprise multi-layer or multi-electrode exhibit a good parabolic phase distribution when tuning the focal length. But the structure of these LC lenses is complex [13–26], the driving voltage are multiple and even the voltage-dependent focal length is irregular [22]. The complicated structures and driving modes make these LC lenses difficult to be manufactured in lens arrays. Compared with the above-mentioned LC lenses, the electrode structure and driving mode in the LC lens with a composited dielectric layer is simple. A composited dielectric layer is used on the glass substrate to form electric field gradient distribution [27–33]. However, when an electric field is applied, it has to penetrate the thick glass substrate to control the LC layer [28–31]. This feature will increase driving voltage and bring bad influence on energyefficient. Furthermore, because of the extra composited dielectric layer, the manufacture technology is not simple enough to fabricate a lens array. In this paper, we use a composited alignment layer (CAL) to fabricate the LC lens array. Compared with the LC lens with a composited dielectric layer, the function of a composited dielectric layer can be replaced by an alignment layer. So, the CAL serves two functions: generate uniform arrangement of the LC molecule and causes electric field gradient distribution in the LC layer. Thus, the structure and production processes of the LC lens array are simplified. Besides, the proposed LC lens has many other desirable features: the diameter of the LC lens array can be achieved in the millimeter range easily. Moreover, the max phase difference of the proposed LC lens array is more than 100π, and it offers a good ability of getting a tunable focal length. Above all, only two flat electrodes are placed on the two sides of the LC layer to drive the proposed LC lens array, and the drive mode is easy to accomplish. 2. Structure and theory The schematic and the cross section of the proposed LC lens array are shown in Figs. 1(a)– 1(c). Two indium-tin oxide (ITO) glass substrates with different alignment layers are used to fabricate the cell. The top ITO glass substrate is coated with a high dielectric layer as the alignment layer (transparent color). The heart of the cell is the CAL on the inner surface of the bottom ITO glass substrate, as shown in Fig. 1(a), and the CAL consists of two materials with different dielectric constants, convex protrusions and a planar dielectric layer with a high dielectric constant. The dielectric constants of the top alignment layer and the bottom high dielectric layer are both 9.5, and it is the mixture of 90% polyvinylidene fluoride(PVDF) and 10% polyimide (Pi) [34]. The convex protrusions are made of photoresists, and their dielectric constants are 2.8~4.2, according to their various kinds. The alignment direction of the top alignment layer and the bottom CAL keep the same with the polarization direction of incident light. So, in the voltage-off state, these two alignment layers lead to a homogeneous planar alignment of the LC molecules, as shown in Fig. 1(b). In the voltage-on state, a spatially non-uniform electric field is induced in the LC layer on account of the CAL. Because the dielectric constant of the planar high dielectric layer is higher than that of the convex protrusion, the electric field in the central part above the convex protrusions in the LC layer will thus be different (weaker) from the electric field above the periphery of the convex protrusions in the LC layer. As shown in Fig. 1(c), this non-uniform electric field will reorient the LC’s director and acquire lens-like refractive index distributions in the LC layer. The electric field distribution in the LC layer is shown in Fig. 1(d).


Fig. 1. Schematic of the liquid crystal lens array using a CAL. (a) Stereogram of the LC lens array. (b) Cross section of the LC lens array in the voltage-off state. (c) Cross section of the LC lens array in the voltage-on state. (d) Electric field distribution in the LC layer.

The trapezoid protrusions can be easily fabricated by lithography because the convex protrusions are made of photoresists. Then a high dielectric layer is used to make the alignment layer flat. The materials of the convex protrusions and planar high dielectric layer are soluble. An oblique incidence UV light is adopted in the experiment for causing a gradient distribution of curing degree. For a protrusion, the solubility capacity is reduced from edges to the center. So, the surfaces of the trapezoid protrusions become curved and smoothed after a high dielectric layer is coated, two different spin-coating speed and time are alternately adopted in the experiment (15 °C , 500r/min, 20s and 15 °C , 2000r/min, 80s). Meanwhile, the trapezoid protrusions are turned into convex protrusions, as shown in Figs. 2(a)–2(b).

Fig. 2. Fabrication of the CAL. (a) Trapezoid protrusions by lithography. (b) Trapezoid protrusions are turned into convex protrusions after a high dielectric layer being coated.


3. Simulation results We performed simulations to validate the device concept. In our simulations, an LC material (5CB) was injected into the cell, and the birefringence of the LC is Δn = 0.204 (ordinary refractive index no = 1.517 and the extraordinary refractive index ne = 1.721). The paralleled dielectric constant is ε// = 27.3 and the perpendicular dielectric constant is ε⊥ = 6.8. The thickness of the LC layer is 200μm. The dielectric constant and the thickness of the convex protrusions are 3.2 and 28.5μm, respectively. The convex protrusions are parabola-shape. The dielectric constant and the thickness of the high dielectric layer are 9.5 and 30μm, respectively. The CAL on the bottom substrate and the alignment layer on the upper substrate are flat. The director distribution of the LC can be calculated when the applied voltages are different by using the commercial software TechWiz LCD 3D (Sanayi System Co., Ltd., Korea). Figures. 3(a)–3(d) show the results of our simulations.

Fig. 3. Director distribution in the cross section of the LC layer with different applied voltages: (a) 11V, (b) 12V, (c) 13V, (d) 14V.

The rubbing direction of the two alignment layers coated on two glass substrates are the same, and the director of the LC is parallel to the glass substrates. So, the polarization direction of the incident light is along the LC’s long axis in the voltage-off state. But when the applied voltage increases, the electric field is unevenly distributed in the LC layer, as shown in Fig. 1(d). The polar angle of the LC molecules above the gap of the protrusions would be increased as high priority because of a larger electric field. Meanwhile, the LC molecules above the protrusions are insensitive to the smaller applied voltage, thus a parabolic refractive index distribution in the LC layer is generated. So, we can control the refractive index distribution in the LC layer only through tuning the applied voltages. Figures 4(a)–4(d) are the refractive index distribution in the cross section of the LC layer with different applied voltages.


Fig. 4. Refractive index distribution in the in the cross section of the LC layer with different applied voltages: (a) 11V, (b) 12V, (c) 13V, (d) 14V.

Fig. 5. Phase profiles of the proposed LC lens array when the applied voltages are different: (a) 11V, (b) 12V, (c) 13V, (d) 14V.

Figures. 5(a)–5(d) show the simulated results of the phase profiles of the proposed LC lens array with different operating voltages. The simulation parameters are the same as above. We only research one lens from 0 to 1.2mm. Beyond this region, the lens fringe is not parabolic anymore. For convenience, we set the phase at the center of the lens to be zero. We can tune the phase difference between the center and the edge of the proposed LC lens


through controlling the applied voltage. As shown in Figs. 4(a)–4(d), when the applied voltage is increased from 11V to 14V, the maximum phase difference of the proposed LC lens is increased from 0.167π to 105.38π. Such a wide phase difference adjustment range will ensure a wide focal length range. Furthermore, we will get a strong light adjustment power and a good lens optical effect device because the maximum phase difference of the proposed LC lens could exceed 100π. Moreover, for the LC lens, the refractive index distribution should remain parabolic to ensure a good lens-like optical effect. When the applied voltage changes, the refractive index distribution (black dots) of the proposed LC lens matches well with the ideal lens (black lines). 4. Experiment and discussion Some experiments are carried out in order to demonstrate that the liquid crystal lens array using a CAL is feasible. Figures. 6(a) and 6(b) are the pictures of the proposed LC lens array. In our experiments, the proposed LC lens array contains 88(11 × 8) LC lenses. The parameters of the LC cell are the same with our simulations. As shown in Fig. 6(a), when a driving voltage is applied, the LC cell can generate a special optical effect, and it is the same as a lens array. The light control power of the LC lens array is obvious, and some light spots are formed in the screen. The optical effect like a lens array can be vanished without the applied voltage, as shown in Fig. 6(b). So, we can tune the light control power or the focal length of the proposed LC lens array by adjusting the applied voltage (see Visualization 1).

Fig. 6. Picture of the proposed LC lens array: (a) On state with an applied voltage. (b) Off state without an applied voltage (see Visualization 1).

We adopted an CCD camera to replace the white screen in Figs. 6(a)–6(d). Figures. 7(a)– 7(d) are the CCD images of the proposed LC lens when the distance between the LC cell and the CCD camera is 25mm, and the applied voltages are 11V~14V correspondingly. As can be seen from Figs. 7(a)–7(d) (2 × 2 LC lens, size:2.8mm × 2.8mm), when the applied voltage is increased but less than 14V, the light spots are becoming smaller and brighter, and the light control power of the proposed LC lens array is also increased accordingly. Figures 8(a)–8(d) (2 × 2 LC lens, size: 2.8mm × 2.8mm) are the absolute value of phase difference distribution of the proposed LC lens array when the applied voltages are different. When the applied voltage is increased from 11V to 14V, the maximum phase difference of the LC lens array can be changed from 0.24π to 95.6π. So, we can tune the focal length of the proposed LC lens array by adjusting the applied voltage. Figures. 9(a)–9(c) are the observed interference rings of the LC lens when the applied voltages are different. As the applied voltage is increased, the refractive index distribution of the LC layer is changed significantly.


Fig. 7. CCD images of the proposed LC lens at different applied voltages: (a)11V, (b) 12V, (c)13V, (d)14V.

Fig. 8. Phase distribution difference (2π) of the proposed LC lens array when the applied voltages are different: (a) 11V, (b) 12V, (c) 13V, (d) 14V.

Fig. 9. Interference rings of the proposed LC lens array when the applied voltages are different: (a) 0V, (b) 13V, (c) 14V. (f = 1kHz, λ = 632.8nm).

The focal length of a LC lens can be expressed as f = R2/2δn(E)dLC, where δn(E) is the index difference between the lens’ center and edge, dLC is the thickness of LC layer, and R is the radius of the LC lens [35]. As mentioned earlier, the maximum phase difference of the proposed LC lens array can achieve 105.38π in our simulations and 95.6π in our experiments. So, the proposed LC lens array has a very small minimum focal length, and this leads to a


wide focal length range. The applied voltage dependence of the focal length is shown in Fig. 10. It can be seen that when the applied voltage is 11V, the focal length is larger than 10000mm. When the applied voltage is 14V, the focal length is 24.5mm in simulation and 26.3mm in experiment. Overall, Fig. 10 shows that our theoretical analysis and simulations are consistent with the experimental results.

Focal length (mm)

10000

Simulation Experiment

1000

100

10

11.0

11.5

12.0 12.5 13.0 Voltage (V)

13.5

14.0

Fig. 10. Applied voltage dependent focal length of the proposed LC lens array (λ = 632.8nm).

5. Conclusions An LC lens array using a CAL is proposed. In general, the alignment layers in the LC cell is only used for molecular reorientation, but in the proposed LC lens array, our simulation and experimental results demonstrate that the CAL can also be used for getting an electric field gradient distribution when a suitable voltage is applied. So, complicated dielectric layers or special electrode structures are unnecessary, and the fabrication process of the proposed LC lens array has a simple manufacture technology. The diameter of the proposed LC lens array is in millimeter level, and the maximum phase difference of the proposed LC lens array can achieve 105.38π in simulations and 95.6π in experiments. As a result, we propose a low manufacture difficulty and cost saving method to fabricate the LC lens array with large aperture and high light control power. Funding National Key R&D Program of China (2017YFB1002900); National Natural Science Foundation of China (NSFC) (61320106015, 61535007).