1. Introduction

Optical lenses are extensively utilized in science, industry, and daily life. The development of tunable lenses with variable focal lengths and focal intensities is very important. One of the methods to achieve such variability is based on the reorientation of nematic liquid crystal (NLC) molecules under an externally applied electric field. The advantage of NLCs is that their large optical birefringence. Therefore, the optical path lengths (OPLs) can be controlled over a wide range by the application of a voltage.

The lens effect occurs when a light beam propagating through a medium with spatially varying OPLs. It can therefore be produced by varying the thickness of material (as in glass lenses), by varying the refractive index across the light beam, or by a combination of these two variations. The development of NLC lenses began in the late 1970s [1,2]. The initial design of an NLC lens was based on conducting film-coated curved substrates of parabolically or spherically for example varying thicknesses, to control the LC orientation. Since then, various approaches have been developed. They can be seen in NLC lenses of a uniform thickness, but with ring-patterned electrodes to achieve various distributions of LC alignments when suitable voltages are applied across the multiple electrodes [3,4], Fresnel-type lenses filled with LCs [5,6], LC lenses with a polymer network of spatially varying densities [7,8], LC lenses produced by patterning electrodes, of either the slit type [9] or the hole type [10], and other lenses [11,12].

Many methods for controlling the distribution of LC pretilt angles have been demonstrated for producing a refractive index distribution in an LC cell of uniform thickness [13,14]. In this investigation, LC cells with the substrates having an axially symmetric gradient distribution of LC pretilt angles were formed by the effective planar and high pretilt (almost-vertical) alignment forces. The former was associated with the axially symmetrical ripple structure formed by the photo-adsorbed azo dye, while the latter was associated with a mixed polyimide alignment layer. Finally, a polarization-independent LC lens was formed by combining axially symmetrical radial and azimuthal LC cells with gradient pretilt angle distributions (Fig. 2 below). The focal intensity of the formed LC lens can be controlled by applying a voltage to the sample.

 

Fig. 2 Images of axially symmetric (a) radial and (b) azimuthal cells under linearly polarized probing light. The insets in (a) and (b) show the LC director alignments. (c) Top-view, (e) side-view of LC structures in axially symmetric radial cell; (d) top-view, and (f) side-view of LC structures in axially symmetric azimuthal cell. P: polarization of probing light.

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2. Device fabrication

The NLC and azo dye that were used in this experiment were E7 (Merck) and Methyl Red (MR; Aldrich), respectively. The MR:E7 mixing ratio was 1:99 wt%. In the part of the film with the high pretilt alignment, a mixture of vertical- (AL-00010) and planar- (AL-1426B) aligned polyimides (PIs), obtained from Daily Polymer was applied [13] to substrates. A mixture of the polyimide AL-00010 (4.76 wt%) and AL-1426B (95.24 wt%), dissolved in dimethyl sulfoxide (DMSO), with a concentration of the polyimide mixture of around 50% by weight relative to the total weight of the solution, was prepared. The polyimide mixture was spin-coated onto indium-tin-oxide (ITO)-coated glass slides at 2000 rpm for 30 s. The slides were prebaked at 80°C for 30 min, and then fully baked at temperatures from 200°C to 220 °C for 60 min. Two ITO-coated glasses with a mixed PI alignment layer, separated by 12 μm ball spacers, were used to fabricate an empty cell. Then, the homogeneously mixed MR/E7 compound was injected into an empty cell in the isotropic state to form a dye-doped liquid crystal (DDLC) sample.

The photo-alignment of both sides of a DDLC cell was performed following our earlier investigation [15] using a linearly polarized DPSS (diode-pump solid state) laser (λ = 532 nm), whose wavelength was close to that of the peak in the MR absorption spectrum as the light source. The Gaussian DPSS pump laser beam, propagating along the z-axis with an intensity of ~0.8 W/cm², was expanded into a collimated beam with a diameter of ~21 mm. It then passed through a linear mask with a line-width of ~200 um, and was focused using a cylindrical lens onto the cell. Notably, the axially symmetric LC devices can also be achieved using a cylindrical lens without a linear mask. The sample was attached to a rotating motor, and maintained at a temperature of ~65°C (which exceeds the clear temperature of E7, ~61°C) with pumping to ensure double-sided photoalignment [15]. The MR dyes underwent trans–cis isomerization after they were pumped using green light. They then exhibited continuous molecular reorientation. Finally, the excited MR dyes diffused and were adsorbed on the two ITO surfaces that were coated with the mixed PI alignment layer to form an axially symmetric ripple structure which is the so-called light-induced ripple structure (LIRS) [16]. The angle, θ, made between the polarization of the pump beam and the x-axis (Fig. 1 ) can be changed using a wave-plate in front of the beam expander. The period of illumination was ~60 minutes and the rate of rotation was ~90 rpm. Since the pump laser was a Gaussian beam, the amplitude of the formed ripple structure peaked in the center of the beam, and decreased toward its edge. Therefore, consistent with the Berreman theory [17], the formed ripple structure herein the investigation exerts the planar alignment force which peaks in the center and declines toward the perimeter of the beam. The combination of the formed ripple structure with the mixed PI alignment layer (that produced an almost vertical alignment) gives rise to the gradient LC pretilt angles in a DDLC cell (Fig. 2).

 

Fig. 1 Sample fabrication setup.

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3. Results and discussion

Figure 2 schematically presents the conformation and the optical images of axially symmetric LC cells obtained under linearly polarized light. Notably, the shaded areas represent the dark areas in Figs. 2(a) and 2(b). Since the dichroic MR dyes absorb light strongly when the polarization of the probing light is parallel to the long axes of the MR dyes, the images in Figs. 2(a) and 2(b) are reasonable. Based on these images, Figs. 2(c), 2(e), and 2(d), 2(f) illustrate the structures of the axially symmetric radial and azimuthal DDLC cells, respectively.

As described above, the formation of LIRP structures is one of the key processes in causing an LC cell to have an axially symmetric, gradient distribution of LC pretilt angles. To verify the formation of the LIRSs of the dyes that are adsorbed on the substrates, a scanning electron microscope (SEM) was used to study the dye-adsorption morphology on the substrates in the radial and azimuthal DDLC cells. Figure 3 presents the LIRS that is formed by the adsorption of dye in an azimuthal cell (Fig. 2(b)) under various SEM magnifications. The spacing (Λ_Exp.) of the formed LIRS is around 345 nm, which is close to the theoretical value Λ = 349 nm, calculated using Λ~λ/n, where λ and n are the wavelength in a vacuum and the refractive index of the material, respectively [16]. The amplitude of LIRSs in the center clearly exceeds that at the periphery because the beam is more intense there. Similar observation (result not shown) was made of an axially symmetric radial sample. We elucidated the mechanism of formation of LIRSs in a DDLC cell elsewhere [16,18]. Briefly, it is believed that the LIRS formation is associated with the interference between the incoming polarized laser beam and the wave that is scatted by the adsorbed dyes on the surface. In this investigation, the excited azo dyes undergo trans–cis isomerization and molecular reorientation, and are then adsorbed onto the two substrate surfaces (double-side photo-alignment) forming LIRSs that exert the aligning force on LC molecules [6,15].

 

Fig. 3 Images of axially symmetric azimuthal cell under scanning electron microscope (SEM). Magnifications are (a) x 2500, (b) x 10000 (c) x 30000. Red dotted rectangles in insets are the observed areas on the azimuthal cell.

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Throughout the photo-isomerization, the pump laser irradiates the sample as the sample is rotated about the z-axis. The illumination is stronger in the center of the beam than at the periphery. The axially symmetric photoalignment exerts a gradient aligning force on the LCs along the surface on the substrates, resulting in the gradient pretilt angle distributions that are shown in Figs. 2(e) and 2(f).

To fabricate an axially symmetric radial (azimuthal) LC cell with an LIRS, the polarization angle of the pumping beam was set to θ = 90° (θ = 0°) with polarization along the y-axis, as shown in Fig. 1. As described above, since the sample was rotated and thermally controlled at a fixed temperature, the excited dyes underwent trans–cis isomerization, molecular reorientation, diffusion and, then adsorption onto the two ITO surfaces, finally forming the LIRSs. The double-side photoalignment forms LIRSs, and causes the formation of axially-symmetric radial and azimuthal LC cells, shown in Figs. 2(a) and 2(b), respectively. The optical properties of the central areas of these axially symmetric LC samples were the same as those observed elsewhere [15,19]. The main difference between the present axially symmetric LC samples with those described elsewhere studies [15,19] is that the formed LIRSs align the LC molecules parallel to the direction of polarization of pumping light, because the aligning force of LC molecules is provided by the microgrooves of LIRSs, which are parallel to the polarization direction of pumping light [16,18], while the studies in Refs. [15,19]. are associated with less illumination dosage of pumping laser on the sample resulting in the dye adsorption without forming a ripple structure on the substrates. The LC molecules are aligned parallel to the adsorbed dye direction, which is perpendicular to the pump-beam polarization.

The transmittances of the axially symmetric DDLC films were measured at various positions under various applied voltages, to determine the relationship between the phase retardation, ψ, of the device at various points with the applied voltage. Here, position x is the distance of a point from the center of the irradiated DDLC area. The measurements were made using an He-Ne laser (λ = 634 nm) with the cell placed between two crossed polarizers. The angle made by the polarizer axis and the projection of the LC director onto the substrate surface was 45°. Figure 4 plots the ψ-x curves obtained under various applied voltages. Figure 4 clearly reveals that the phase retardation of an axially symmetric cell peaks at the center of the beam, and decreases towards the perimeter of the beam indicating a gradient pretilt-angle distribution across the beam [18]. The phase retardation decreases as the voltage increases because LCs (Δε>0) align with their long axes parallel to the electrical field when a voltage is applied.

 

Fig. 4 Measured phase retardations of an (a) radial and (b) azimuthal axially symmetric DDLC cell with a gradient pretilt angle.

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The gradient phase retardation has a focusing effect. Two orthogonally oriented LC layers with gradient distribution alignment have been shown to produce a polarization-independent lens if the phase modulations of the two films are identical [20,21]. To demonstrate a polarization-independent LC lens, radial and azimuthal symmetric cells with orthogonal directors were stacked together, as shown in Fig. 5 .

 

Fig. 5 Unpolarized light incident onto a LC lens based on stacked radial axially symmetric DDLC cells.

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The properties of the formed polarization-independent liquid crystal lens were measured using the setup that is shown in Fig. 6 . A rotatable analyzer was placed behind a polarizer and a λ/4 plate to produce circularly polarized light and change the polarization of the probing beam that is incident onto the lens. AC voltages V_a and V_b (square waveform; 1 KHz) were applied to the radially (sample A) and azimuthally (sample B) symmetric cells, respectively to equalize the phase retardations that they caused. Figure 7 presents the measurements of the relationship between the analyzer-axis angle (ω^o) and the focal intensity under various measuring conditions. Triangular data points represent the intensity of a probing beam that does not propagate through the lens. Rhombus and square points represent the focal intensities when voltages V_a = 1.3 V, V_b = 0 V, and V_a = 10 V, V_b = 10 V, respectively, are applied. The results are quite consistent with the phase-retardation distribution curves in Fig. 4. When V_a = 1.3 V and V_b = 0 V, the phase retardations in the radial (A cell) and azimuthal cells (B cell) equal each other, and so the lens focuses the probing beam effectively, as revealed by rhombuses in Fig. 7. The focal intensities are independent of the analyzer angle, indicating that the lens is a polarization-independent liquid crystal lens. In this experiment, the focal length of the LC lens device is around 0.5 m. However, the effective focal length can be increased by increasing the applying voltage. Notably, the focal length of the lens without the application of a voltage can be varied by changing the pump-beam intensity distribution, since the distribution of the pump-beam intensity determines the LIRSs on the substrates, which affect the gradient LC pretilt distribution, and the intrinsic focal length of the lens. Notably, it is found that the MRs adsorbed on the ITO-coated glass substrates are stable. No change of the lens performance is observed, when the lens is further exposed to the green laser used in the present study. Yet, the performance may be slightly changed with the lens being probed in the green-blue spectrum range due to light absorption. In this case, we can resolve it simply by using a MR dye with no absorption in the visible.

 

Fig. 6 Setup for measuring properties of polarization-independent liquid crystal lens device. (Cells A and B are radial and azimuthal, respectively.)

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Fig. 7 Focal intensities of transmitted light are measured at under various operating conditions using a rotating analyzer.

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4. Conclusion

In conclusion, a polarization-independent LC lens that is based on stacking radially and azimuthally symmetric cells with mutually orthogonal directors is demonstrated. These axially symmetric liquid crystal cells are fabricated from dye-doped liquid crystal cells by double-side photoalignment with LCs oriented with a gradient pretilt angle. The focal length of the polarization-independent liquid crystal lens can be controlled by applying various voltages. The numerical aperture (NA) of the present lens is ~0.035. To increase the NA value of the lens, we can simply use a laser having a large enough power. Additionally, the lens is simple to fabricate, and convenient to use. It therefore has great potential for practical applications.