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This work investigates an electrically and optically tunable Fresnel lens in a liquid crystal (LC) cell with an erasable and rewritable photoconductive layer. By using a Sagnac interferometer, a Fresnel-like pattern can be induced on the photoconductive polymer layer which results in conductive and nonconductive structures in bright and dark zones. This effect causes the mismatch of the LC refractive index between adjacent zones with external voltage, generating a LC Fresnel lens. The focal length of the proposed Fresnel lens can be easily tuned by varying the Fresnel pattern size, and the focusing efficiency can be optically and electrically controlled.
© 2016 Optical Society of America
1. Introduction
Liquid crystal (LC) lenses have been of interest and investigated widely for an increasing variety of optoelectronic applications including image processing, photonic devices, optical communications, eye glasses and 3D displays [1–5]. Specifically, in recent years, electrically switchable LC Fresnel lenses have gained attention and have been widely developed [6–13]. The previous literature has focused on the combination of Fresnel zone plates and LC materials in order to extend and optimize the optoelectronic applications of Fresnel lenses. The LC Fresnel lens could control diffraction efficiency by varying electronic fields because the reorientation LC molecule in the odd-even zone generates a phase difference.
Conventional Fresnel zone plates have been fabricated by photomasking or electron-beam writing, but have limitations because the focal length is dependent on the radius of the central zone [6–15]. An interference method is proposed to control the size of the Fresnel zone pattern, and to develop the LC Fresnel lens of optically controllable different focal lengths [16,17]. Comparing with other configurations, such as Michelson and Mach-Zehnder interferometer, an interference pattern created by the two divergence beams in the Sagnac interferometer exists the higher optical stability and optical resolution between the bright and dark zones. By doing so, the applications of LC Fresnel lenses can be expanded.
In particular, this work proposes that LC Fresnel lenses with a photoconductive layer can be erased and rewritten. This electrically and optically controllable Fresnel lens is formed by using the Fresnel zone pattern obtained from a Sagnac interferometer irradiation on the photoconductive polymer layer of the LC cell with the application of direct-current (DC) voltage. The LC Fresnel lens can be measured, and the highest value of a focusing efficiency is 34.9% by tuning the intensity of the pumped Fresnel-pattern blue beam and by controlling an appropriate voltage. The focal lengths can be varied in the range of 28.5 cm by moving the position of the LC cell.
2. Sample preparation and experimental setups
The photoconductive polymer is obtained by doping Buckminsterfullerene (C60) into poly[N-vinyl carbazole] (PVK, from Acros) [18–20]. The chemical structures of the above two materials are shown in Fig. 1(a) and 1(b) respectively. Figure 1(c) shows the absorption spectra of PVK (blue line) and C60 doped PVK(red line). The function of the PVK/C60 layer and its mechanism has been explained by Wang [21]. The charge-generating process will be occurred for the C60 doped PVK under the light exposure, which is due to the energy transfer from PVK to C60 resulting in the excitation of C60. The dopant C60 leads to the absorption spectra of the PVK extended from the UV regime to the visible regime. The PVK: C60 ratio in the photoconductive polymer is 99.85:0.15 wt%. A photoconductive layer with a thickness of ~100 nm is coated on an indium-tin oxide (ITO) glass plate. Two polyimide films are deposited on the photoconductive layer and another one on the ITO-coated substrate, and they are rubbed to form homogeneous alignment. The above two glass plates are combined to form an empty cell, and are separated by two 12 μm-thick plastic spacers. The nematic LC HTW114200-100 (ne = 1.77, no = 1.51, from Fusol) is injected into the empty cell to complete the LC cell with a photoconductive layer.
Fig. 1 Chemical structures of (a) PVK and (b) C60. (c)The absorption spectra of the PVK (blue line) and C60 doped PVK (red line) layers.
Figure 2 schematically illustrates the experimental setup for generating the Fresnel LC lens and the analysis of the focusing characteristics. The blue writing beam with a wavelength of 488 nm originating from an Ar+ laser is divided into two beams via a beam splitter. An interference pattern is produced by the superposition of the two beams that have the same path and propagate in opposite directions in the Sagnac interferometer loop [17]. A lens in the loop is used to produce divergence of the beams and to amplify the interference pattern. The pattern is shown in Fig. 3(a). The amplified interference is similar to the Fresnel zone pattern. The spot size of the Fresnel pattern in the LC cell can be adjusted by moving the position of the sample due to the divergence of the interfering beams. The focusing properties of the LC Fresnel zone plate are probed by using the red probe beam that originates from the He-Ne laser (wavelength 632.8 nm, 0.23 mW/cm2) with linear polarization, and are analyzed by using a CCD camera and a power meter.
Fig. 2 Illustrates the experimental setup for generating the Fresnel zone pattern in a homogeneous aligned LC cell using the Sagnac interferometer and the analysis of the focusing characteristics. The symbols are denoted as follows: P, polarizer; λ/4, quarter-wave plate; A, analyzer; DM, dichroic mirror; BS, beam splitter; L, lens; M, mirror; F, long-wave pass filter.
Fig. 3 (a) The Fresnel pattern generated by the Sagnac interferometer. (b) The operating principles of the LC Fresnel lens with a photoconductive layer at an applied voltage.
3. Results and discussion
Figure 3(b) shows a schematic diagram and the operating principles of the LC Fresnel lens with a photoconductive layer. The conductivity of the PVK/C60 layer increases as it is irradiated by the blue beam. The PVK/C60 photoconductive layer exhibits highly conductive odd zones and lowly conductive even zones as the Fresnel-patterned blue beam irradiates on the sample. As an appropriate external DC voltage is applied to the cell, the electric-field-induced reorientations of LCs in the odd zones occur, while the LCs in even zones maintain the initial state [19]. Therefore, a mismatch of the refractive index between the adjacent odd and even zones is induced, and then a LC Fresnel lens is formed. The phase difference between the odd and even zones of the LC Fresnel lens is
where d is the cell gap, λ is the wavelength of the probe beam, and neven and nodd are the refractive indices of the even and odd zones, respectively. According to the theory of Fresnel [22,23], the first-order focusing efficiency of the LC Fresnel lens can be written asAs the phase difference between the adjacent zones equals approximately π, the first-order focusing efficiency reaches the maximal value of ~41%.Figure 4 shows focused images of the LC Fresnel lens that are taken from the CCD camera at an applied voltage of 1.4 V. As no Fresnel-patterned blue beam irradiates the LC cell that is applied with a voltage of 1.4 V, the focusing effect does not occur and exhibits uniform intensity in the focal plane, as shown in Fig. 4(a). Figures 4(b)–4(d) show the focusing performance of the LC Fresnel lens where the intensity (I) of the Fresnel-pattern blue beam is at I = 9.85 mW/cm2 and applied voltages V = 1.4 V, and the polarizing angles of the probe beam are at 0°, 45°, and 90°. The polarizing angle 0° of the probe beam parallels the rubbing direction of the LC cell. As the above polarizing angle increases, the focusing effect becomes weaker. Due to the increase in the polarizing angle of the probe beam, it experiences the refractive index that will be close to no in the even zones, and therefore the phase difference between the odd and even zones decreases.
Fig. 4 shows the focused images of the LC Fresnel lens at an applied voltage V = 1.4 V: Without irradiation intensity I = 0 (a); with the irradiation intensity I = 9.85 mW/cm2 and polarizing angles of the probe beam at (b) 0°, (c) 45°, (d) 90° respectively.
Figure 5 displays the voltage-dependent focusing efficiency at the various irradiation intensities of the Fresnel-pattern blue beam. When the irradiation intensity increases from I = 0.394 mW/cm2 to I = 9.85 mW/cm2, the focusing efficiency of the LC Fresnel lens gradually increases. Because the intensity of the Fresnel-pattern blue beam increases, the conductivity of the PVK/C60 layer increases. The voltage via the PVK/C60 layer is applied on the LC bulk (VLC) in the steady-state regime, which can be written as [19,24]
where V is the applied voltage, σPVK/C60 (dPVK/C60) and σLC (dLC) are the conductivities (film thickness) of the PVK/C60 layer and LC bulk. This equation indicates that the voltage applied on the LC bulk depends on the ratio of σLC to σPVK/C60. When the intensity of the Fresnel-pattern blue beam is increased, the conductivity of the PVK/C60 layer increases, resulting in an increase in voltage applied on the LC bulk. Consequently, with the high-intensity irradiation of the Fresnel-pattern blue beam, the phase difference between the odd and even zones is larger than that of low-intensity irradiation under the same applied voltage. At V = 0 V, the adjacent zones have the same phase shift, and the LC Fresnel lens has the lowest focusing efficiency. When the irradiation intensity I = 9.85 mW/cm2 and the applied voltage V = 1.4 V, a phase difference (close to π) occurs between the adjacent odd and even zones, and hence, the focusing efficiency reaches its highest value. The highest focusing efficiency of the proposed LC Fresnel lens is 34.9%, which is slightly lower than the theoretical maximum value of 41%.Fig. 5 The voltage-dependent diffraction efficiency of the LC Fresnel lens generated by pumping the Fresnel-pattern blue beam with various intensities.
Figure 6 presents the measured focusing efficiency of the LC Fresnel lens as a function of the intensity of the Fresnel-pattern blue beam with the various applied voltages. Without the irradiation of the Fresnel-pattern blue beam, no focusing effect occurs. Once the Fresnel-pattern blue beam is turned on, the focusing efficiency gradually increases with the increase in irradiation intensity. The applied voltage is required to exceed 1.0 V, so that the electric field would be high enough to induce the reorientation of the LCs in the odd zones (high conductivity regions), which results in an increase in the focusing efficiency due to the increase in the phase difference between the odd and even zones. The maximum focusing efficiency occurs at the applied voltage V = 1.4 V with irradiation intensity I = 9.85 mW/cm2. As the applied voltage increases to V ≥ 1.6 V, the LCs in the even zones (low conductivity regions) start to reorient, and the phase difference between the odd and even zones gradually decreases. According to the above results, the focusing efficiency gradually declines when the applied voltage V ≥ 1.6 V..
Fig. 6 Diffraction efficiency of the LC Fresnel lens as a function of the intensity of the Fresnel-pattern blue beam with various applied voltage.
Figure 7 presents the measurement of focusing response times for the rewritable Fresnel LC lens under the conditions of the blue beam switched on/off. In the entire process of measurement, the applied voltage on the LC cell is always 1.4 V and the intensity of the blue beam is maintained to be 9.8 mW/cm2 due to the highest focusing efficiency of the Fresnel LC lens. When the Fresnel-pattern blue beam is switched on, the focusing efficiency is increased up to 34.5%. When the Fresnel-pattern blue beam is switched off, the highly conductive odd zones of the photoconductive layer is erased and the focusing efficiency is gradually disappeared. The rise time of focus and decay time of defocus are measured to be 7 s and 13 s, respectively. Due to the property of repeatability, the photoconductive layer can be rewritable by the Fresnel-pattern blue beam. The experimental result shows that the diffraction efficiency between two rewritable cycles with blue beam switching on/off are approximately equal, which provide the rewritable evidence of the photoconductive layer. The focusing switches of Fresnel LC lens can undergo more than 50 cycles of photo-rewriting processes.
Fig. 7 The measured focusing response times of the rewritable Fresnel LC lens with the blue beam switched on/off.
Figure 8 displays the focal length as a function of the central ring radius of the pumped Fresnel pattern. According to the theory of binary phase Fresnel lenses, the focal length (f) can be written as
where r1 is the radius of the central zone. In this work, because the pumped Fresnel pattern is divergent, the focal length can be controlled by adjusting the position of the LC cell. As depicted in Fig. 8, the focal length increases linearly with the increase in the square central zone radius of the pumped Fresnel pattern. The measured focal lengths (red dot) are consistent with the theoretical value (dashed line).Fig. 8 The measured focal length as a function of the square central ring radius of the pumped Fresnel pattern.
4. Conclusion
In sum, we have demonstrated a focusing efficiency and focal length tunable Fresnel lens in a LC cell with a PVK/C60 layer utilizing an interference method. By irradiating a Fresnel pattern through the Sagnac interferometer on the PVK/C60 layer, the LC Fresnel lens can be formed transiently under the application of voltage. The focusing efficiency of the proposed LC Fresnel lens can be tuned from 5% to 34.9% by tuning the intensity of the Fresnel-pattern blue beam or by controlling the applied voltage. Additionally, the focal lengths can be varied from 29.5 cm to 58 cm by altering the position of the LC cell.
Acknowledgments
This work is supported by the Ministry of Science and Technology in Taiwan (Contract No. MOST 104-2112-M-110-009).
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