Volume 7 Issue 4 - January 16, 2009
Electrically switchable and optically rewritable reflective Fresnel zone plate in dye-doped cholesteric liquid crystals
Andy Y.-G. Fuh*, Ko-Ting Cheng, Cheng-Kai Liu, Chi-Lun Ting

Department of Physics, College of Sciences, National Cheng Kung University
andyfuh@mail.ncku.edu.tw

OPTICS EXPRESS 15, 14078-14085 (2007)

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Lenses based on binary-type Fresnel zones are called Fresnel lenses. The Fresnel zones are formed by concentric circles in such a way that the radius rm of the mth zone satisfies , where is the radius of the innermost zone. Obstructing the odd zones (or even zones) of the Fresnel zones, we get the Fresnel zone plate, which can function as a lens with the primary focal length , where λ is the wavelength of the incident beam. (See Fig. 1). Fresnel lenses are suitable for long distance optical communication, millimeter-wave devices, and three dimensional display systems. The conventional Fresnel lenses fabricated by electron-beam writing or thin-film deposition techniques have many drawbacks such as complicated fabrication process and fixed diffraction efficiency. In order to overcome those drawbacks, the original zones need to be replaced by other materials such as liquid crystal (LC). A LC is a very good candidate for electrically switchable devices because of its good electro-optical property and low operating voltage. Various methods have been developed for fabricating electrically switchable LC Fresnel lenses. Comparing with the conventional process by electron-beam writing or thin-film deposition techniques, these LC Fresnel lens are electrically switchable and the fabrications are quite simple. The new device presented herein possesses a novel characteristic; it can be operated either as a reflective or transflective Fresnel zone plate, depending on the polarization of the incident beam.
Fig. 1. Schematic diagram of a Fresnel zone plate

In this study, we successfully demonstrated a reflective Fresnel zone plate based on dye-doped cholesteric liquid crystals (DDCLCs) using the photo-induced realignment technique. Illumination of a DDCLC film with a laser beam through a Fresnel-zone-plate mask yields a reflective lens with binary-amplitude structures - planar and focal conic textures, which reflect and scatter probed light, respectively. The formed lens persists without any external disturbance, and its focusing efficiency, analyzed using circularly polarized light, is ~ 23.7%, which almost equals the measured diffraction efficiency of the used Fresnel-zone-plate mask (~ 25.6%). The lens is thermally erasable, optically rewritable and electrically switchable between focusing and defocusing states.

The materials used herein were right-handed cholesteric liquid crystals (CLC), prepared by mixing 64 wt% nematic liquid crystal (E7, Merck) with 36 wt% chiral agent (CB15, Merck). The measured reflection band was between 615 and 665 nm. The dye adopted in this experiment was an azo dye of 2 wt%, methyl red (MR, Aldrich), whose absorption band in the trans-state spans 440 to 550 nm and peaks at about 530 nm. Each empty cell was fabricated by combining two indium tin oxide (ITO)-coated glass slides, separated by two 11 m-thick spacers, each of which was coated with an alignment film of poly(vinyl alcohol) (PVA) and rubbed in the direction R. Finally, the homogeneously mixed compound was injected into an empty cell to produce a DDCLC in planar texture. The edges of the DDCLC cells were sealed with epoxy.

Figure 2 schematically depicts the fabrication of a reflective Fresnel zone plate based on a DDCLC. Basically, a Fresnel-zone-plate mask is in contact with a DDCLC sample. A linearly polarized diode-pumped solid state (DPSS) laser beam (λ = 532 nm, 100 mW/cm2) is incident onto the sample from the mask for 10 minutes. A reflective Fresnel zone plate was formed. The mask has transparent even zones and opaque odd zones, and has a primary focal length f ~ 40 cm at a wavelength of 632.8 nm. Figure 3 presents the experimental setup for analyzing a reflective Fresnel zone plate. Right-hand circularly polarized red light with an intensity of 1.2 mW/cm2 (ER, from a He-Ne laser, λR = 632.8 nm) was adopted to analyze the characteristics of the reflective Fresnel zone plate.
Fig. 2. Schematic fabrication of a DDCLC reflective Fresnel zone plate
Fig. 3. Setup for analyzing a DDCLC reflective Fresnel zone plate

The binary structures of the present reflective Fresnel zone plate are planar (opaque zones in the mask) and focal conic textures (transparent zones in the mask), which are both stable. The former are in the initial state, and the latter are generated by the adsorbed dyes and thermal effect. The mechanisms of MR-adsorption are briefly described as follows. After the MR molecules were excited by the absorption of blue-green light, they exhibited a series of transformations, including photoisomerization, three-dimensional (3D) reorientation, diffusion and adsorption. The SEM image (not shown) of the photo-induced adsorption layer of dyes herein indicates that the layer is rough. Restated, the PVA alignment film loses its ability to align CLCs in the planar texture after being covered with randomly adsorbed dyes. Thus, the structure of CLCs in the illuminated regions changes to the focal conic texture. In addition to the adsorption effect, the thermal effect should be considered. The chiral dopant impurities reduced the clearing temperature of LC from ~ 61˚C to ~ 30.7˚C. Such a lower clearing temperature corresponds to a lower threshold to change the cell texture from the planar to isotropic by the absorption of the energy of light. Additionally, after the pump laser was switched off, the cell cooled to less than the clearing temperature. The isotropic DDCLC in the regions without adsorbed dyes may return to the stable planar textures because of the homogeneous PVA alignment film. However, this effect does not occur in the regions with randomly adsorbed dyes. Rather, the texture in these regions transforms to the focal conic texture. Since the phase difference between two adjacent Fresnel zones is π, light reflected from one planar-texture zone to the next one is phase-shifted 2π Thus, the lights reflected from the planar textures are constructively added, and a reflective Fresnel zone plate is finally formed.

Figures 4(a) and 4(b) display optical microscopic images of the Fresnel-zone-plate mask and the fabricated DDCLC Fresnel zone plate, respectively. Comparing Fig. 4(a) with Fig. 4(b), it clearly indicates that the regions behind the transparent even (opaque odd) zones in the DDCLC cell were focal conic (planar) textures. Restated, the probed light was scattered and reflected by focal conic (even zones) and planar (odd zones) textures in the DDCLC Fresnel zone plate, respectively. In the case of Fig. 4(a), AT (AO) is a transparent (opaque) zone in the Fresnel-zone-plate mask, and thus the image has a higher contrast.
Fig. 4. Images of (a) Fresnel-zone-plate mask (b) formed reflective Fresnel zone plate observed under crossed-polarizer optical microscope. AT and AO represent transparent and opaque regions. AP and AF are the planar and focal conic texture regions, respectively. P and A are, respectively, the transmissive axes of the polarizer and the analyzer.

Figure 5 depicts the focusing patterns that were probed using a circularly polarized red light from the formed reflective Fresnel zone plate at various points around the primary focal point. Notably, the visible dark cross-hair patterns in Fig. 5 are the marks on the screen, which are used for focusing a camera. The focusing efficiency, or the so-called diffraction efficiency, defined as the intensity ratio of the focused beam at the primary focal point to the reflection beam from a planar DDCLC cell, is measured to be ~ 23.7%. The measured value is very close to the measured diffraction efficiency of the used Fresnel-zone-plate mask (~ 25.6%), defined as the intensity ratio of the focused beam at the primary focal point to the transmission beam from the mask.
Fig. 5. Focusing patterns of the reflective Fresnel zone plate using right-hand circularly polarized red light. The distances between lens and screen are (a) 20 cm; (b) 30 cm; (c) 40 cm; (d) 50 cm; (e) 60 cm. The Fresnel-zone-plate mask has a focal length ~ 40 cm at a wavelength of 632.8 nm.

Figure 6 plots the measured focusing efficiency of a reflective Fresnel zone plate under the applied AC (1 kHz) voltages. The inset (a) in Fig. 6 presents the focusing pattern obtained without an application of an AC voltage. When a voltage is applied, the diffraction efficiency remains almost unchanged initially, and then decreases sharply at voltages just above the threshold of ~ 3 V, at which the cell transits from planar to focal conic textures, and finally saturates at a diffraction efficiency of ~ 2% at voltages that markedly exceeds the threshold. The inset (b) in Fig. 6 displays an image recorded at an applied voltage of ~ 10 V. The focusing effect disappears in inset (b). Additionally, when a high voltage of 50 V is applied and abruptly switched off, the focused image quickly returns to that presented in inset (a). The measured rise- and fall-times (10-90%) for the reflective Fresnel zone plate are, respectively, 620 ms and 5 ms.   
Fig. 7. Images of reflective Fresnel zone plate observed under a crossed-polarizer optical microscope (a) before, and (b) after thermal treatment. (c) Image of rewritten reflective Fresnel zone plate. Additionally, P and A are transmissive axes of polarizer and analyzer, respectively.
Fig. 6. Measured focusing efficiency of reflective Fresnel zone plate in DDCLC as a function of applied AC (1 kHz) voltage. Inset (a) and (b) present focusing patterns of lens without and with applied voltage (10 V), respectively. Notably, the focusing pattern of the lens returns to (a) after a higher voltage of 50 V is applied and rapidly switched off.


The fabricated lens was heated to ~ 80˚C and the cell was kept at this temperature for 10 minutes to erase the randomly adsorbed dyes. Figures 7(a) and 7(b) depict images, obtained under an optical microscope, of the fabricated reflective Fresnel zone plate before and after thermal treatment, respectively. Thermal disturbance can cause desorption of adsorbed MR. Hence, the reflective Fresnel zone plate recovers to its initial planar texture throughout the cell when the temperature returns below the clearing temperature of the DDCLC. Figure 7(c) depicts the rewritten reflective Fresnel zone plate (focusing efficiency ~ 23.1%) using the setup presented in Fig. 2.

In conclusion, this investigation successfully demonstrated a Fresnel zone plate based on a DDCLC with binary structures that comprise planar and focal conic textures. It can be operated as a reflective (transflective) lens, if the incident beam is circularly polarized (linearly polarized). The focusing efficiency of the reflective Fresnel zone plate is close to that of the used Fresnel-zone-plate mask. The formed Fresnel zone plates are electrically switchable, thermally erasable and optically rewritable.
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