This work demonstrates a reflective Fresnel zone plate based on dye-doped cholesteric liquid crystals (DDCLC) 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, rewritable and switchable between focusing and defocusing states, upon application of a voltage.
© 2007 Optical Society of America
Liquid crystal (LC) devices, such as optical switches, optical filters, holographic gratings, wave plates, lens and so fourth, have been widely developed. Scientists recently have paid much attention to LC lenses formed using the lithographic technique , patterned electrodes [2, 3], spherical aberration compensation , integral photography  and LC Fresnel lenses [6–10]. Reviews of previous studies reveal that LC Fresnel lenses have been demonstrated using polymer-dispersed liquid crystals , polymer-stabilized liquid crystals , polymer-insensitive liquid crystal  and dye-doped nematic liquid crystals [9, 10]. All of these LC Fresnel lenses are transmissive.
This study reports on a highly efficient reflective Fresnel zone plate made using dye-doped cholesteric liquid crystals (DDCLC). The DDCLC sample was irradiated with a green light (~ 100 mW/cm2) through a Fresnel-zone-plate mask to induce the dye adsorbed and un-adsorbed regions through the transmissive and opaque zones, respectively . Thus, the illuminated sample yields binary-amplitude structures ; reflective planar and scattering focal conic textures. As illustrated in Fig. 2(b), when the helix of CLCs is oriented randomly in the cell, the CLC is in a focal conic texture, while the helix of planar CLCs is normal to the plates . Since the average phase change is 2π from one planar-texture zone to the next one, the incident beam reflected from the planar textures in a Fresnel zone plate are finally constructively added and focused at the focal point. It should be noted that the formed Fresnel zone plate can be operated as a transflective lens, if the incident beam is linearly polarized. The focusing efficiency, or the so-called diffraction efficiency, of the formed reflective lens measured using circularly polarized light is ~ 23.7%, which almost equals the measured diffraction efficiency of the used Fresnel-zone-plate mask (~ 25.6%). Although the diffraction efficiency of the present device is lower than those devices we reported previously [9, 10], the new device possesses two novel characteristics; it can be operated either as a reflective or transflective Fresnel zone plate, depending on the polarization of the incident beam; its fabrication is simple. In principle, a reflective Fresnel lens could be fabricated combining a transmissive Fresnel lens  with a mirror placed just behind the lens. Such a design, however, is not practical, since the incident beam and the reflection beam from the mirror may go through different zones, if a beam is obliquely incident onto the lens. This effect results in a degraded focused pattern. In addition to those advantages described above, the present device can be switched between focusing and defocusing states by applying a voltage. The fabricated reflective/transflective Fresnel zone plate is persistent without any external disturbance, but is erasable and rewritable by thermal and optical treatments, respectively.
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 pitch length of the used CLC is approximately 380 nm. The chiral dopant impurities reduce the clearing temperature from ~ 61°C (clearing temperature of pure E7) to ~ 30.7°C. The dye adopted in this experiment was an azo dye, methyl red (MR, Aldrich), whose absorption band in the trans-state spans 440 to 550 nm and peaks at about 530 nm. The mixing ratio of MR to CLC was 2:98 by weight. Each empty cell was fabricated by combining two indium tin oxide (ITO)-coated glass slides, separated by two 11 μm-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. Notably, the cell gap should be larger than ~ ten pitch lengths in order to achieve a complete Bragg reflection from a cholesteric planar texture film . The reason why we employed an 11 μm-thick cell in the present work is the consideration of having a complete Bragg reflection and a good contrast ratio of light intensity reflected from the planar texture regions to that scattered from the focal conic texture regions.
Figure 1 schematically depicts the fabrication of a reflective Fresnel zone plate based on a DDCLC. The setup is similar to that in our previous study . 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) is incident onto the sample from the mask. The mask has transparent even zones and opaque odd zones, manufactured by etching the chromium oxide layer using electron beam lithography, and has a primary focal length f ~ 40 cm at a wavelength of 632.8 nm.
Figures 2(a) and 2(b) present the experimental setup for fabricating and analyzing a reflective Fresnel zone plate, respectively. In Fig. 2(a), linearly polarized green light with an intensity of 100 mW/cm2 (E G, from a diode-pumped solid state laser, DPSS laser, λG = 532 nm), expanded and collimated to a beam diameter of 1 cm through two convex lenses, was used to pump the DDCLC cell through the mask for 10 minutes. The polarization of the pumped beam, E G, relative to the PVA-rubbing direction, R, could be set arbitrarily, since the absorption in all polarization directions is always equal in a planar DDCLC cell. Here, E G and R were set to be parallel. Finally, a reflective Fresnel zone plate was formed. Right-hand circularly polarized red light with an intensity of 1.2 mW/cm2 (E R, from a He-Ne laser, λR = 632.8 nm), whose wavelength was in range of the reflection band of the used DDCLC, was adopted to analyze the characteristics of the zone plate. The red-light beam, expanded by two convex lenses, made a small angle of ~ 1° with the normal of the DDCLC cell, to enable the focused image to be observed easily on the screen and photographed.
3. Results and discussion
The setup of Fig. 2(a) yields a binary-amplitude-structure lens. 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 property of the adsorbed dye layer is determined by a few factors, such as the concentration of the dyes doped in CLCs, the intensity of the pumped beam, the illumination duration, and so on. A smooth and rough layer of adsorbed dyes may be developed using weak- and strong-intensity light, respectively . The orientations of the adsorbed dyes are perpendicular to the polarization of the pump beam in smooth layers, but random in rough layers. The adsorbed smooth dye layer can align the LC molecules [11, 16]. The SEM image (not shown) of the photo-induced adsorption layer of dyes herein indicates that the layer is rough when it was excited using strong-intensity light (100 mW/cm2). 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. Usually, the dye adsorption rate is increasing with the pump-beam intensity. In the present case, it was found that the intensity of the green light should be higher than ~ 30 mW/cm2 in order to obtain a randomly adsorbed dye layer. However, if the intensity is over ~ 100 mW/cm2, the focusing efficiency of the formed DDCLC lens is poor. The cause is believed to result from the strong light-scattering in the transparent regions by the adsorbed dyes. The light scattered into the opaque regions causes the randomly dye adsorption, which degrades the planar texture in these regions. 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. A separate experiment (not shown) verifies that if the clearing temperature is set high, and the thermal effect of the absorption of light is too small to transform the cell from planar to isotropic textures, then the final texture of the illuminated regions with roughly and randomly adsorbed dyes remains stable planar. Restated, a higher set clearing temperature is associated with greater difficult of developing the focal conic texture in a cell recorded under a given condition. However, if a planar DDCLC cell with the adsorbed dyes is heated to over its clearing temperature, and then cooled, then a focal conic texture is obtained. Figures 3(a) and 3(b) display optical microscopic images of the Fresnel-zone-plate mask and the fabricated DDCLC Fresnel zone plate, respectively. Comparing Fig. 3(a) with Fig. 3(b) 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. Notably, the contrast between even and odd rings in Fig. 3(b) is lower compared with that of Fig. 3(a). The reason is that Fig. 3(a) is the image of the Fresnel-zone-plate mask observed using an optical microscope (non-polarizer), while Fig. 3(b) is the image of the fabricated DDCLC Fresnel zone plate taken under a cross-polarizer optical microscope. In the latter case, the incident linearly polarized light is decomposed into right- and left-hand circularly polarized components with the former light reflecting from and the latter transmitting through the planar-texture regions in a DDCLC Fresnel zone plate. Therefore, the AP, planar-texture region, is bright under the cross-polarizer optical microscope. The incident linearly polarized light is scattered in the AF region having a focal conic texture. Therefore, part of the scattering light leaks through the analyzer, and degrades the contrast. In the case of Fig. 3(a), AT (AO) is a transparent (opaque) zone in the Fresnel-zone-plate mask, and thus the image has a higher contrast.
Since the average phase change is 2π from one planar-texture zone to the next one, the red light reflected from the odd zones of the planar textures in a Fresnel zone plate are finally constructively added and focused at the focal point. Figure 4 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. 4 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%), which is defined as the intensity ratio of the focused beam at the primary focal point to the transmission beam from the mask.
Figure 5 plots the measured focusing efficiency of a reflective Fresnel zone plate under the applied AC (1 kHz) voltages. The inset (a) in Fig. 5 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. 5 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 behavior that is shown in Fig. 5 is reasonable, and is understood as follows. Applying an AC voltage below the threshold cannot orient the LCs in the DDCLC sample. The LCs of the odd (even) zones remain in their original states with planar (focal conic) textures. However, when the applied voltage exceeds the threshold voltage, the planar texture in the odd zones should be transferred to foal conic textures. Therefore, the textures of both the odd and the even zones in a DDCLC sample are focal conic, the focusing effect disappears. Finally, the diffraction efficiency saturated at ~ 2% is associated with the scattering of light from the focal-conic-texture cell. Accordingly, the reflective Fresnel zone plate is clearly electrically switchable. The measured rise- and fall-times (10–90%) for the reflective Fresnel zone plate are, respectively, 620 ms and 5 ms with the sample being applied with an AC voltage (50 V, 1 kHz).
The sample is thermally treated to confirm that the fabricated lens is erasable and rewritable. 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. The experimental results that are shown in Fig. 6 reveal that the reflective Fresnel zone plate was thermally erasable and optically rewritable. Figures 6(a) and 6(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. Additionally, the thermally treated sample is rewritable using the setup presented in Fig. 2(a). Figure 6(c) depicts the rewritten reflective Fresnel zone plate. The measured focusing efficiency is ~ 23.1%, which is close to that before erasure (~ 23.7%). Therefore, the reflective Fresnel zone plate after thermal erasure treatment is optically rewritable.
Notably, the demonstrated reflective Fresnel zone plate in DDCLC can act as a transflective lens if the polarization of the probe beam is linear, elliptical or un-polarized, rather than circularly polarized. Figures 7(a) and 7(b) depict, respectively, the reflective and transmissive focusing patterns at the primary focal point with the formed Fresnel zone plate probed using a linearly polarized red light. The polarizations of the reflective and transmissive focusing light are right- and left-hand circular, respectively. Restated, such a device can function as a polarization-beam-splitter lens. Additionally, the lifetime of the lens is very long. The reflective Fresnel zone plate is persistent, and its focusing efficiency remains unchanged over two months without any external disturbance, such as optical, thermal or electrical, because of the memory effect of MR-adsorption and the bistable states of planar and focal conic textures.
In conclusion, this investigation successfully demonstrated a Fresnel zone plate based on a dye-doped cholesteric liquid crystal 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 rewritable. The lifetime of the fabricated lens is long. The lens is persistent without any external disturbance. In additions, the direction of the reflective beam can be slightly turned by simply rotating the lens. Therefore, it has potential for real applications. For an example, it can be used in the maskless photolithographic process. The reflective wavelength can be set exactly to match the chosen photoresist materials.
The authors would like to thank the National Science Council (NSC) of the Republic of China (Taiwan) for financially supporting this research under Grant No. NSC 95-2112-M-006-022-MY3.
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