Volume 1 Issue 6 - September 28, 2007
Highly Efficient and Polarization-Independent Fres-nel Lens Based on Dye-Doped Liquid Crystal
Andy Y.-G. Fuh, Liang-Chen Lin, Hung-Chang Jau, and Tsung-Hsien Lin

Department of Physics, and Institute of Electro-optical Science and Eng.
National Cheng Kung University, Tainan, Taiwan 701, ROC

OPTICS EXPRESS 15, 2900-2906 (2007)

Lenses based on binary-type Fresnel zones are called Fresnel lenses. The Fresnel zones (see Fig. 1) are formed by concentric circles in such a way that the radius rm of the mth zone satisfies rm2 = m r12, where r1 is the radius of the innermost zone. Obstructing the odd zones (or even zones), we have the Fresnel zone plate, which can function as a lens with the primary focal length f= r12 / λ, where λ is the wavelength of the incident beam.
Fig. 1. Schematic fabrication method of the DDLC Fresnel lens.

Fresnel lenses are suitable for long distance optical communication, millimeter-wave devices, and three dimensional display systems. Th e 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. Besides, they sacrifice the diffraction efficiency to get focus property at the focal points by blocking the even (or odd) zones. 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. But there still exists some problems such as the high operation voltage, low focusing efficiency, polarization-dependent efficiency, and low tuning range of the phase shift , etc.

In this research, we successfully demonstrated a highly efficient and polarization-independent Fresnel lens based on dye-doped liquid crystal (DDLC) by using double-side photoalignment technique. The diffraction efficiency of a DDLC Fresnel lens is electrically controllable, and the maximum diffraction efficiency reaches ~37%, which is approaching the theoretical limit ~41%. Comparing with other methods, the major advantages of such a DDLC Fresnel lens are one-step exposure fabrication, high diffraction efficiency, polarization-independent and half-wave plate characteristic, fast response between focusing and defocusing state, and electrically tunability under the low applied voltage.

Figure 1 illustrates the schematic fabrication of the DDLC Fresnel lens. The key element is the photo-mask imbedded with Fresnel zone plate patt erns. This photo-mask has transparent odd zones and opaque even zones by etching the chromium oxide layer using electron beam lithography. It’s known that in a binary-type Fresnel lens, the radius rm of the mth zone satisfies rm2 = m r12, where r1 is the radius of the innermost zone. The primary focal length f is related to the innermost radius r1 as f= r12 / λ, where λ is the wavelength of the incident beam. Th is photo-mask has a primary focal length f ~39.5cm for λ= 632.8 nm and r1 = 0.5 mm.

Two indium-tin-oxide (ITO)-coated glass slides slightly rubbed with a nylon cloth were assembled to produce an empty cell with 3 μm ball spacer. Th e LC E7 (Merck) and azo dye Methyl Red (MR) were mixed homogeneously to make the DDLC material and then injected into the empty cell. Materials such as MR dyes may undergo photo-isomerization between the trans isomer and the cis isomer. Azo-dyes are usually in the stable trans-state in the dark. When the DDLC cell is excited by light in the absorption spectrum range at the room temperature, MR dyes are transformed from the trans to the cis form, inducing the diffusion, and adsorption onto the substrate facing the incident pump beam with the long axes of dyes being perpendicular to the pump-beam polarization. The adsorbed dyes then align LCs. Recently, we have observed that the adsorption of dyes can be made onto both of the two substrates of the cell, if the cell is optically excited at a temperature just above the clear temperature of LC. We call it a double-side photoalignment.

Fig. 2. Microscopic images of the fabricated DDLC Fresnel lens observed under a crossed-polarizer optical microscope with the rubbing direction of the cell making an angle of, (a) 0o, and (b) 45o to the polarizer axis.
Base on the observation mentioned, a linearly polarized diode-pump solid state (DPSS) laser light (λ= 532 nm), which is within the absorption band of the MR dyes was used to illuminate the DDLC cell through the Fresnel zone plate mask as shown in Fig.1. Th e pump beam had an intensity of ~24 mW/cm2, and its polarization was parallel to the rubbing direction of ITO surface. The illumination time was 3 hours. In order to obtain doubleside photoalignment, the cell was thermally controlled at a temperature ~65°C (which is above the clear temperature of E7 ~61° C) during pumping. As a result, a DDLC Fresnel lens photoaligned with orthogonally alternating homogeneous binary structure was achieved. Th is orthogonally binary confi guration leads the fabricated DDLC Fresnel lens to a key property of being irrespective of the polarization of incident light. Under a crossed-polarizer optical microscope, the DDLC Fresnel lens appears black and white, respectively, by placing the cell with the rubbing direction (R) making angles 0° and 45° to polarizer axis as depicted in Fig. 2(a) and 2(b). Th e lines in Fig. 2 are due to the transition of LC alignment between the two domains.

Fig. 3. The measured primary diff raction efficiency of the DDLC Fresnel lens as a function of the applied voltage.
Figure 3 plots the measured diffraction efficiency of the DDLC Fresnel lens under the applied AC voltages (1 KHz). The diffraction efficiency is defined as the ratio of the diffracted intensity at the primary focal point to the total pumping laser intensity just passing through the sample. Initially, a DDLC Fresnel lens diffracts ~21%. As the applied voltage exceeds a threshold voltage (~0.9 V), the LCs start to be reoriented by the applied field, the diffraction efficiency is then varied. The minimum and maximum diff raction efficiencies are seen to occur at Vrms = 1.1 V and Vrms = 1.8 V, respectively, which correspond to the phase differences of the LCs between the adjacent odd and even zones being 2π and π. It should be noted that the total phase shifts (i.e. the summation of the shift due to LCs and optical path length for the zone plate) between the adjacent odd and even zones are then 3π and 2π at Vrms = 1.1 V and Vrms = 1.8 V, respectively. The maximum diffraction efficiency reaches ~37% at V= 1.8 Vrms, which is close to the theoretical limit ~41%. Figure 4 gives the comparison of the focusing efficiency using a Fresnel zone plate (a), and the DDLC Fresnel lens (b). Th e focusing efficiency of the DDLC Fresnel lens not reaching the theoretical value discrepancy is believed to result from the transition of LC alignment at the boundaries between the adjacent odd and even zones (bright rings in Fig. 2(a)). At voltages much larger than the threshold, all the bulk LCs are reoriented perpendicularly to the glass substrate. The relative phase difference of the LCs between the adjacent odd and even zones approaches zero, so the function of the Fresnel Zone plate disappears. Therefore, the diffraction efficiency of the fabricated DDLC Fresnel lens could be tunable through the applied voltage.
Fig. 4. (a) Focusing image by the Fresnel zone plate mask (Fig. 1), (b) Focusing image using DDLC Fresnel lens with an application of a voltage of 1.8 V.

Figure 5 plots the measured diffraction efficiency as a function of the polarization of the incident linearly beam at the primary focal point under the applied voltages of V= 0Vrms and 1.8Vrms. Based on the measured results shown in Fig. 5, we can conclude that the fabricated DDLC Fresnel lens possesses a polarization-independent property as predicted theoretically.
Fig. 5. Measured diffraction efficiency at the primary focal point of the DDLC Fresnel lens as a function of the incident linearly polarization angle at the applied voltages of V = 0Vrms and 1.8Vrms.

Notably, the fabricated DDLC Fresnel lens has not only high diffraction efficiency, but a fast response performance. The measured focusing (10-90%) and defocusing (90-10%) times are ~ 8ms and ~ 18ms.

In conclusion, we successfully demonstrated a highly efficient, polarization-independent and electrically tunable Fresnel lens based on DDLC cell using the double-side photoalignment technique. In addition, the fabrication of this DDLC Fresnel lens is simple, and the device has fast switching responses between focusing and defocusing state. Thus, it has a high potential for use in various optical systems.
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