A liquid-crystal ͑LC͒-based polarization rotator which can rotate the polarization axis of an incident linearly polarized light from 0°to 90°is demonstrated. In the LC cell, the top substrate has a uniform rubbing but the bottom substrate has two orthogonal rubbings which are separated by a nonrubbing zone. Between these two rubbed strips, the LC directors twist continuously from 0°to 90°. As a result, the optic axis of the incident linearly polarized light can be rotated continuously depending

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... on the beam position. A liquid-crystal ͑LC͒-based polarization converter is an intriguing optical device because it can convert a linearly polarized light into circular, elliptical, axial, radial, or azimuthal polarization depending on the LC configurations. 1-7 If the employed LC presents a homogeneous alignment, 1 then it can generate linear, circular, or elliptical polarization by controlling the applied voltage. On the other hand, if the LC has radial or twisted radial orientation, then a spacevariant output light with axial, radial, or azimuthal polarization can be generated. However, there is still lack of LC converter that can continuously rotate the optic axis of a linearly polarized light. Such a LC polarization converter would be used as a polarization axis finder, phase modulator for analyzing biological tissues and polarizing materials, diffractive optics, and other optical elements. Nematic LC molecules have rodlike structures and their directors can be reoriented either by electric field, rubbing treatment, or both. If the LC directors are twisted, 8 then the device can rotate the optic axis of a linearly polarized light due to the waveguiding effect. Here, we call such a converter a polarization rotator. Various LC rotators based on different LC configurations have been proposed. For example, Yamaguchi et al. 2 demonstrated a LC polarization rotator by controlling the azimuthal anchoring strength of the LC cell with different UV exposures. After rubbing treatment, they demonstrated a LC rotator with multiple twist angle patterning. A LC rotator using such a fabrication method causes two concerns: discontinuous twist angle and complicated fabrication process. A linear polarization rotator which can continuously twist the plane of a linearly polarized light can be widely used in optical splitters, variable filters, optical data storage, grating, and other optical elements. In this letter, we demonstrate a LC-based linear polarization rotator using a simple rubbing method. Our device can rotate the optic axis of an incident linearly polarized light spatially. The major advantages of our approach are twofold: simple fabrication process and large size capability. Moreover, using this method a polarization rotator array can be fabricated easily. To achieve a continuous twist from 0°to 90°, we fabricated the LC cell as follows. The top glass substrate surface was coated with a thin polyimide ͑PI͒ layer and rubbed along the −x axis, as shown in Fig. 1 . The bottom substrate surface was divided into the left, middle, and right regions; each region had different rubbing treatments. In the first step, we rubbed the left part of the bottom substrate along the y axis while keeping the middle and right regions covered with a thin glass plate. We then rubbed the right strip along the x axis while keeping the middle and left strips covered. Afterwards, we assembled these two substrates together to form a cell. The cell consists of three different regions corresponding to the surface treatments of the bottom substrate. In the left region, the rubbing directions of the top and bottom substrates are perpendicular while in the right region the rubbing directions are antiparallel. In the middle region, only the top surface has rubbing. When a LC material was filled to the cell, the LC molecules were aligned by the rubbed surfaces. Figure 2 depicts the schematic side view of the ideal LC configurations in the cell. From left to right, the cell is divided into three zones. Positions A and B represent the edges of the nonrubbed region. Induced by the two rubbed surfaces, the LC directors in the left region exhibit a 90°twist while in the right region they are homogeneous. Between A and B, the LC directors on the top surface are homogeneously aligned along the rubbing direction due to the strong anchoring force of the PI layer. But the LC directors near the bottom substrate surface would twist continuously from 90°to 0°, as depicted in Fig. 2 . Because of the weak anchoring energy of the bottom glass surface which has no PI layer, the LC directors in the nonrubbing region are influenced by the LCs in the left and right regions. Moreover, the LC is a continuum medium. In an equilibrium state, the boundary layers in the bottom substrate gradually twist. As a result, the bulk LC directors between A and B gradually transition from 90°twist to homogeneous, as Fig. 2 depicts. In Fig. 2 when a linearly polarized light is incident normally to the LC cell with its polarization direction parallel to the x axis, the transmitted light remains linearly polarized but its polarization axis follows the LC director twist, provided that the following Mauguin condition is satisfied: 9 2d⌬n/ ӷ . ͑1͒ In Eq. ͑1͒, is the twist angle, d is the LC layer thickness, ⌬n is the LC birefringence, and is the wavelength. For a 90°twisted nematic cell, = / 2 and the Mauguin condition is simplified to a͒ Electronic