1. Introduction

The increasing need to manipulate optical signals, following in the wake of the introduction of fiber optics into communications, computations and the development of parallel optical information processing systems, has stimulated interest in highly functionalized optical devices. Polymers are widely exploited because of their advantages properties, including mechanical strength, stability, flexibility, low cost, and ease of processing. Furthermore, the promise of combining these properties with large optical anisotropy has prompted a great interest in polymer liquid crystals [1–4]. The usefulness of our recently proposed photo-cross-linkable polymer liquid crystals has been demonstrated by preparing thermally stable anisotropic optical films by the use of linearly polarized ultraviolet light and subsequent annealing [5–7]. The orientation direction of the mesogenic side chains in the polymer liquid crystal is parallel to the polarization direction of the linearly polarized ultraviolet light, and three-dimensional orientation is feasible by oblique irradiation with ultraviolet light.

Polarization holographic grating was first reported in the early 1980s [8]. Theoretical and experimental research followed in the 1980s with the achievement of real-time recording and erasing in azo-dye-doped polymer films [9–10]. Since the 1990s, numerous studies have reported that irradiating polymers containing azobenzene molecules with linearly polarized light results in the reorientation of the azobenzene groups perpendicularly to the polarized light based on the axis-selective photoisomerization and creates polarization-dependent optical recordings [12–21]. These studies show the feasibility of recording an interference pattern formed by the interaction of two optical waves with orthogonal polarizations, both linear and circular, bearing information about the polarization of the object wave. Here, we report on polymer liquid crystals with periodically oriented mesogenic side chains and demonstrate that the resulting two-dimensional polarization gratings multiplex-diffract the laser beam and convert the polarization state at the same time. Because of their stable photochemically cross-linked structures, the pure polarization grating devices show high-temperature durability for a practical use.

2. Theoretical background of polarization conversion

The interference pattern of two coherent waves of equal amplitude and orthogonal polarizations (orthogonal linear; OL, and orthogonal circular; OC) has a constant intensity, but it has a polarization state that is periodically modulated. The interference pattern of two coherent waves, E ₁ and E ₂, of equal amplitude E and orthogonal polarizations has a constant intensity, but it has a polarization state that is periodically modulated as described in Table 1. In the case of orthogonal linear (OL) exposure, E ₁ is vertically linearly polarized, while E ₂ is horizontally linearly polarized, and the resulting two waves are linearly polarized waves with mutually perpendicular polarization directions. The resulting light field is described for the OL exposure case by [8, 13, 14, 22]

where the phase difference between two writing waves δ is a function of the position x and of the grating spacing Λ, and can be expressed as

In the case of orthogonal circular (OC) exposure, E ₁ and E ₂ are left- and right-hand side circularly polarized waves. The resulting light field is described for the OC exposure case by [8, 13, 14, 22]

Table 1 summarizes the polarization states of the two writing beams and the resulting electric field distribution of the two beams coupling for each irradiation mode.

Table 1. Types of polarization modulation in recording with two waves with orthogonal polarization.

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We assume that only linear birefringence is induced in the polarization-sensitive material. In the case of OL exposure, the intensity of the interfering field is constant and only changes in the resultant polarizations among linear, elliptical, and circular states are effective as shown in Table 1. The characteristic ellipsoid does not change the direction of its principal axes but only its ratio. The Jones matrix describing the transmission of the recorded holograms has the form [8–10, 13, 14, 22]

where ere Δφ=πΔnd/λ, Δn is the photoinduced birefringence, d is the film thickness, and λ is the wavelength of the reading beam. The Jones matrix describing the holographic recording in the case of OC exposure is [8–10, 13, 14, 22]

for phase recording. In order to determine the polarization properties of the reconstructing light wave from the polarization holograms described by Eqs. (4) and (5), we consider the light field S diffracted from them, given by

where R is the reading beam. The polarization of S depends on the polarization of R. Table 2 summarizes the polarization properties of the reconstructing light on varying the polarization state of the reading beam.

Table 2. Summarize of theoretical calculations for the polarization states of the diffracted beams on varying polarization state of the reading beam.

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3. Experimental results and discussion

In order to realize the optical device with the functions summarized in Table 2, polarization-sensitive materials, in which linear birefringence is induced by irradiating the polarized light, are necessary. As one of the candidates, numerous kinds of azobenzene-containing polymers have received a considerable amount of attention over the last decade [1–4, 8–21]. The polarization holographic recording originates in the photoinduced reorientation of the azo-dye molecules. These unique features of azobenzene-containing polymers are preferable to reversible holographic media because the recorded information can be erased by either optical or thermal processes in most cases. However, setting aside the applications far into the future, this phenomenon is disadvantageous for many sophisticated optical systems in which such reversibility, that is, instability cannot be accepted.

In the present article, we used a photo-cross-linkable polymethylmethacrylate liquid crystal with 4-(4-methoxycinnamoyloxy)biphenyl side groups in order to fabricate thermally stable polarization gratings. According to our previous studies, the polymer used here exhibits thermally stable reorientation of mesogenic side groups by the use of linearly polarized ultraviolet light and subsequent annealing [5–7]. The chemical structure and details about the synthesis and polymer characterization can be found elsewhere [5–7], and preliminary data for simple one-dimensional phase gratings have also been presented [23–25]. Photo-cross-linkable polymer liquid crystal films were prepared from a methylene chloride solution by spin-coating onto a quartz substrate, which resulted in 300-nm-thick films. The films were irradiated with two different types of polarization holographic exposures using 325 nm light beams from a He-Cd laser. A linearly polarized beam from a continuous-wave He-Cd laser was divided into two beams with equal intensity by a beam splitter. The two writing beams with equal intensities crossing at the θ=9.8° angle impinge upon the sample films. The corresponding spatial periodicity of the holographic gratings was 1.9 µm. The polarization states of the two coherent writing beams were controlled by half- and/or quarter-wave plates and set to be orthogonal linear or orthogonal circular. The diffraction was invisible after irradiating with interference light, while the sample was annealed at the liquid crystal temperature of 150°C. The grating was thereupon thermally organized and the diffraction spot appeared. The resulting grating devices were characterized by probing them with a linearly or circularly polarized He-Ne laser (633 nm) beam. The polarization state of the diffracted beam was characterized by Glan-Thompson polarizing prisms, and the diffraction efficiencies were characterized by plots varying the polarization directions (polar plots). Additionally, in order to decide the rotation direction of the circular polarization, we used a combination of a quarter-wave plate and Glan-Thompson polarizing prisms.

Figure 1 shows the typical examples of fundamental functions of our optical devices. For the polarization grating formed by OL exposure [Fig. 1(a)], the ± first-order diffraction beams were linearly p-polarized when the reading beam was linearly s-polarized. The zero-order polarization state was linearly p-polarized, that is, the same as that of the reading beam. For the polarization grating formed by OC exposure [Figs. 1(b) and 1(c)], when the reading beam was linearly s-polarized [Fig. 1(b)], the polarization of the+first-order diffraction beam was left-hand circularly polarized and that of the - first-order diffraction beam was right-hand circularly polarized. When the reading beam was right-hand circularly polarized, the+first-order diffraction beam was left-hand circularly polarized and the - first-order diffraction beam was invisible [Fig. 1(c)]. These experimentally observed properties were consistent with the theoretical expectations, as summarized in Table 2.

 

Fig. 1. Typical examples of the diffraction patterns passed through one-dimensional gratings. The gratings were written using two orthogonally polarized (OL; orthogonal linear and OC: orthogonal circular), mutually coherent ultraviolet laser beams. In each picture, the polarization states are shown at the top, the diffraction patterns are shown in the middle, and the polar plots are shown at the bottom. (a), Diffraction pattern from the gratings formed by OL exposure. The reading beam is linearly s-polarized. (b), Diffraction pattern from the gratings formed by OC exposure. The reading beam is linearly p-polarized. (c), Diffraction pattern from the gratings formed by OC exposure. The reading beam is right-hand circularly polarized.

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Additionally, two-dimensional crossed polarization gratings were also fabricated using the same photo-cross-linkable polymer liquid crystal by overwriting the polarization gratings at the same place. These two-dimensional polarization gratings can generate two-dimensional diffraction patterns with various kinds of polarization states, as demonstrated in Figs. 2 and 3. Figure 2 shows the diffraction patterns from the crossed gratings formed by overwriting the same polarization gratings, while Fig. 3 displays the diffraction patterns from the crossed gratings formed by alternately overwriting the two kinds of polarization gratings. Thus, in response to the demands from various types of optical systems, two-dimensional diffraction patterns with various kinds of polarization states can be generated by designing a combination of one-dimensional polarization gratings. The thermal durability of the developed device is very important for a practical uses. Our polarization-grating device exhibited thermal stability up to 150°C. These results are a considerable advance towards the realization of highly functionalized passive optical devices and will have a significant impact on the future of optoelectronics.

 

Fig. 2. Diffraction patterns passed through the crossed gratings formed by overwriting the same polarization gratings. The grating vectors are slanted with 0, 45, 90, 135 degrees with reference to the horizon. The gratings were written using two orthogonally polarized (OL; orthogonal linear and OC: orthogonal circular), mutually coherent ultraviolet laser beams. In each picture, polarization state of each diffraction spot is schematically presented by an arrow. (a), Diffraction pattern from the crossed gratings consisting of four OL gratings. The reading beam is linearly polarized and the polarization direction is slanted with 40 degrees. (b), Diffraction pattern from the crossed gratings consisting of four OC gratings. The reading beam is linearly s-polarized. (c), Diffraction pattern from the crossed gratings consisting of four OC gratings. The reading beam is right-hand circularly polarized.

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Fig. 3. Diffraction patterns passed through the crossed gratings formed by alternately overwriting the orthogonal linear (OL) and orthogonal circular (OC) gratings. The grating vectors are slanted with 0, 45, 90, 135 degrees with reference to the horizon. In each picture, the polarization state of each diffraction spot is schematically presented by an arrow. (a), The reading beam is linearly s-polarized and the polarization direction is slanted with 40 degrees. (b), The reading beam is right-hand circularly polarized.

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4. Conclusion

The pure polarization crossed gratings were fabricated by the thermally stable reorientation of mesogenic side groups in the photocrosslinkable polymer liquid crystal by the use of two orthogonal polarized beams and subsequent annealing. The stable crossed gratings can control the two-dimensional propagation direction and convert the polarization state of the light at the same time. The high temperature durability of the crossed polarization gratings, not observed in other kinds of materials, suggest that the choice of the photocrosslinkable polymer liquid crystal is significant for a practical device and this study is a considerable advance towards the realization of highly functionalized passive optical devices.