Abstract

An approach for generating cycloidal pattern of liquid crystal (LC) molecules based on interference-free and single exposure is illustrated. The spatial manipulation of polarization state is achieved using birefringent prism and wave plates. And then, the spatially variant polarization of exposure beam is transferred to LC molecules by azo-dye photo-sensitive layer. Consequently, the LC samples fabricated shows periodically cycloidal texture and diffraction efficiency more than 99%. The measured period Λ and diffraction angle are in good consistency with theoretical results. Thus, this exposure method provides an effective and robust way for fabricating large-area LC elements, therefore paving the way for widespread applications of high-performance diffractive LC devices.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Optical elements incorporating geometric phase (GP) effect have attracted extensive research interest, due to their capability of generating light waves with complex amplitude, phase and polarization by embodying inhomogeneous anisotropy [14]. One of the great benefits is to replace massive optical system by flat and ultrathin GP elements to achieve highly efficient beam deflecting, focusing, filtering, etc. [58]. Among various implementation methods, liquid crystals (LCs) based GP elements shows high flexibility in developing highly functional optical devices due to their high birefringence, high sensitivity to external field and surfaces anchoring forces [912]. Recently, LC GP elements, such as lenses, gratings, vortex phase plate, or ones with arbitrary phase profile, were generated by patterning the directors of LCs [10,1316]. Specifically, LC elements with a cycloidal molecular orientation pattern, known as polarization grating (PG), are extensively used in displays, optical communications, and imaging systems [1721]. There are basically two methods for generating cycloidal patterns of LC directors utilizing photo-sensitive aligning. One is based on polarization holograms by exposing photo-aligning layer with two orthogonal circular polarization [22,23]. This method possesses the characteristics of high spatial resolution, but its complex optical setup and vulnerability to environmental disturbance hinders its industrial application [24]. The other is digitalized polarization holographic approach. For instance, DMD (digital mirror device) based microlithography or laser direct writing provides flexibility of arbitrary pattern, but multi-exposure process and high-precision mechanical rotation of polarizer limit the productivity [13,25]. Recently improved digital polarization holography employing phase-type spatial light modulator (SLM) for single-exposure process [24,26]. However, the alignment patterns of LCs are quasi-continuous, and in one exposure the spatial resolution and effective area are in conflict. Thus, the challenge still exists for fabricating continuous cycloidal LC plate with large-area and high-precision.

Here we propose a novel method to generate cycloidal pattern of LC directors that enables highly efficient and large area thin-film LC PGs for visible wavelengths. The polarization manipulation of exposure beam was achieved using birefringent prism and quarter wave plate, and then the polarization orientation pattern created was recorded on photo-sensitive aligning layer and passed on to LC molecules. To prove the concept, the fabricated LC PGs and binary gratings were tested and compared with theoretical results. This fabrication technique features low cost, continuous pattern, high stability, and single-step exposure. In addition, this non-interferometric and passive optical elements-based design provides a novel approach for fabrication GP elements. Thus, it could significantly facilitate the fabrication and practical usage of LC PG.

2. Principle and experiments

LC gratings with cycloidal pattern of liquid crystal alignment are efficient polarization-sensitive GP elements which separate monochrome plane wave to sub-waves with corresponding polarization state. The spatially continuous in-plane axis variance of liquid crystal director within one period is critical for theoretical 100% diffraction efficiency, since non-continuous distribution will lead to higher order diffraction and result in stray light and the loss of first order efficiency. Since the grating pattern generated based on digitalized polarization holography method is widely employed [2426], it is necessary to evaluate the influence of domain number per period on diffractive efficiency for quasi-continuous gratings.

The simulated result shown in Fig. 1 was done using FDTD method for evenly segmented LC PG with domain number N when incident is linearly polarized. The cycloidal pattern degenerates to binary pattern with domain number of two. In this case, the polarization of output beam follows that of incidence to be linear polarized. With half-wave condition satisfied, the diffractive efficiency of fist orders, defined as intensity of + 1 and −1 order divided by that of incidence, is ${\eta _{ \pm 1}} = 81\%$. With N increases from 3, the intensity evolves into first order gradually, also the higher order vanish gradually, finally the efficiency η±1 increase to saturation. Thus, to achieve more than 95% of first order efficiency, at least eight domains are required when fabricated using digitalized polarization holography method. As for the polarization state of diffractive beams in the case of cycloidal pattern, the zeroth order follows incidence to be linearly polarization, and the + 1 and −1 order are left-hand circular (LHC) and right-hand circular (RHC) polarization respectively. The simulated results show that the first order beams are almost circular polarized when N is greater than 3, as illustrated in Fig. 1 by the ratio of horizontal and vertical electrical field E/E. For the applications of LC PG with high requirement of polarization and certain tolerance of efficiency loss, small domain number is preferable considering the fabrication complexity. However, for large area devices, fabrication methods based on digitalized polarization holography confront the tradeoff between spatial resolution and effective area.

 figure: Fig. 1.

Fig. 1. Simulated results of the degeneration of efficiency and polarization of first order beams due to number of domains N of non-continuous LC PG.

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A simple exposure scheme with high robustness is achieved in this work for fabricating continuous cycloidal pattern on a large area device by employing a birefringent prism aligned with quarter wave plate (QWP). Cycloidal distribution of linear polarization direction of exposure beam is created and then embedded on photosensitive SD1 layer with a single exposure, as illustrated in Fig. 2(a). By setting the optical axis of birefringent prism with an angle of 45° to the polarization direction of incidence, the oscillation pattern between circular polarization and linear polarization is generated due to continuously varied optical path length. In this case, the linear polarization is with ± 45°to the optical axis of birefringent prism.

 figure: Fig. 2.

Fig. 2. (a) Schematics of generation of continuous cycloidal pattern using birefringent prism aligned with QWP. (b) Fabrication of large area LC PG. (c) Top view and (d) Side view of LC PG’s molecules directors

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Since the incident polarization has an angle of 45° with respect to the optical axis of the birefringent prism, it can be considered as a waveplate with spatially varied phase retardation. As illustrated is Fig. 2(a), the phase retardation induced varies linearly along y-axis with a coefficient, which is determined by the wedge angle and birefringence of the prism:

$$\delta = ky=\frac{{2\pi }}{\lambda }\Delta n\tan \alpha y$$
Thus, the polarization distribution of exposure beam analyzed using Jones calculus is as follows:
$${J_{exposure}} = M_{QWP}^{\prime}{J_1} = M_{QWP}^{\prime}{M_{prism}}{J_{in}}=M_{QWP}^{\prime}\left[ {\begin{array}{{c}{c}} {\exp \left( {i\frac{\delta }{2}} \right)}&0\\ 0&{\exp \left( { - i\frac{\delta }{2}} \right)} \end{array}} \right]\left[ {\begin{array}{{c}} {\cos {{45}^ \circ }}\\ {\sin {{45}^ \circ }} \end{array}} \right]$$
The Jones vector of beam passed through the birefringent prism is:
$${J_1} = \frac{{\sqrt 2 }}{2}\left[ {\begin{array}{{c}} {\exp \left( {i\frac{\delta }{2}} \right)}\\ {\exp \left( { - i\frac{\delta }{2}} \right)} \end{array}} \right]$$
As we can see from Eq. (3), the linearly polarized light is transferred to spatial variant polarization between linear and circular due to the continuously varying phase retardation of birefringent prism. With the fast axis of QWP aligned 45° to the optical axis of birefringent prism, the slope of the spatially variant phase retardation is converted to the change of linearly polarized direction:
$${J_{exposure}}={\textrm{R}^T}({45^\circ } )M_{QWP}^{}\textrm{R}({45^\circ } ){J_1} = \left[ {\begin{array}{{c}} {\cos (\frac{\delta }{2} + \frac{\pi }{4})}\\ {\sin (\frac{\delta }{2} + \frac{\pi }{4})} \end{array}} \right]$$
As we can see from Eq. (4), the emergent light is linearly polarized with polarization direction rotating along y-axis. Based on this configuration, the exposure setup is designed and realized as shown in Fig. 3. A semiconductor laser with wavelength of 450 nm and a crystalline quartz prism (Crystock, Inc) with optical aperture of 1*1 cm2 are arranged as the geometry shown in Fig. 2(a) with 3D-printed holders. This method is much simpler and more robust compared to the existing exposure techniques. Moreover, our approach expands the range of choice for exposure light source compared with method based on polarization holography, since the latter one requires laser source with sufficient coherent length.

 figure: Fig. 3.

Fig. 3. (a)Geometry of the exposure path. (b) Photograph of fabricated sample. (c) Experiment setup formed by cascaded 3D-printed holders.

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The emergent light irradiates on glass substrate coated with photosensitive alignment layer. In this research, sulfonic azo-dye SD1 (DIC. Japan) is selected as photo aligning layer fabricated in following steps: dissolved in dimethylformamide (DMF) solvent at concentration of 0.4% wt./wt., then spin-coated and soft-baked to form a 10 nm-thick layer, and exposed on the designed stage with the dosage of 1.5 J/cm2. The polymerizable LC material UCL-P100 (DIC. Japan) is adopted as the birefringent layer aligned by SD1 and cured by UV to form a PG due to its easy adjustment of layer thickness, which is controlled during fabrication by spin-coating speed. Similarly, nematics or smectics can also be aligned by exposed SD1 layer. The photograph of fabricated sample with effective area of approximate 0.7*0.8 cm2 shown as the black square in Fig. 3(b). The effective area is determined by optical aperture of prims and shows no conflict with spatial resolution.

3. Results and discussion

Based on our method, the textures of fabricated sample are shown in Fig. 4. Observed under polarized microscope with crossed polarizer and analyzer, bright and dark strips appear due to rotation of directors along y-direction. The polarization direction of linearly-polarized exposure beam is illustrated by blue arrows at the bottom of Fig. 4(d), and the photoaligned directors are represented by red bars since the preferable orientation of SD1 is perpendicular to the exposure polarization. The period of grating measured using microscope image is 89.5 µm. The corresponding diffraction pattern of LC PG is shown in Fig. 4(b) using optical setup in Fig. 4(a).

 figure: Fig. 4.

Fig. 4. (a) Optical setup for measuring fabricated grating samples. Diffraction pattern of (b) polarization grating and (c)binary grating. Textures of (d) polarization grating and (c)binary grating observed under polarized microscope with black arrows showing polarizer and analyzer direction. The blue arrows/ellipses represent the polarization state of exposure beam, and the red bars represents the aligned LC director.

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To realize a binary phase grating with only two director orientations instead of continuously rotating ones, we simply remove the QWP in exposure path in Fig. 2(a). One unique property of photoalignment layer SD1 playing a crucial role here is that the easy axis is determined by the long axis of the ellipse and unsensitive to the ellipticity of exposure light [27]. The exposure beam passed through birefringent prism shows the oscillation of ellipticity with polarization direction fixed at ± 45° to y-axis, as described by J1 in Eq. (3) and shown by blue ellipses at the bottom of Fig. 4(e). Consequently, the binary phase grating with orthogonal alignment directions is obtained, as texture shown in Fig. 4(e) and corresponding alignment directions represented by red bars. This method for binary phase grating has the potential in achieving submicron period compared with commonly used chrome mask-based method [28,29] since no diffraction arises during exposure process.

As described by Eq. (3), the orientation of LC director changes periodically. The period of LC grating fabricated can be derived:

$$\Lambda = \frac{\lambda }{{\Delta n\tan \alpha }}$$
The crystalline quartz prism with birefringence of $\Delta n = 0.0094$ and wedge angle of 30° provides grating period with the value of 82.9 µm.

In the real case, the exposure beam is bended from the incidence due to refraction. Considering the deflection of propagating direction, the modified calculation gives the period value of 90.6 µm in the case of laser arranged vertically and no inclination of the sample (inclined angle $\beta = {0^ \circ }$ in Fig. 3(a)). The grating period is adjusted by the inclined angle β of exposed sample. The minimum value of period occurs when the exposure beam is normal to the substrate surface, which is 86.6 µm with corresponding $\beta = {18^ \circ }$ by calculation, as shown in Fig. 5.

 figure: Fig. 5.

Fig. 5. The dependence of grating period on inclined angle of sample during exposure.

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The diffraction efficiency of LC PG, as summarized in Table 1, is determined by the thickness and birefringence of LC layer and the incident polarization [20,30,31].

Tables Icon

Table 1. Summarization of Polarization and Efficiency of Diffractive Orders

With half-wave condition satisfied $\Delta nd = \lambda /2$, the 0th order disappears, and efficiency of ± 1st orders achieve maximum value of 100%. The intensity ratio between + 1st and −1st orders depends on the RHC or LHC fraction of the incidence. Here the corresponding index is defined from the Stokes parameter of the output as ${\gamma _{RHC}}=(1+{\textrm{S}_3} + {S_0})/2$ and ${\gamma _{LHC}}=(1-{\textrm{S}_3} + {S_0})/2$ respectively.

The measured efficiency, calculated from the intensity of ± 1st orders divided by that of incidence, is shown in Fig. 6. The thickness of LC layer is controlled by the concentration of monomer and the spin-coating speed, and measured by a stepper (KOSAKA ET150). The maximum value of LC PG efficiency measured reaches 99.74% using 532 nm green laser, and over 95% for 450 nm blue laser and 633 nm red laser. The optimal thickness in terms of efficiency varies for different wavelengths based on the configuration. The achromatic LC PG by Oh expands the high-efficiency band by a double twist configuration [32].

 figure: Fig. 6.

Fig. 6. (a) The PG efficiency of + 1st and −1st orders vs. thickness of LC layer. (b) Diffraction pattern of LCPG using blue green and red lasers with corresponding thickness.

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4. Conclusion

This research put forward a new approach to fabricate a cycloidal pattern of LC directors to form PGs based on photoalignment technology. The method is to employ birefringent elements to continuously modulate the polarization state of exposure beam instead of digitalized phase or amplitude masks. Based on this, a cascaded configuration including polarizer, birefringent prism and quarter wave plate with designed orientation is demonstrated for generating a cycloidal distribution of linearly polarized direction. And then the quality of the fabricated gratings has been verified by the efficiency and ellipticity measurement. The advantages of this method include high robustness, low cost, less optical element deployed and simple optical design. Hence, the single-step exposure process can greatly simplify the fabrication and increase the yield with large area and high quality maintained, and the method has potential in designing and developing various geometric phase LC devices.

Funding

National Natural Science Foundation of China (61405009, 61875004).

Disclosures

The authors declare no conflicts of interest.

References

1. J. Anandan, “The geometric phase,” Nature 360(6402), 307–313 (1992). [CrossRef]  

2. S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. - Indian Acad. Sci., Sect. A 44(6), 398–417 (1956). [CrossRef]  

3. M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London, Ser. A 392(1802), 45–57 (1984). [CrossRef]  

4. D. M. Tong, E. Sjöqvist, L. C. Kwek, and C. H. Oh, “Kinematic approach to the mixed state geometric phase in nonunitary evolution,” Phys. Rev. Lett. 93(8), 1–4 (2004). [CrossRef]  

5. M. W. Kudenov, M. N. Miskiewicz, M. J. Escuti, and E. L. Dereniak, “Spatial heterodyne interferometry with polarization gratings,” Opt. Lett. 37(21), 4413–4415 (2012). [CrossRef]  

6. J. Kobashi, H. Yoshida, and M. Ozaki, “Planar optics with patterned chiral liquid crystals,” Nat. Photonics 10(6), 389–392 (2016). [CrossRef]  

7. G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015). [CrossRef]  

8. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014). [CrossRef]  

9. Y. Shi, Y. J. Liu, F. Song, V. G. Chigrinov, H.-S. Kwok, M. Hu, D. Luo, and X. W. Sun, “Photoalignment-induced two-dimensional liquid crystal polarization structure via multi-beam polarization interferometry,” Opt. Express 26(6), 7683–7692 (2018). [CrossRef]  

10. A. M. W. Tam, F. Fan, T. Du, W. Hu, W. Zhang, C. Zhao, X. Wang, K. L. Ching, G. Li, H. Luo, V. G. Chigrinov, S. Wen, and H.-S. Kwok, “Bifocal Optical-Vortex Lens with Sorting of the Generated Nonseparable Spin-Orbital Angular-Momentum States,” Phys. Rev. Appl. 7(3), 034010 (2017). [CrossRef]  

11. K. Hisano, M. Aizawa, M. Ishizu, Y. Kurata, W. Nakano, N. Akamatsu, C. J. Barrett, and A. Shishido, “Scanning wave photopolymerization enables dye-free alignment patterning of liquid crystals,” Sci. Adv. 3(11), e1701610 (2017). [CrossRef]  

12. C. Provenzano, P. Pagliusi, and G. Cipparrone, “Electrically tunable two-dimensional liquid crystals gratings induced by polarization holography,” Opt. Express 15(9), 5872–5878 (2007). [CrossRef]  

13. J. Kim, Y. Li, M. N. Miskiewicz, C. Oh, M. W. Kudenov, and M. J. Escuti, “Fabrication of ideal geometric-phase holograms with arbitrary wavefronts,” Optica 2(11), 958–964 (2015). [CrossRef]  

14. W. Duan, P. Chen, S.-J. Ge, X. Liang, and W. Hu, “A Fast-Response and Helicity-Dependent Lens Enabled by Micro-Patterned Dual-Frequency Liquid Crystals,” Crystals 9(2), 111 (2019). [CrossRef]  

15. Y. Weng, D. Xu, Y. Zhang, X. Li, and S.-T. Wu, “Polarization volume grating with high efficiency and large diffraction angle,” Opt. Express 24(16), 17746–17759 (2016). [CrossRef]  

16. A. Shishido, “Rewritable holograms based on azobenzene-containing liquid-crystalline polymers,” Polym. J. 42(7), 525–533 (2010). [CrossRef]  

17. X. Xiang, J. Kim, and M. J. Escuti, “Bragg polarization gratings for wide angular bandwidth and high efficiency at steep deflection angles,” Sci. Rep. 8(1), 7202 (2018). [CrossRef]  

18. M. W. Kudenov, M. J. Escuti, N. Hagen, E. L. Dereniak, and K. Oka, “Snapshot imaging Mueller matrix polarimeter using polarization gratings,” Opt. Lett. 37(8), 1367–1369 (2012). [CrossRef]  

19. T. Zhan, Y.-H. Lee, G. Tan, J. Xiong, K. Yin, F. Gou, J. Zou, N. Zhang, D. Zhao, J. Yang, S. Liu, and S.-T. Wu, “Pancharatnam–Berry optical elements for head-up and near-eye displays,” J. Opt. Soc. Am. B 36(5), D52–D65 (2019). [CrossRef]  

20. Q. Guo, L. Xu, J. Sun, X. Yang, H. Liu, K. Yan, H. Zhao, V. G. Chigrinov, and H. S. Kwok, “Fast switching beam steering based on ferroelectric liquid crystal phase shutter and polarisation grating,” Liq. Cryst. 46(9), 1383–1388 (2019). [CrossRef]  

21. K. Hisano, M. Ota, M. Aizawa, N. Akamatsu, C. J. Barrett, and A. Shishido, “Single-step creation of polarization gratings by scanning wave photopolymerization with unpolarized light,” J. Opt. Soc. Am. B 36(5), D112–D118 (2019). [CrossRef]  

22. T. Du, F. Fan, A. M. W. Tam, J. Sun, V. G. Chigrinov, and H. Sing Kwok, “Complex Nanoscale-Ordered Liquid Crystal Polymer Film for High Transmittance Holographic Polarizer,” Adv. Mater. 27(44), 7191–7195 (2015). [CrossRef]  

23. T. Todorov, L. Nikolova, and N. Tomova, “Polarization holography 2: Polarization holographic gratings in photoanisotropic materials with and without intrinsic birefringence,” Appl. Opt. 23(24), 4588–4591 (1984). [CrossRef]  

24. Y. Li, Y. Liu, S. Li, P. Zhou, T. Zhan, Q. Chen, Y. Su, and S.-T. Wu, “Single-exposure fabrication of tunable Pancharatnam-Berry devices using a dye-doped liquid crystal,” Opt. Express 27(6), 9054–9060 (2019). [CrossRef]  

25. P. Chen, B.-Y. Wei, W. Ji, S.-J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y.-Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015). [CrossRef]  

26. L. De Sio, D. E. Roberts, Z. Liao, S. Nersisyan, O. Uskova, L. Wickboldt, N. Tabiryan, D. M. Steeves, and B. R. Kimball, “Digital polarization holography advancing geometrical phase optics,” Opt. Express 24(16), 18297–18306 (2016). [CrossRef]  

27. A. D. Kiselev, V. G. Chigrinov, and H. S. Kwok, “Kinetics of photoinduced ordering in azo-dye films: Two-state and diffusion models,” Phys. Rev. E 80(1), 011706 (2009). [CrossRef]  

28. W. Hu, A. Srivastava, F. Xu, J.-T. Sun, X.-W. Lin, H.-Q. Cui, V. Chigrinov, and Y.-Q. Lu, “Liquid crystal gratings based on alternate TN and PA photoalignment,” Opt. Express 20(5), 5384–5391 (2012). [CrossRef]  

29. A. K. Srivastava, W. Hu, V. G. Chigrinov, A. D. Kiselev, and Y. Q. Lu, “Fast switchable grating based on orthogonal photo alignments of ferroelectric liquid crystals,” Appl. Phys. Lett. 101(3), 031112 (2012). [CrossRef]  

30. L. Nikolova and T. Todorov, “Diffraction Efficiency and Selectivity of Polarization Holographic Recording,” Opt. Acta 31(5), 579–588 (1984). [CrossRef]  

31. G. Cipparrone, A. Mazzulla, and L. Blinov, “Permanent polarization gratings in photosensitive Langmuir-Blodgett films,” J. Opt. Soc. Am. B 19(5), 1157–1161 (2002). [CrossRef]  

32. C. Oh and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33(20), 2287–2289 (2008). [CrossRef]  

References

  • View by:

  1. J. Anandan, “The geometric phase,” Nature 360(6402), 307–313 (1992).
    [Crossref]
  2. S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. - Indian Acad. Sci., Sect. A 44(6), 398–417 (1956).
    [Crossref]
  3. M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London, Ser. A 392(1802), 45–57 (1984).
    [Crossref]
  4. D. M. Tong, E. Sjöqvist, L. C. Kwek, and C. H. Oh, “Kinematic approach to the mixed state geometric phase in nonunitary evolution,” Phys. Rev. Lett. 93(8), 1–4 (2004).
    [Crossref]
  5. M. W. Kudenov, M. N. Miskiewicz, M. J. Escuti, and E. L. Dereniak, “Spatial heterodyne interferometry with polarization gratings,” Opt. Lett. 37(21), 4413–4415 (2012).
    [Crossref]
  6. J. Kobashi, H. Yoshida, and M. Ozaki, “Planar optics with patterned chiral liquid crystals,” Nat. Photonics 10(6), 389–392 (2016).
    [Crossref]
  7. G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
    [Crossref]
  8. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
    [Crossref]
  9. Y. Shi, Y. J. Liu, F. Song, V. G. Chigrinov, H.-S. Kwok, M. Hu, D. Luo, and X. W. Sun, “Photoalignment-induced two-dimensional liquid crystal polarization structure via multi-beam polarization interferometry,” Opt. Express 26(6), 7683–7692 (2018).
    [Crossref]
  10. A. M. W. Tam, F. Fan, T. Du, W. Hu, W. Zhang, C. Zhao, X. Wang, K. L. Ching, G. Li, H. Luo, V. G. Chigrinov, S. Wen, and H.-S. Kwok, “Bifocal Optical-Vortex Lens with Sorting of the Generated Nonseparable Spin-Orbital Angular-Momentum States,” Phys. Rev. Appl. 7(3), 034010 (2017).
    [Crossref]
  11. K. Hisano, M. Aizawa, M. Ishizu, Y. Kurata, W. Nakano, N. Akamatsu, C. J. Barrett, and A. Shishido, “Scanning wave photopolymerization enables dye-free alignment patterning of liquid crystals,” Sci. Adv. 3(11), e1701610 (2017).
    [Crossref]
  12. C. Provenzano, P. Pagliusi, and G. Cipparrone, “Electrically tunable two-dimensional liquid crystals gratings induced by polarization holography,” Opt. Express 15(9), 5872–5878 (2007).
    [Crossref]
  13. J. Kim, Y. Li, M. N. Miskiewicz, C. Oh, M. W. Kudenov, and M. J. Escuti, “Fabrication of ideal geometric-phase holograms with arbitrary wavefronts,” Optica 2(11), 958–964 (2015).
    [Crossref]
  14. W. Duan, P. Chen, S.-J. Ge, X. Liang, and W. Hu, “A Fast-Response and Helicity-Dependent Lens Enabled by Micro-Patterned Dual-Frequency Liquid Crystals,” Crystals 9(2), 111 (2019).
    [Crossref]
  15. Y. Weng, D. Xu, Y. Zhang, X. Li, and S.-T. Wu, “Polarization volume grating with high efficiency and large diffraction angle,” Opt. Express 24(16), 17746–17759 (2016).
    [Crossref]
  16. A. Shishido, “Rewritable holograms based on azobenzene-containing liquid-crystalline polymers,” Polym. J. 42(7), 525–533 (2010).
    [Crossref]
  17. X. Xiang, J. Kim, and M. J. Escuti, “Bragg polarization gratings for wide angular bandwidth and high efficiency at steep deflection angles,” Sci. Rep. 8(1), 7202 (2018).
    [Crossref]
  18. M. W. Kudenov, M. J. Escuti, N. Hagen, E. L. Dereniak, and K. Oka, “Snapshot imaging Mueller matrix polarimeter using polarization gratings,” Opt. Lett. 37(8), 1367–1369 (2012).
    [Crossref]
  19. T. Zhan, Y.-H. Lee, G. Tan, J. Xiong, K. Yin, F. Gou, J. Zou, N. Zhang, D. Zhao, J. Yang, S. Liu, and S.-T. Wu, “Pancharatnam–Berry optical elements for head-up and near-eye displays,” J. Opt. Soc. Am. B 36(5), D52–D65 (2019).
    [Crossref]
  20. Q. Guo, L. Xu, J. Sun, X. Yang, H. Liu, K. Yan, H. Zhao, V. G. Chigrinov, and H. S. Kwok, “Fast switching beam steering based on ferroelectric liquid crystal phase shutter and polarisation grating,” Liq. Cryst. 46(9), 1383–1388 (2019).
    [Crossref]
  21. K. Hisano, M. Ota, M. Aizawa, N. Akamatsu, C. J. Barrett, and A. Shishido, “Single-step creation of polarization gratings by scanning wave photopolymerization with unpolarized light,” J. Opt. Soc. Am. B 36(5), D112–D118 (2019).
    [Crossref]
  22. T. Du, F. Fan, A. M. W. Tam, J. Sun, V. G. Chigrinov, and H. Sing Kwok, “Complex Nanoscale-Ordered Liquid Crystal Polymer Film for High Transmittance Holographic Polarizer,” Adv. Mater. 27(44), 7191–7195 (2015).
    [Crossref]
  23. T. Todorov, L. Nikolova, and N. Tomova, “Polarization holography 2: Polarization holographic gratings in photoanisotropic materials with and without intrinsic birefringence,” Appl. Opt. 23(24), 4588–4591 (1984).
    [Crossref]
  24. Y. Li, Y. Liu, S. Li, P. Zhou, T. Zhan, Q. Chen, Y. Su, and S.-T. Wu, “Single-exposure fabrication of tunable Pancharatnam-Berry devices using a dye-doped liquid crystal,” Opt. Express 27(6), 9054–9060 (2019).
    [Crossref]
  25. P. Chen, B.-Y. Wei, W. Ji, S.-J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y.-Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
    [Crossref]
  26. L. De Sio, D. E. Roberts, Z. Liao, S. Nersisyan, O. Uskova, L. Wickboldt, N. Tabiryan, D. M. Steeves, and B. R. Kimball, “Digital polarization holography advancing geometrical phase optics,” Opt. Express 24(16), 18297–18306 (2016).
    [Crossref]
  27. A. D. Kiselev, V. G. Chigrinov, and H. S. Kwok, “Kinetics of photoinduced ordering in azo-dye films: Two-state and diffusion models,” Phys. Rev. E 80(1), 011706 (2009).
    [Crossref]
  28. W. Hu, A. Srivastava, F. Xu, J.-T. Sun, X.-W. Lin, H.-Q. Cui, V. Chigrinov, and Y.-Q. Lu, “Liquid crystal gratings based on alternate TN and PA photoalignment,” Opt. Express 20(5), 5384–5391 (2012).
    [Crossref]
  29. A. K. Srivastava, W. Hu, V. G. Chigrinov, A. D. Kiselev, and Y. Q. Lu, “Fast switchable grating based on orthogonal photo alignments of ferroelectric liquid crystals,” Appl. Phys. Lett. 101(3), 031112 (2012).
    [Crossref]
  30. L. Nikolova and T. Todorov, “Diffraction Efficiency and Selectivity of Polarization Holographic Recording,” Opt. Acta 31(5), 579–588 (1984).
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  31. G. Cipparrone, A. Mazzulla, and L. Blinov, “Permanent polarization gratings in photosensitive Langmuir-Blodgett films,” J. Opt. Soc. Am. B 19(5), 1157–1161 (2002).
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  32. C. Oh and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33(20), 2287–2289 (2008).
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2019 (5)

2018 (2)

2017 (2)

A. M. W. Tam, F. Fan, T. Du, W. Hu, W. Zhang, C. Zhao, X. Wang, K. L. Ching, G. Li, H. Luo, V. G. Chigrinov, S. Wen, and H.-S. Kwok, “Bifocal Optical-Vortex Lens with Sorting of the Generated Nonseparable Spin-Orbital Angular-Momentum States,” Phys. Rev. Appl. 7(3), 034010 (2017).
[Crossref]

K. Hisano, M. Aizawa, M. Ishizu, Y. Kurata, W. Nakano, N. Akamatsu, C. J. Barrett, and A. Shishido, “Scanning wave photopolymerization enables dye-free alignment patterning of liquid crystals,” Sci. Adv. 3(11), e1701610 (2017).
[Crossref]

2016 (3)

2015 (4)

P. Chen, B.-Y. Wei, W. Ji, S.-J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y.-Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

T. Du, F. Fan, A. M. W. Tam, J. Sun, V. G. Chigrinov, and H. Sing Kwok, “Complex Nanoscale-Ordered Liquid Crystal Polymer Film for High Transmittance Holographic Polarizer,” Adv. Mater. 27(44), 7191–7195 (2015).
[Crossref]

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref]

J. Kim, Y. Li, M. N. Miskiewicz, C. Oh, M. W. Kudenov, and M. J. Escuti, “Fabrication of ideal geometric-phase holograms with arbitrary wavefronts,” Optica 2(11), 958–964 (2015).
[Crossref]

2014 (1)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref]

2012 (4)

2010 (1)

A. Shishido, “Rewritable holograms based on azobenzene-containing liquid-crystalline polymers,” Polym. J. 42(7), 525–533 (2010).
[Crossref]

2009 (1)

A. D. Kiselev, V. G. Chigrinov, and H. S. Kwok, “Kinetics of photoinduced ordering in azo-dye films: Two-state and diffusion models,” Phys. Rev. E 80(1), 011706 (2009).
[Crossref]

2008 (1)

2007 (1)

2004 (1)

D. M. Tong, E. Sjöqvist, L. C. Kwek, and C. H. Oh, “Kinematic approach to the mixed state geometric phase in nonunitary evolution,” Phys. Rev. Lett. 93(8), 1–4 (2004).
[Crossref]

2002 (1)

1992 (1)

J. Anandan, “The geometric phase,” Nature 360(6402), 307–313 (1992).
[Crossref]

1984 (3)

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London, Ser. A 392(1802), 45–57 (1984).
[Crossref]

L. Nikolova and T. Todorov, “Diffraction Efficiency and Selectivity of Polarization Holographic Recording,” Opt. Acta 31(5), 579–588 (1984).
[Crossref]

T. Todorov, L. Nikolova, and N. Tomova, “Polarization holography 2: Polarization holographic gratings in photoanisotropic materials with and without intrinsic birefringence,” Appl. Opt. 23(24), 4588–4591 (1984).
[Crossref]

1956 (1)

S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. - Indian Acad. Sci., Sect. A 44(6), 398–417 (1956).
[Crossref]

Aizawa, M.

K. Hisano, M. Ota, M. Aizawa, N. Akamatsu, C. J. Barrett, and A. Shishido, “Single-step creation of polarization gratings by scanning wave photopolymerization with unpolarized light,” J. Opt. Soc. Am. B 36(5), D112–D118 (2019).
[Crossref]

K. Hisano, M. Aizawa, M. Ishizu, Y. Kurata, W. Nakano, N. Akamatsu, C. J. Barrett, and A. Shishido, “Scanning wave photopolymerization enables dye-free alignment patterning of liquid crystals,” Sci. Adv. 3(11), e1701610 (2017).
[Crossref]

Akamatsu, N.

K. Hisano, M. Ota, M. Aizawa, N. Akamatsu, C. J. Barrett, and A. Shishido, “Single-step creation of polarization gratings by scanning wave photopolymerization with unpolarized light,” J. Opt. Soc. Am. B 36(5), D112–D118 (2019).
[Crossref]

K. Hisano, M. Aizawa, M. Ishizu, Y. Kurata, W. Nakano, N. Akamatsu, C. J. Barrett, and A. Shishido, “Scanning wave photopolymerization enables dye-free alignment patterning of liquid crystals,” Sci. Adv. 3(11), e1701610 (2017).
[Crossref]

Anandan, J.

J. Anandan, “The geometric phase,” Nature 360(6402), 307–313 (1992).
[Crossref]

Barrett, C. J.

K. Hisano, M. Ota, M. Aizawa, N. Akamatsu, C. J. Barrett, and A. Shishido, “Single-step creation of polarization gratings by scanning wave photopolymerization with unpolarized light,” J. Opt. Soc. Am. B 36(5), D112–D118 (2019).
[Crossref]

K. Hisano, M. Aizawa, M. Ishizu, Y. Kurata, W. Nakano, N. Akamatsu, C. J. Barrett, and A. Shishido, “Scanning wave photopolymerization enables dye-free alignment patterning of liquid crystals,” Sci. Adv. 3(11), e1701610 (2017).
[Crossref]

Berry, M. V.

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London, Ser. A 392(1802), 45–57 (1984).
[Crossref]

Blinov, L.

Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref]

Chen, P.

W. Duan, P. Chen, S.-J. Ge, X. Liang, and W. Hu, “A Fast-Response and Helicity-Dependent Lens Enabled by Micro-Patterned Dual-Frequency Liquid Crystals,” Crystals 9(2), 111 (2019).
[Crossref]

P. Chen, B.-Y. Wei, W. Ji, S.-J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y.-Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

Chen, Q.

Chigrinov, V.

P. Chen, B.-Y. Wei, W. Ji, S.-J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y.-Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

W. Hu, A. Srivastava, F. Xu, J.-T. Sun, X.-W. Lin, H.-Q. Cui, V. Chigrinov, and Y.-Q. Lu, “Liquid crystal gratings based on alternate TN and PA photoalignment,” Opt. Express 20(5), 5384–5391 (2012).
[Crossref]

Chigrinov, V. G.

Q. Guo, L. Xu, J. Sun, X. Yang, H. Liu, K. Yan, H. Zhao, V. G. Chigrinov, and H. S. Kwok, “Fast switching beam steering based on ferroelectric liquid crystal phase shutter and polarisation grating,” Liq. Cryst. 46(9), 1383–1388 (2019).
[Crossref]

Y. Shi, Y. J. Liu, F. Song, V. G. Chigrinov, H.-S. Kwok, M. Hu, D. Luo, and X. W. Sun, “Photoalignment-induced two-dimensional liquid crystal polarization structure via multi-beam polarization interferometry,” Opt. Express 26(6), 7683–7692 (2018).
[Crossref]

A. M. W. Tam, F. Fan, T. Du, W. Hu, W. Zhang, C. Zhao, X. Wang, K. L. Ching, G. Li, H. Luo, V. G. Chigrinov, S. Wen, and H.-S. Kwok, “Bifocal Optical-Vortex Lens with Sorting of the Generated Nonseparable Spin-Orbital Angular-Momentum States,” Phys. Rev. Appl. 7(3), 034010 (2017).
[Crossref]

T. Du, F. Fan, A. M. W. Tam, J. Sun, V. G. Chigrinov, and H. Sing Kwok, “Complex Nanoscale-Ordered Liquid Crystal Polymer Film for High Transmittance Holographic Polarizer,” Adv. Mater. 27(44), 7191–7195 (2015).
[Crossref]

A. K. Srivastava, W. Hu, V. G. Chigrinov, A. D. Kiselev, and Y. Q. Lu, “Fast switchable grating based on orthogonal photo alignments of ferroelectric liquid crystals,” Appl. Phys. Lett. 101(3), 031112 (2012).
[Crossref]

A. D. Kiselev, V. G. Chigrinov, and H. S. Kwok, “Kinetics of photoinduced ordering in azo-dye films: Two-state and diffusion models,” Phys. Rev. E 80(1), 011706 (2009).
[Crossref]

Ching, K. L.

A. M. W. Tam, F. Fan, T. Du, W. Hu, W. Zhang, C. Zhao, X. Wang, K. L. Ching, G. Li, H. Luo, V. G. Chigrinov, S. Wen, and H.-S. Kwok, “Bifocal Optical-Vortex Lens with Sorting of the Generated Nonseparable Spin-Orbital Angular-Momentum States,” Phys. Rev. Appl. 7(3), 034010 (2017).
[Crossref]

Cipparrone, G.

Cui, H.-Q.

De Sio, L.

Dereniak, E. L.

Du, T.

A. M. W. Tam, F. Fan, T. Du, W. Hu, W. Zhang, C. Zhao, X. Wang, K. L. Ching, G. Li, H. Luo, V. G. Chigrinov, S. Wen, and H.-S. Kwok, “Bifocal Optical-Vortex Lens with Sorting of the Generated Nonseparable Spin-Orbital Angular-Momentum States,” Phys. Rev. Appl. 7(3), 034010 (2017).
[Crossref]

T. Du, F. Fan, A. M. W. Tam, J. Sun, V. G. Chigrinov, and H. Sing Kwok, “Complex Nanoscale-Ordered Liquid Crystal Polymer Film for High Transmittance Holographic Polarizer,” Adv. Mater. 27(44), 7191–7195 (2015).
[Crossref]

Duan, W.

W. Duan, P. Chen, S.-J. Ge, X. Liang, and W. Hu, “A Fast-Response and Helicity-Dependent Lens Enabled by Micro-Patterned Dual-Frequency Liquid Crystals,” Crystals 9(2), 111 (2019).
[Crossref]

Escuti, M. J.

Fan, F.

A. M. W. Tam, F. Fan, T. Du, W. Hu, W. Zhang, C. Zhao, X. Wang, K. L. Ching, G. Li, H. Luo, V. G. Chigrinov, S. Wen, and H.-S. Kwok, “Bifocal Optical-Vortex Lens with Sorting of the Generated Nonseparable Spin-Orbital Angular-Momentum States,” Phys. Rev. Appl. 7(3), 034010 (2017).
[Crossref]

T. Du, F. Fan, A. M. W. Tam, J. Sun, V. G. Chigrinov, and H. Sing Kwok, “Complex Nanoscale-Ordered Liquid Crystal Polymer Film for High Transmittance Holographic Polarizer,” Adv. Mater. 27(44), 7191–7195 (2015).
[Crossref]

Ge, S.-J.

W. Duan, P. Chen, S.-J. Ge, X. Liang, and W. Hu, “A Fast-Response and Helicity-Dependent Lens Enabled by Micro-Patterned Dual-Frequency Liquid Crystals,” Crystals 9(2), 111 (2019).
[Crossref]

P. Chen, B.-Y. Wei, W. Ji, S.-J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y.-Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

Gou, F.

Guo, Q.

Q. Guo, L. Xu, J. Sun, X. Yang, H. Liu, K. Yan, H. Zhao, V. G. Chigrinov, and H. S. Kwok, “Fast switching beam steering based on ferroelectric liquid crystal phase shutter and polarisation grating,” Liq. Cryst. 46(9), 1383–1388 (2019).
[Crossref]

Hagen, N.

Hisano, K.

K. Hisano, M. Ota, M. Aizawa, N. Akamatsu, C. J. Barrett, and A. Shishido, “Single-step creation of polarization gratings by scanning wave photopolymerization with unpolarized light,” J. Opt. Soc. Am. B 36(5), D112–D118 (2019).
[Crossref]

K. Hisano, M. Aizawa, M. Ishizu, Y. Kurata, W. Nakano, N. Akamatsu, C. J. Barrett, and A. Shishido, “Scanning wave photopolymerization enables dye-free alignment patterning of liquid crystals,” Sci. Adv. 3(11), e1701610 (2017).
[Crossref]

Hu, M.

Hu, W.

W. Duan, P. Chen, S.-J. Ge, X. Liang, and W. Hu, “A Fast-Response and Helicity-Dependent Lens Enabled by Micro-Patterned Dual-Frequency Liquid Crystals,” Crystals 9(2), 111 (2019).
[Crossref]

A. M. W. Tam, F. Fan, T. Du, W. Hu, W. Zhang, C. Zhao, X. Wang, K. L. Ching, G. Li, H. Luo, V. G. Chigrinov, S. Wen, and H.-S. Kwok, “Bifocal Optical-Vortex Lens with Sorting of the Generated Nonseparable Spin-Orbital Angular-Momentum States,” Phys. Rev. Appl. 7(3), 034010 (2017).
[Crossref]

P. Chen, B.-Y. Wei, W. Ji, S.-J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y.-Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

A. K. Srivastava, W. Hu, V. G. Chigrinov, A. D. Kiselev, and Y. Q. Lu, “Fast switchable grating based on orthogonal photo alignments of ferroelectric liquid crystals,” Appl. Phys. Lett. 101(3), 031112 (2012).
[Crossref]

W. Hu, A. Srivastava, F. Xu, J.-T. Sun, X.-W. Lin, H.-Q. Cui, V. Chigrinov, and Y.-Q. Lu, “Liquid crystal gratings based on alternate TN and PA photoalignment,” Opt. Express 20(5), 5384–5391 (2012).
[Crossref]

Ishizu, M.

K. Hisano, M. Aizawa, M. Ishizu, Y. Kurata, W. Nakano, N. Akamatsu, C. J. Barrett, and A. Shishido, “Scanning wave photopolymerization enables dye-free alignment patterning of liquid crystals,” Sci. Adv. 3(11), e1701610 (2017).
[Crossref]

Ji, W.

P. Chen, B.-Y. Wei, W. Ji, S.-J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y.-Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

Kenney, M.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref]

Kim, J.

X. Xiang, J. Kim, and M. J. Escuti, “Bragg polarization gratings for wide angular bandwidth and high efficiency at steep deflection angles,” Sci. Rep. 8(1), 7202 (2018).
[Crossref]

J. Kim, Y. Li, M. N. Miskiewicz, C. Oh, M. W. Kudenov, and M. J. Escuti, “Fabrication of ideal geometric-phase holograms with arbitrary wavefronts,” Optica 2(11), 958–964 (2015).
[Crossref]

Kimball, B. R.

Kiselev, A. D.

A. K. Srivastava, W. Hu, V. G. Chigrinov, A. D. Kiselev, and Y. Q. Lu, “Fast switchable grating based on orthogonal photo alignments of ferroelectric liquid crystals,” Appl. Phys. Lett. 101(3), 031112 (2012).
[Crossref]

A. D. Kiselev, V. G. Chigrinov, and H. S. Kwok, “Kinetics of photoinduced ordering in azo-dye films: Two-state and diffusion models,” Phys. Rev. E 80(1), 011706 (2009).
[Crossref]

Kobashi, J.

J. Kobashi, H. Yoshida, and M. Ozaki, “Planar optics with patterned chiral liquid crystals,” Nat. Photonics 10(6), 389–392 (2016).
[Crossref]

Kudenov, M. W.

Kurata, Y.

K. Hisano, M. Aizawa, M. Ishizu, Y. Kurata, W. Nakano, N. Akamatsu, C. J. Barrett, and A. Shishido, “Scanning wave photopolymerization enables dye-free alignment patterning of liquid crystals,” Sci. Adv. 3(11), e1701610 (2017).
[Crossref]

Kwek, L. C.

D. M. Tong, E. Sjöqvist, L. C. Kwek, and C. H. Oh, “Kinematic approach to the mixed state geometric phase in nonunitary evolution,” Phys. Rev. Lett. 93(8), 1–4 (2004).
[Crossref]

Kwok, H. S.

Q. Guo, L. Xu, J. Sun, X. Yang, H. Liu, K. Yan, H. Zhao, V. G. Chigrinov, and H. S. Kwok, “Fast switching beam steering based on ferroelectric liquid crystal phase shutter and polarisation grating,” Liq. Cryst. 46(9), 1383–1388 (2019).
[Crossref]

A. D. Kiselev, V. G. Chigrinov, and H. S. Kwok, “Kinetics of photoinduced ordering in azo-dye films: Two-state and diffusion models,” Phys. Rev. E 80(1), 011706 (2009).
[Crossref]

Kwok, H.-S.

Y. Shi, Y. J. Liu, F. Song, V. G. Chigrinov, H.-S. Kwok, M. Hu, D. Luo, and X. W. Sun, “Photoalignment-induced two-dimensional liquid crystal polarization structure via multi-beam polarization interferometry,” Opt. Express 26(6), 7683–7692 (2018).
[Crossref]

A. M. W. Tam, F. Fan, T. Du, W. Hu, W. Zhang, C. Zhao, X. Wang, K. L. Ching, G. Li, H. Luo, V. G. Chigrinov, S. Wen, and H.-S. Kwok, “Bifocal Optical-Vortex Lens with Sorting of the Generated Nonseparable Spin-Orbital Angular-Momentum States,” Phys. Rev. Appl. 7(3), 034010 (2017).
[Crossref]

Lee, Y.-H.

Li, G.

A. M. W. Tam, F. Fan, T. Du, W. Hu, W. Zhang, C. Zhao, X. Wang, K. L. Ching, G. Li, H. Luo, V. G. Chigrinov, S. Wen, and H.-S. Kwok, “Bifocal Optical-Vortex Lens with Sorting of the Generated Nonseparable Spin-Orbital Angular-Momentum States,” Phys. Rev. Appl. 7(3), 034010 (2017).
[Crossref]

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref]

Li, S.

Li, X.

Li, Y.

Liang, X.

W. Duan, P. Chen, S.-J. Ge, X. Liang, and W. Hu, “A Fast-Response and Helicity-Dependent Lens Enabled by Micro-Patterned Dual-Frequency Liquid Crystals,” Crystals 9(2), 111 (2019).
[Crossref]

Liao, Z.

Lin, X.-W.

Liu, H.

Q. Guo, L. Xu, J. Sun, X. Yang, H. Liu, K. Yan, H. Zhao, V. G. Chigrinov, and H. S. Kwok, “Fast switching beam steering based on ferroelectric liquid crystal phase shutter and polarisation grating,” Liq. Cryst. 46(9), 1383–1388 (2019).
[Crossref]

Liu, S.

Liu, Y.

Liu, Y. J.

Lu, Y. Q.

A. K. Srivastava, W. Hu, V. G. Chigrinov, A. D. Kiselev, and Y. Q. Lu, “Fast switchable grating based on orthogonal photo alignments of ferroelectric liquid crystals,” Appl. Phys. Lett. 101(3), 031112 (2012).
[Crossref]

Lu, Y.-Q.

P. Chen, B.-Y. Wei, W. Ji, S.-J. Ge, W. Hu, F. Xu, V. Chigrinov, and Y.-Q. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photonics Res. 3(4), 133–139 (2015).
[Crossref]

W. Hu, A. Srivastava, F. Xu, J.-T. Sun, X.-W. Lin, H.-Q. Cui, V. Chigrinov, and Y.-Q. Lu, “Liquid crystal gratings based on alternate TN and PA photoalignment,” Opt. Express 20(5), 5384–5391 (2012).
[Crossref]

Luo, D.

Luo, H.

A. M. W. Tam, F. Fan, T. Du, W. Hu, W. Zhang, C. Zhao, X. Wang, K. L. Ching, G. Li, H. Luo, V. G. Chigrinov, S. Wen, and H.-S. Kwok, “Bifocal Optical-Vortex Lens with Sorting of the Generated Nonseparable Spin-Orbital Angular-Momentum States,” Phys. Rev. Appl. 7(3), 034010 (2017).
[Crossref]

Mazzulla, A.

Miskiewicz, M. N.

Mühlenbernd, H.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref]

Nakano, W.

K. Hisano, M. Aizawa, M. Ishizu, Y. Kurata, W. Nakano, N. Akamatsu, C. J. Barrett, and A. Shishido, “Scanning wave photopolymerization enables dye-free alignment patterning of liquid crystals,” Sci. Adv. 3(11), e1701610 (2017).
[Crossref]

Nersisyan, S.

Nikolova, L.

Oh, C.

Oh, C. H.

D. M. Tong, E. Sjöqvist, L. C. Kwek, and C. H. Oh, “Kinematic approach to the mixed state geometric phase in nonunitary evolution,” Phys. Rev. Lett. 93(8), 1–4 (2004).
[Crossref]

Oka, K.

Ota, M.

Ozaki, M.

J. Kobashi, H. Yoshida, and M. Ozaki, “Planar optics with patterned chiral liquid crystals,” Nat. Photonics 10(6), 389–392 (2016).
[Crossref]

Pagliusi, P.

Pancharatnam, S.

S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. - Indian Acad. Sci., Sect. A 44(6), 398–417 (1956).
[Crossref]

Provenzano, C.

Roberts, D. E.

Shi, Y.

Shishido, A.

K. Hisano, M. Ota, M. Aizawa, N. Akamatsu, C. J. Barrett, and A. Shishido, “Single-step creation of polarization gratings by scanning wave photopolymerization with unpolarized light,” J. Opt. Soc. Am. B 36(5), D112–D118 (2019).
[Crossref]

K. Hisano, M. Aizawa, M. Ishizu, Y. Kurata, W. Nakano, N. Akamatsu, C. J. Barrett, and A. Shishido, “Scanning wave photopolymerization enables dye-free alignment patterning of liquid crystals,” Sci. Adv. 3(11), e1701610 (2017).
[Crossref]

A. Shishido, “Rewritable holograms based on azobenzene-containing liquid-crystalline polymers,” Polym. J. 42(7), 525–533 (2010).
[Crossref]

Sing Kwok, H.

T. Du, F. Fan, A. M. W. Tam, J. Sun, V. G. Chigrinov, and H. Sing Kwok, “Complex Nanoscale-Ordered Liquid Crystal Polymer Film for High Transmittance Holographic Polarizer,” Adv. Mater. 27(44), 7191–7195 (2015).
[Crossref]

Sjöqvist, E.

D. M. Tong, E. Sjöqvist, L. C. Kwek, and C. H. Oh, “Kinematic approach to the mixed state geometric phase in nonunitary evolution,” Phys. Rev. Lett. 93(8), 1–4 (2004).
[Crossref]

Song, F.

Srivastava, A.

Srivastava, A. K.

A. K. Srivastava, W. Hu, V. G. Chigrinov, A. D. Kiselev, and Y. Q. Lu, “Fast switchable grating based on orthogonal photo alignments of ferroelectric liquid crystals,” Appl. Phys. Lett. 101(3), 031112 (2012).
[Crossref]

Steeves, D. M.

Su, Y.

Sun, J.

Q. Guo, L. Xu, J. Sun, X. Yang, H. Liu, K. Yan, H. Zhao, V. G. Chigrinov, and H. S. Kwok, “Fast switching beam steering based on ferroelectric liquid crystal phase shutter and polarisation grating,” Liq. Cryst. 46(9), 1383–1388 (2019).
[Crossref]

T. Du, F. Fan, A. M. W. Tam, J. Sun, V. G. Chigrinov, and H. Sing Kwok, “Complex Nanoscale-Ordered Liquid Crystal Polymer Film for High Transmittance Holographic Polarizer,” Adv. Mater. 27(44), 7191–7195 (2015).
[Crossref]

Sun, J.-T.

Sun, X. W.

Tabiryan, N.

Tam, A. M. W.

A. M. W. Tam, F. Fan, T. Du, W. Hu, W. Zhang, C. Zhao, X. Wang, K. L. Ching, G. Li, H. Luo, V. G. Chigrinov, S. Wen, and H.-S. Kwok, “Bifocal Optical-Vortex Lens with Sorting of the Generated Nonseparable Spin-Orbital Angular-Momentum States,” Phys. Rev. Appl. 7(3), 034010 (2017).
[Crossref]

T. Du, F. Fan, A. M. W. Tam, J. Sun, V. G. Chigrinov, and H. Sing Kwok, “Complex Nanoscale-Ordered Liquid Crystal Polymer Film for High Transmittance Holographic Polarizer,” Adv. Mater. 27(44), 7191–7195 (2015).
[Crossref]

Tan, G.

Todorov, T.

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[Crossref]

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X. Xiang, J. Kim, and M. J. Escuti, “Bragg polarization gratings for wide angular bandwidth and high efficiency at steep deflection angles,” Sci. Rep. 8(1), 7202 (2018).
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Figures (6)

Fig. 1.
Fig. 1. Simulated results of the degeneration of efficiency and polarization of first order beams due to number of domains N of non-continuous LC PG.
Fig. 2.
Fig. 2. (a) Schematics of generation of continuous cycloidal pattern using birefringent prism aligned with QWP. (b) Fabrication of large area LC PG. (c) Top view and (d) Side view of LC PG’s molecules directors
Fig. 3.
Fig. 3. (a)Geometry of the exposure path. (b) Photograph of fabricated sample. (c) Experiment setup formed by cascaded 3D-printed holders.
Fig. 4.
Fig. 4. (a) Optical setup for measuring fabricated grating samples. Diffraction pattern of (b) polarization grating and (c)binary grating. Textures of (d) polarization grating and (c)binary grating observed under polarized microscope with black arrows showing polarizer and analyzer direction. The blue arrows/ellipses represent the polarization state of exposure beam, and the red bars represents the aligned LC director.
Fig. 5.
Fig. 5. The dependence of grating period on inclined angle of sample during exposure.
Fig. 6.
Fig. 6. (a) The PG efficiency of + 1st and −1st orders vs. thickness of LC layer. (b) Diffraction pattern of LCPG using blue green and red lasers with corresponding thickness.

Tables (1)

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Table 1. Summarization of Polarization and Efficiency of Diffractive Orders

Equations (5)

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δ = k y = 2 π λ Δ n tan α y
J e x p o s u r e = M Q W P J 1 = M Q W P M p r i s m J i n = M Q W P [ exp ( i δ 2 ) 0 0 exp ( i δ 2 ) ] [ cos 45 sin 45 ]
J 1 = 2 2 [ exp ( i δ 2 ) exp ( i δ 2 ) ]
J e x p o s u r e = R T ( 45 ) M Q W P R ( 45 ) J 1 = [ cos ( δ 2 + π 4 ) sin ( δ 2 + π 4 ) ]
Λ = λ Δ n tan α

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