Abstract

Liquid-crystal-based Pancharatnam–Berry phase optical elements (PBOEs), also known as diffractive wave plates (DWPs), geometric phase optics (GPO), or geometric phase holograms (GPHs), are functional planar structures with patterned orientation of anisotropy axis. Several scientifically interesting yet practically useful electro-optical effects, such as focusing, beam splitting, waveguide coupling, and wavelength filtering, have been realized with PBOEs. Because of the high degree of optical tunability, polarization selectivity, nearly 100% diffraction efficiency, and simple fabrication process, PBOEs have found widespread applications in emerging display systems, particularly virtual/augmented/mixed reality displays and head-up displays. In this review, we will describe the basic operation principles, present device fabrication procedures, discuss numerical modeling methods, and address applications of PBOEs in emerging display systems.

© 2019 Optical Society of America

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2018 (18)

O. Sakhno, Y. Gritsai, H. Sahm, and J. Stumpe, “Fabrication and performance of efficient thin circular polarization gratings with Bragg properties using bulk photo-alignment of a liquid crystalline polymer,” Appl. Phys. B 124, 52 (2018).
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K. J. Hornburg, X. Xiang, J. Kim, M. Kudenov, and M. Escuti, “Design and fabrication of an aspheric geometric-phase lens doublet,” Proc. SPIE 10735, 1073513 (2018).
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X. Xiang, M. Kudenov, M. Escuti, and K. J. Hornburg, “Optimization of aspheric geometric-phase lenses for improved field-of-view,” Proc. SPIE 10743, 1074305 (2018).
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J. Wang, C. McGinty, R. Reich, V. Finnemeyer, H. Clark, S. Berry, and P. Bos, “Process for a reactive monomer alignment layer for liquid crystals formed on an azodye sublayer,” Materials 11, 1195 (2018).
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E. Ouskova, R. Vergara, J. Hwang, D. Roberts, D. M. Steeves, B. R. Kimball, and N. Tabiryan, “Dual-function reversible/irreversible photoalignment material,” J. Mol. Liq. 267, 205–211 (2018).
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M. Jiang, H. Yu, X. Feng, Y. Guo, I. Chaganava, T. Turiv, O. D. Lavrentovich, and Q. Wei, “Liquid crystal Pancharatnam-Berry micro-optical elements for laser beam shaping,” Adv. Opt. Mater. 6, 1800961 (2018).
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C. Vieri, G. Lee, N. Balram, S. H. Jung, J. Y. Yang, S. Y. Yoon, and I. B. Kang, “An 18 megapixel 4.3″ 1443 ppi 120 Hz OLED display for wide field of view high acuity head mounted displays,” J. Soc. Inf. Disp. 26, 314–324 (2018).
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Y. Iwase, A. Tagawa, Y. Takeuchi, T. Watanabe, S. Horiuchi, Y. Asai, K. Yamamoto, T. Daitoh, and T. Matsuo, “A novel low-power gate driver architecture for large 8 K 120 Hz liquid crystal display employing IGZO technology,” J. Soc. Inf. Disp. 26, 304–313 (2018).
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D. Roberts, Z. Liao, J. Y. Hwang, S. R. Nersisyan, and N. Tabirian, “Chromatic aberration corrected switchable optical systems,” Proc. SPIE 10735, 107350Q (2018).
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Y. H. Lee, G. Tan, K. Yin, T. Zhan, and S. T. Wu, “Compact see-through near-eye display with depth adaption,” J. Soc. Inf. Disp. 26, 64–70 (2018).
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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, 10–15 (2018).
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T. Zhan, Y.-H. Lee, and S.-T. Wu, “High-resolution additive light field near-eye display by switchable Pancharatnam-Berry phase lenses,” Opt. Express 26, 4863–4872 (2018).
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C. M. Bigler, P.-A. Blanche, and K. Sarma, “Holographic waveguide heads-up display for longitudinal image magnification and pupil expansion,” Appl. Opt. 57, 2007–2013 (2018).
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G. Tan, Y.-H. Lee, T. Zhan, J. Yang, S. Liu, D. Zhao, and S.-T. Wu, “Foveated imaging for near-eye displays,” Opt. Express 26, 25076–25085 (2018).
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G. Tan, T. Zhan, Y.-H. Lee, J. Xiong, and S.-T. Wu, “Polarization-multiplexed multiplane display,” Opt. Lett. 43, 5651–5654 (2018).
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Y. Weng, Y. Zhang, J. Cui, A. Liu, Z. Shen, X. Li, and B. Wang, “Liquid-crystal-based polarization volume grating applied for full-color waveguide displays,” Opt. Lett. 43, 5773–5776(2018).
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T. Zhan, J. Xiong, Y.-H. Lee, and S.-T. Wu, “Polarization-independent Pancharatnam-Berry phase lens system,” Opt. Express 26, 35026–35033 (2018).
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L. De Sio, D. E. Roberts, Z. Liao, J. Hwang, N. Tabiryan, D. M. Steeves, and B. R. Kimball, “Beam shaping diffractive wave plates,” Appl. Opt. 57, A118–A121 (2018).
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2017 (14)

Z. Liu, Y. Pang, C. Pan, and Z. Huang, “Design of a uniform-illumination binocular waveguide display with diffraction gratings and freeform optics,” Opt. Express 25, 30720–30731 (2017).
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K. Gao, C. McGinty, H. Payson, S. Berry, J. Vornehm, V. Finnemeyer, B. Roberts, and P. Bos, “High-efficiency large-angle Pancharatnam phase deflector based on dual-twist design,” Opt. Express 25, 6283–6293 (2017).
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X. Xiang, J. Kim, R. Komanduri, and M. J. Escuti, “Nanoscale liquid crystal polymer Bragg polarization gratings,” Opt. Express 25, 19298–19308 (2017).
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F. Gou, F. Peng, Q. Ru, Y.-H. Lee, H. Chen, Z. He, T. Zhan, K. L. Vodopyanov, and S.-T. Wu, “Mid-wave infrared beam steering based on high-efficiency liquid crystal diffractive waveplates,” Opt. Express 25, 22404–22410 (2017).
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Y.-H. Lee, K. Yin, and S.-T. Wu, “Reflective polarization volume gratings for high efficiency waveguide-coupling augmented reality displays,” Opt. Express 25, 27008–27014 (2017).
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Y.-H. Lee, T. Zhan, and S.-T. Wu, “Enhancing the resolution of a near-eye display with a Pancharatnam-Berry phase deflector,” Opt. Lett. 42, 4732–4735 (2017).
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X. Xiang and M. J. Escuti, “Numerical analysis of Bragg regime polarization gratings by rigorous coupled-wave analysis,” Proc. SPIE 10127, 101270D (2017).
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J. Kim, K. J. Hornburg, M. J. Escuti, and N. Z. Warriner, “Chromatic-aberration correction in geometric-phase lenses, for red, green, and blue operation,” Proc. SPIE 10361, 1036113 (2017).
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E. Beltran, I. Gardiner, and M. Goebel, “Coatable optical films for advanced displays,” SID Symp. Dig. 48, 790–792 (2017).
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A. Jamali and P. Bos, “A thin film liquid crystal based compensator for the chromatic aberration of optical lenses,” Mol. Cryst. Liq. Cryst. 657, 46–50 (2017).
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S. V. Serak, D. E. Roberts, J. Y. Hwang, S. R. Nersisyan, N. V. Tabiryan, T. J. Bunning, D. M. Steeves, and B. R. Kimball, “Diffractive waveplate arrays,” J. Opt. Soc. Am. 34, B56–B63 (2017).
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Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in Pancharatnam-Berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3, 79–88 (2017).
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P. Chen, S. J. Ge, W. Duan, B. Y. Wei, G. X. Cui, W. Hu, and Y. Q. Lu, “Digitalized geometric phases for parallel optical spin and orbital angular momentum encoding,” ACS Photon. 4, 1333–1338 (2017).
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J. Wang, C. McGinty, J. West, D. Bryant, V. Finnemeyer, R. Reich, S. Berry, H. Clark, O. Yaroshchuk, and P. Bos, “Effects of humidity and surface on photoalignment of brilliant yellow,” Liq. Cryst. 44, 863–872 (2017).
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2016 (14)

J. Kobashi, H. Yoshida, and M. Ozaki, “Planar optics with patterned chiral liquid crystals,” Nat. Photonics 10, 389–392 (2016).
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M. C. Tseng, O. Yaroshchuk, T. Bidna, A. K. Srivastava, V. Chigrinov, and H. S. Kwok, “Strengthening of liquid crystal photoalignment on azo dye films: passivation by reactive mesogens,” RSC Adv. 6, 48181–48188 (2016).
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W. Ji, C. H. Lee, P. Chen, W. Hu, Y. Ming, L. Zhang, T. H. Lin, V. Chigrinov, and Y. Q. Lu, “Meta-q-plate for complex beam shaping,” Sci. Rep. 6, 25528 (2016).
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P. Chen, Y. Q. Lu, and W. Hu, “Beam shaping via photopatterned liquid crystals,” Liq. Cryst. 43, 2051–2061 (2016).
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S. Yang, H. Lee, and J.-H. Lee, “Negative dispersion retarder with a wide viewing angle made by stacking reactive mesogen on a polymethylmethacrylate film,” Opt. Eng. 55, 027106 (2016).
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S. Lee, C. Jang, S. Moon, J. Cho, and B. Lee, “Additive light field displays: realization of augmented reality with holographic optical elements,” ACM Trans. Graph. 35, 60 (2016).
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X. Xiang and M. J. Escuti, “Numerical modeling of polarization gratings by rigorous coupled wave analysis,” Proc. SPIE 9769, 976918 (2016).
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W. Duan, P. Chen, B.-Y. Wei, S.-J. Ge, X. Liang, W. Hu, and Y.-Q. Lu, “Fast-response and high-efficiency optical switch based on dual-frequency liquid crystal polarization grating,” Opt. Mater. Express 6, 597–602 (2016).
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K. Gao, H.-H. Cheng, A. Bhowmik, C. McGinty, and P. Bos, “Nonmechanical zoom lens based on the Pancharatnam phase effect,” Appl. Opt. 55, 1145–1150 (2016).
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Y. Qin and H. Hua, “Continuously zoom imaging probe for the multi-resolution foveated laparoscope,” Biomed. Opt. Express 7, 1175–1182 (2016).
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N. V. Tabiryan, S. V. Serak, S. R. Nersisyan, D. E. Roberts, B. Y. Zeldovich, D. M. Steeves, and B. R. Kimball, “Broadband waveplate lenses,” Opt. Express 24, 7091–7102 (2016).
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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, 17746–17759 (2016).
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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, 18297–18306 (2016).
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C.-K. Lee, S. Moon, S. Lee, D. Yoo, J.-Y. Hong, and B. Lee, “Compact three-dimensional head-mounted display system with Savart plate,” Opt. Express 24, 19531–19544 (2016).
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2015 (8)

Z. Luo, F. Peng, H. Chen, M. Hu, J. Li, Z. An, and S.-T. Wu, “Fast-response liquid crystals for high image quality wearable displays,” Opt. Mater. Express 5, 603–610 (2015).
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P. Chen, B. Wei, W. Ji, S. Ge, W. Hu, F. Xu, V. Chigrinov, and Y. Lu, “Arbitrary and reconfigurable optical vortex generation: a high-efficiency technique using director-varying liquid crystal fork gratings,” Photon. Res. 3, 133–139 (2015).
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R. Zhu, Z. Luo, H. Chen, Y. Dong, and S.-T. Wu, “Realizing Rec 2020 color gamut with quantum dot displays,” Opt. Express 23, 23680–23693 (2015).
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N. V. Tabiryan, S. V. Serak, D. E. Roberts, D. M. Steeves, and B. R. Kimball, “Thin waveplate lenses of switchable focal length—new generation in optics,” Opt. Express 23, 25783–25794 (2015).
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K. Gao, H.-H. Cheng, A. K. Bhowmik, and P. J. Bos, “Thin-film Pancharatnam lens with low f-number and high quality,” Opt. Express 23, 26086–26094 (2015).
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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, 958–964 (2015).
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H. S. Park, R. Hoskinson, H. Abdollahi, and B. Stoeber, “Compact near-eye display system using a superlens-based microlens array magnifier,” Opt. Express 23, 30618–30632 (2015).
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F.-C. Huang, D. Luebke, and G. Wetzstein, “The light field stereoscope,” ACM Trans. Graph. 34, 60 (2015).
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2014 (1)

2013 (7)

R. K. Komanduri, K. F. Lawler, and M. J. Escuti, “Multi-twist retarders: broadband retardation control using self-aligning reactive liquid crystal layers,” Opt. Express 21, 404–420 (2013).
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S. R. Nersisyan, N. V. Tabiryan, D. Mawet, and E. Serabyn, “Improving vector vortex waveplates for high-contrast coronagraphy,” Opt. Express 21, 8205–8213 (2013).
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D. Lanman and D. Luebke, “Near-eye light field displays,” ACM Trans. Graph. 32, 1–10 (2013).
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J. Geng, “Three-dimensional display technologies,” Adv. Opt. Photonics 5, 456–535 (2013).
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B. Lee, “Three-dimensional displays, past and present,” Phys. Today 66(4), 36–41 (2013).
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M. Homan, “The use of optical waveguides in head up display (HUD) applications,” Proc. SPIE 8736, 87360E (2013).
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T. Seki, S. Nagano, and M. Hara, “Versatility of photoalignment techniques: from nematics to a wide range of functional materials,” Polymer 54, 6053–6072 (2013).
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2012 (7)

J. Kim, R. K. Komanduri, and M. J. Escuti, “A compact holographic recording setup for tuning pitch using polarizing prisms,” Proc. SPIE 8281, 82810R (2012).
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M. N. Miskiewicz, J. Kim, Y. Li, R. K. Komanduri, and M. J. Escuti, “Progress on large-area polarization grating fabrication,” Proc. SPIE 8395, 83950G (2012).
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H. Ono, T. Wada, and N. Kawatsuki, “Polarization imaging screen using vector gratings fabricated by photocrosslinkable polymer liquid crystals,” Jpn. J. Appl. Phys. 51, 082501 (2012).
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M. N. Miskiewicz, P. T. Bowen, and M. J. Escuti, “Efficient 3D FDTD analysis of arbitrary birefringent and dichroic media with obliquely incident sources,” Proc. SPIE 8255, 82550W (2012).
[Crossref]

R. C. Rumpf, “Simple implementation of arbitrarily shaped total-field/scattered-field regions in finite-difference frequency-domain,” Prog. Electromagn. Res. B 36, 221–248 (2012).
[Crossref]

J. Francés, S. Bleda, M. L. Álvarez López, F. J. Martínez Guardiola, A. Márquez, C. Neipp, and A. Beléndez, “Analysis of periodic anisotropic media by means of split-field FDTD method and GPU computing,” Proc. SPIE 8498, 84980K (2012).
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H. Wu, W. Hu, H. Hu, X. Lin, G. Zhu, J.-W. Choi, V. Chigrinov, and Y. Lu, “Arbitrary photo-patterning in liquid crystal alignments using DMD based lithography system,” Opt. Express 20, 16684–16689 (2012).
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2011 (2)

2010 (1)

2009 (6)

D. Mawet, E. Serabyn, K. Liewer, C. Hanot, S. McEldowney, D. Shemo, and N. O’Brien, “Optical vectorial vortex coronagraphs using liquid crystal polymers: theory, manufacturing and laboratory demonstration,” Opt. Express 17, 1902–1918 (2009).
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M. Fratz, S. Sinzinger, and D. Giel, “Design and fabrication of polarization-holographic elements for laser beam shaping,” Appl. Opt. 48, 2669–2677 (2009).
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S. Nersisyan, N. Tabiryan, D. M. Steeves, and B. R. Kimball, “Fabrication of liquid crystal polymer axial waveplates for UV-IR wavelengths,” Opt. Express 17, 11926–11934 (2009).
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H. Xianyu, S. T. Wu, and C. L. Lin, “Dual frequency liquid crystals: a review,” Liq. Cryst. 36, 717–726 (2009).
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P. Äyräs, P. Saarikko, and T. Levola, “Exit pupil expander with a large field of view based on diffractive optics,” J. Soc. Inf. Disp. 17, 659–664 (2009).
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A. Emoto, T. Matsumoto, A. Yamashita, T. Shioda, H. Ono, and N. Kawatsuki, “Large birefringence and polarization holographic gratings formed in photocross-linkable polymer liquid crystals comprising bistolane mesogenic side groups,” J. Appl. Phys. 106, 073505 (2009).
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2008 (6)

R. K. Komanduri, C. Oh, M. J. Escuti, and D. J. Kekas, “18:3: Late-News Paper: Polarization independent liquid crystal microdisplays,” SID Symp. Dig. Tech. Pap. 39, 236–239 (2008).
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P. Saarikko, “Diffractive exit-pupil expander with a large field of view,” Proc. SPIE 7001, 700105 (2008).
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D. M. Hoffman, A. R. Girshick, and M. S. Banks, “Vergence–accommodation conflicts hinder visual performance and cause visual fatigue,” J. Vis. 8(3):33 (2008).
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S. C. McEldowney, D. M. Shemo, R. A. Chipman, and P. K. Smith, “Creating vortex retarders using photoaligned liquid crystal polymers,” Opt. Lett. 33, 134–136 (2008).
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H. Hua and S. Liu, “Dual-sensor foveated imaging system,” Appl. Opt. 47, 317–327 (2008).
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C. Oh and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33, 2287–2289 (2008).
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2007 (2)

C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
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C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
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2006 (2)

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (2006).
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S. Boonruang, A. Greenwell, and M. G. Moharam, “Multiline two-dimensional guided-mode resonant filters,” Appl. Opt. 45, 5740–5747 (2006).
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2005 (3)

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
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J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1, 51–61 (2005).
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S. J. Watt, K. Akeley, M. O. Ernst, and M. S. Banks, “Focus cues affect perceived depth,” J. Vis. 5(10): 7 (2005).
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2004 (1)

2003 (4)

Q. Hong, T. X. Wu, and S. T. Wu, “Optical wave propagation in a cholesteric liquid crystal using the finite element method,” Liq. Cryst. 30, 367–375 (2003).
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H. Ono, A. Emoto, F. Takahashi, N. Kawatsuki, and T. Hasegawa, “Highly stable polarization gratings in photocrosslinkable polymer liquid crystals,” J. Appl. Phys. 94, 1298–1303 (2003).
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E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328–330 (2003).
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V. Chigrinov, A. Muravski, H. S. Kwok, H. Takada, H. Akiyama, and H. Takatsu, “Anchoring properties of photoaligned azo-dye materials,” Phys. Rev. E 68, 061702 (2003).
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2002 (1)

2001 (2)

R. Rosenhauer, T. Fischer, S. Czapla, J. Stumpe, A. Viñuales, M. Pinol, and J. L. Serrano, “Photo-induced alignment of LC polymers by photoorientation and thermotropic self-organization,” Mol. Cryst. Liq. Cryst. Sci. Technol. Sect. A 364, 295–304 (2001).
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J. L. Young and R. O. Nelson, “A summary and systematic analysis of FDTD algorithms for linearly dispersive media,” IEEE Antennas Propag. Mag. 43(1), 61–126 (2001).
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2000 (3)

S. J. Bryant, C. R. Nuttelman, and K. S. Anseth, “Cytocompatibility of UV and visible light photoinitiating systems on cultured NIH/3T3 fibroblasts in vitro,” J. Biomater. Sci. Polym. Ed. 11, 439–457 (2000).

K. Ichimura, “Photoalignment of liquid-crystal systems,” Chem. Rev. 100, 1847–1874 (2000).
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J. Tervo and J. Turunen, “Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings,” Opt. Lett. 25, 785–786 (2000).
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1998 (1)

1996 (2)

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
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W. Sun, K. Liu, and C. A. Balanis, “Analysis of singly and doubly periodic absorbers by frequency-domain finite-difference method,” IEEE Trans. Antennas Propag. 44, 798–805 (1996).
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1995 (1)

1994 (1)

1993 (1)

J. Schneider and S. Hudson, “The finite-difference time-domain method applied to anisotropic material,” IEEE Trans. Antennas Propag. 41, 994–999 (1993).
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Figures (18)

Fig. 1.
Fig. 1. Schematic distribution of LC anisotropy axis orientation in (a) a PB deflector and (b) a PB lens. The corresponding phase change of the (c) PBD and (d) PBL.
Fig. 2.
Fig. 2. Illustration of polarization dependency of PBOEs: (a) PBD diffracts RCP light to + 1 order and LCP light to 1 order; (b) PBL serves as a diverging lens for input LCP light but a converging one for input RCP light.
Fig. 3.
Fig. 3. Schematic illustration of PBOEs made of LCs sandwiched between transparent electrodes (upper) before and (lower) after dynamic switching.
Fig. 4.
Fig. 4. Schematic presentation of the anisotropy axis orientation: (a) Bragg PBD, also referred as polarization volume grating (PVG) or Bragg polarization grating; (b) reflective PBL based on cholesteric liquid crystal (CLC).
Fig. 5.
Fig. 5. Schematic illustration of fabrication procedures of PBOEs. Surface alignment for (a) LC polymer film PBOEs and (b) electrically responsive LC PBOEs. (c) Bulk alignment using a PCLCP film.
Fig. 6.
Fig. 6. Schematic illustration of polarized exposure pattern generation optical setups based on (a) two beam, (b) Sagnac, (c) Michelson, and (d) Mach–Zehnder interferometry. (NPBS, non-polarizing beam splitter; M, mirror; QWP, quarter-wave plate; S, substrate; HWP, half-wave plate; TL, template lens).
Fig. 7.
Fig. 7. Schematic illustration of optical setups for polarized exposure pattern generation, including (a) digital polarization holography enabled by a spatial light modulator, (b) DMD-based digital lithography and direct writing method with (c) 1D and (d) 2D spatial scanning. (P, polarizer; QWP, quarter-wave plate; SLM, spatial light modulator; L, lens; S, substrate; DMD, digital micromirror device; NPBS, non-polarizing beam splitter; RP, rotatable polarizer; CCD, charge-coupled device; PR, motorized polarization rotator; M, mirror; CL, cylindrical lens; MS, motorized motion stage).
Fig. 8.
Fig. 8. (a) Schematic illustration of the optical system for pixel density enhancement with a PBD. (b) The generation of a half-pitch pixel grid by overlapping the original (orange) and shifted (green) pixel grid. (DP, display panel; L, magnifying lens.)
Fig. 9.
Fig. 9. Observed images from the near-eye display system with (lower) and without (upper) pixel density enhancement enabled by a PBD.
Fig. 10.
Fig. 10. (a) Schematic diagram of a foveated near-eye display system. (DP, display panel; NPBS, non-polarizing beam splitter; CL, concave lens; QWP, quarter-wave plate; M, mirror; L, lens.) (b) Photography of foveated images from the near-eye display system before (upper) and after (lower) image shifting using a PBD.
Fig. 11.
Fig. 11. (a) Schematic diagram of a polarization-multiplexed two-plane near-eye display system. (DP, display panel; VP, virtual plane; PML, polarization management layer; QWP, quarter-wave plate; L, lens.) (b) Schematic illustration of polarization change in the polarization multiplexed system.
Fig. 12.
Fig. 12. Schematic illustrations of different dispersion scenarios: (a) positive chromatic dispersion in a refractive lens, (b) negative dispersion in a PBL, and (c) zero dispersion in a compensated hybrid optical system.
Fig. 13.
Fig. 13. Simulated first-order diffraction efficiency of r -PBDs ( Λ x = 678 nm , Λ z = 182 nm ) with different birefringence.
Fig. 14.
Fig. 14. Schematic diagram of the input coupling regime employing (a)  r -PBD and (b) Bragg t -PBD in see-through display systems based on the waveguide structure.
Fig. 15.
Fig. 15. Schematic illustration of exit pupil expansion in the waveguide-based display systems using (a) a gradient-efficiency output grating coupler and (b) a uniform-efficiency output grating coupler with a PML.
Fig. 16.
Fig. 16. (a) Simulated first-order diffraction efficiency of PBOEs made of LC materials with different resonance wavelengths, where the axial thicknesses are optimized for the half-wave condition at 532 nm. (b) The simulated diffraction efficiency of PBOEs made of negative dispersion LC materials, wherein the birefringence data is from [105].
Fig. 17.
Fig. 17. (a) Schematic illustration of the LC orientation in the dual-twist and the sandwich structure. (b) The simulated first-order diffraction efficiency of PBOEs made of two-layer dual-twist and three-layer sandwich structure, optimized for the highest average efficiency at three RGB primary colors (630, 532, and 467 nm) in Rec. 2020.
Fig. 18.
Fig. 18. Schematic diagram of the 3-PBL and 2-HWP system with corrected chromatic aberration for the RGB primary colors.

Tables (2)

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Table 1. Driving Method of PBDs and PBLs

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Table 2. Physical Properties of LCs and Corresponding Response Time of PBD Samples at T = 22 ° C and λ = 633 nm

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

J ± = 1 2 [ 1 ± j ] ,
J ± = R ( ψ ) W ( π ) R ( ψ ) J ± = j e ± 2 j ψ J ,
η = sin 2 ( π Δ n d λ ) ,
Δ n = G λ 2 λ * 2 λ 2 λ * 2 ,
Δ n eff = α G a λ 2 λ a * 2 λ 2 λ a * 2 ( 1 α ) G b λ 2 λ b * 2 λ 2 λ b * 2 ,
λ r K r = λ g K g = λ b K b ,
τ 0 = γ 1 K 11 d 2 π 2 ,
τ on = τ 0 ( V / V th ) 2 1 .

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