Abstract

We report a reflective chirped polarization volume grating (CPVG) with a dramatically wider angular bandwidth and significantly higher first-order diffraction efficiency than the holographic volume grating and surface relief grating for large field-of-view (FOV) augmented reality (AR) displays. By introducing gradient pitch structure along the beam propagation direction, the angular bandwidth is extended from 18° to 54° while keeping over 80% diffraction efficiency. We also prepare a two-layer reflective PVG and compare its performance with the chirped structure. Based on the simulation and experimental results, CPVG is a strong contender for large FOV AR displays.

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

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  4. T. Rasmussen, “Overview of high-efficiency transmission gratings for molecular spectroscopy,” Spectroscopy (Springf.) 29(4), 32–39 (2014).
  5. F. Bruder, T. Fäcke, R. Hagen, D. Hönel, E. Orselli, C. Rewitz, T. Rölle, and G. Walze, “Diffractive optics with high Bragg selectivity: volume holographic optical elements in Bayfol® HX photopolymer film,” Proc. SPIE 9626, 96260T (2015).
    [Crossref]
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    [Crossref]
  7. M. J. Escuti, P. Kossyrev, G. P. Crawford, T. G. Fiske, J. Colegrove, and L. D. Silverstein, “Expanded viewing-angle reflection from diffuse holographic-polymer dispersed liquid crystal films,” Appl. Phys. Lett. 77(26), 4262–4264 (2000).
    [Crossref]
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    [Crossref]
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    [Crossref]
  16. D. J. Broer, J. Lub, and G. N. Mol, “Wide-band reflective polarizers from cholesteric polymer networks with a pitch gradient,” Nature 378(6556), 467–469 (1995).
    [Crossref]
  17. D. Katsis, D. U. Kim, H. P. Chen, L. J. Rothberg, S. H. Chen, and T. Tsutsui, “Circularly polarized photoluminescence from gradient-pitch chiral-nematic films,” Chem. Mater. 13(2), 643–647 (2001).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2019 (2)

2018 (2)

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(2), 64–70 (2018).
[Crossref]

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]

2017 (3)

J. Kobashi, Y. Mohri, H. Yoshida, and M. Ozaki, “Circularly-polarized, large-angle reflective deflectors based on periodically patterned cholesteric liquid crystals,” Opt. Data Process. Storage 3(1), 61–66 (2017).
[Crossref]

Y. H. Lee, K. Yin, and S. T. Wu, “Reflective polarization volume gratings for high efficiency waveguide coupling augmented reality displays,” Opt. Express 25(22), 27008–27014 (2017).
[Crossref]

B. C. Kress and W. J. Cummings, “Towards the ultimate mixed reality experience: HoloLens display architecture choices,” Dig. Tech. Pap. - Soc. Inf. Disp. Int. Symp. 48(1), 127–131 (2017).
[Crossref]

2016 (2)

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

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]

2015 (2)

F. Bruder, T. Fäcke, R. Hagen, D. Hönel, E. Orselli, C. Rewitz, T. Rölle, and G. Walze, “Diffractive optics with high Bragg selectivity: volume holographic optical elements in Bayfol® HX photopolymer film,” Proc. SPIE 9626, 96260T (2015).
[Crossref]

N. Zhang, J. Liu, J. Han, X. Li, F. Yang, X. Wang, B. Hu, and Y. Wang, “Improved holographic waveguide display system,” Appl. Opt. 54(12), 3645–3649 (2015).
[Crossref]

2014 (1)

T. Rasmussen, “Overview of high-efficiency transmission gratings for molecular spectroscopy,” Spectroscopy (Springf.) 29(4), 32–39 (2014).

2011 (1)

2010 (1)

2009 (1)

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

2003 (1)

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(3), 367–375 (2003).
[Crossref]

2001 (2)

I. Kasai, Y. Tanijiri, E. Takeshi, and U. Hiroaki, “A practical see-through head mounted display using a holographic optical element,” Opt. Rev. 8(4), 241–244 (2001).
[Crossref]

D. Katsis, D. U. Kim, H. P. Chen, L. J. Rothberg, S. H. Chen, and T. Tsutsui, “Circularly polarized photoluminescence from gradient-pitch chiral-nematic films,” Chem. Mater. 13(2), 643–647 (2001).
[Crossref]

2000 (1)

M. J. Escuti, P. Kossyrev, G. P. Crawford, T. G. Fiske, J. Colegrove, and L. D. Silverstein, “Expanded viewing-angle reflection from diffuse holographic-polymer dispersed liquid crystal films,” Appl. Phys. Lett. 77(26), 4262–4264 (2000).
[Crossref]

1995 (1)

D. J. Broer, J. Lub, and G. N. Mol, “Wide-band reflective polarizers from cholesteric polymer networks with a pitch gradient,” Nature 378(6556), 467–469 (1995).
[Crossref]

Aiki, K.

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

Akutsu, K.

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

Bai, B.

Bastiaansen, C. W.

Broer, D. J.

D. J. Broer, J. Lub, and G. N. Mol, “Wide-band reflective polarizers from cholesteric polymer networks with a pitch gradient,” Nature 378(6556), 467–469 (1995).
[Crossref]

Bruder, F.

F. Bruder, T. Fäcke, R. Hagen, D. Hönel, E. Orselli, C. Rewitz, T. Rölle, and G. Walze, “Diffractive optics with high Bragg selectivity: volume holographic optical elements in Bayfol® HX photopolymer film,” Proc. SPIE 9626, 96260T (2015).
[Crossref]

Chen, H. P.

D. Katsis, D. U. Kim, H. P. Chen, L. J. Rothberg, S. H. Chen, and T. Tsutsui, “Circularly polarized photoluminescence from gradient-pitch chiral-nematic films,” Chem. Mater. 13(2), 643–647 (2001).
[Crossref]

Chen, S. H.

D. Katsis, D. U. Kim, H. P. Chen, L. J. Rothberg, S. H. Chen, and T. Tsutsui, “Circularly polarized photoluminescence from gradient-pitch chiral-nematic films,” Chem. Mater. 13(2), 643–647 (2001).
[Crossref]

Colegrove, J.

M. J. Escuti, P. Kossyrev, G. P. Crawford, T. G. Fiske, J. Colegrove, and L. D. Silverstein, “Expanded viewing-angle reflection from diffuse holographic-polymer dispersed liquid crystal films,” Appl. Phys. Lett. 77(26), 4262–4264 (2000).
[Crossref]

Crawford, G. P.

M. J. Escuti, P. Kossyrev, G. P. Crawford, T. G. Fiske, J. Colegrove, and L. D. Silverstein, “Expanded viewing-angle reflection from diffuse holographic-polymer dispersed liquid crystal films,” Appl. Phys. Lett. 77(26), 4262–4264 (2000).
[Crossref]

Cummings, W. J.

B. C. Kress and W. J. Cummings, “Towards the ultimate mixed reality experience: HoloLens display architecture choices,” Dig. Tech. Pap. - Soc. Inf. Disp. Int. Symp. 48(1), 127–131 (2017).
[Crossref]

de Boer, D. K.

de Jong, T. M.

Escuti, M. 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]

M. J. Escuti, P. Kossyrev, G. P. Crawford, T. G. Fiske, J. Colegrove, and L. D. Silverstein, “Expanded viewing-angle reflection from diffuse holographic-polymer dispersed liquid crystal films,” Appl. Phys. Lett. 77(26), 4262–4264 (2000).
[Crossref]

Fäcke, T.

F. Bruder, T. Fäcke, R. Hagen, D. Hönel, E. Orselli, C. Rewitz, T. Rölle, and G. Walze, “Diffractive optics with high Bragg selectivity: volume holographic optical elements in Bayfol® HX photopolymer film,” Proc. SPIE 9626, 96260T (2015).
[Crossref]

Fiske, T. G.

M. J. Escuti, P. Kossyrev, G. P. Crawford, T. G. Fiske, J. Colegrove, and L. D. Silverstein, “Expanded viewing-angle reflection from diffuse holographic-polymer dispersed liquid crystal films,” Appl. Phys. Lett. 77(26), 4262–4264 (2000).
[Crossref]

Hagen, R.

F. Bruder, T. Fäcke, R. Hagen, D. Hönel, E. Orselli, C. Rewitz, T. Rölle, and G. Walze, “Diffractive optics with high Bragg selectivity: volume holographic optical elements in Bayfol® HX photopolymer film,” Proc. SPIE 9626, 96260T (2015).
[Crossref]

Han, J.

He, Z.

Hiroaki, U.

I. Kasai, Y. Tanijiri, E. Takeshi, and U. Hiroaki, “A practical see-through head mounted display using a holographic optical element,” Opt. Rev. 8(4), 241–244 (2001).
[Crossref]

Hönel, D.

F. Bruder, T. Fäcke, R. Hagen, D. Hönel, E. Orselli, C. Rewitz, T. Rölle, and G. Walze, “Diffractive optics with high Bragg selectivity: volume holographic optical elements in Bayfol® HX photopolymer film,” Proc. SPIE 9626, 96260T (2015).
[Crossref]

Hong, Q.

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(3), 367–375 (2003).
[Crossref]

Hu, B.

Kasai, I.

I. Kasai, Y. Tanijiri, E. Takeshi, and U. Hiroaki, “A practical see-through head mounted display using a holographic optical element,” Opt. Rev. 8(4), 241–244 (2001).
[Crossref]

Katsis, D.

D. Katsis, D. U. Kim, H. P. Chen, L. J. Rothberg, S. H. Chen, and T. Tsutsui, “Circularly polarized photoluminescence from gradient-pitch chiral-nematic films,” Chem. Mater. 13(2), 643–647 (2001).
[Crossref]

Kim, D. U.

D. Katsis, D. U. Kim, H. P. Chen, L. J. Rothberg, S. H. Chen, and T. Tsutsui, “Circularly polarized photoluminescence from gradient-pitch chiral-nematic films,” Chem. Mater. 13(2), 643–647 (2001).
[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]

Kobashi, J.

J. Kobashi, Y. Mohri, H. Yoshida, and M. Ozaki, “Circularly-polarized, large-angle reflective deflectors based on periodically patterned cholesteric liquid crystals,” Opt. Data Process. Storage 3(1), 61–66 (2017).
[Crossref]

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

Kossyrev, P.

M. J. Escuti, P. Kossyrev, G. P. Crawford, T. G. Fiske, J. Colegrove, and L. D. Silverstein, “Expanded viewing-angle reflection from diffuse holographic-polymer dispersed liquid crystal films,” Appl. Phys. Lett. 77(26), 4262–4264 (2000).
[Crossref]

Kress, B. C.

B. C. Kress and W. J. Cummings, “Towards the ultimate mixed reality experience: HoloLens display architecture choices,” Dig. Tech. Pap. - Soc. Inf. Disp. Int. Symp. 48(1), 127–131 (2017).
[Crossref]

Kuittinen, M.

Kuwahara, M.

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

Laukkanen, J.

Lee, Y. H.

Li, X.

Liu, J.

Lub, J.

D. J. Broer, J. Lub, and G. N. Mol, “Wide-band reflective polarizers from cholesteric polymer networks with a pitch gradient,” Nature 378(6556), 467–469 (1995).
[Crossref]

Matsumura, I.

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

Mohri, Y.

J. Kobashi, Y. Mohri, H. Yoshida, and M. Ozaki, “Circularly-polarized, large-angle reflective deflectors based on periodically patterned cholesteric liquid crystals,” Opt. Data Process. Storage 3(1), 61–66 (2017).
[Crossref]

Mol, G. N.

D. J. Broer, J. Lub, and G. N. Mol, “Wide-band reflective polarizers from cholesteric polymer networks with a pitch gradient,” Nature 378(6556), 467–469 (1995).
[Crossref]

Mukawa, H.

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

Nakano, S.

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

Orselli, E.

F. Bruder, T. Fäcke, R. Hagen, D. Hönel, E. Orselli, C. Rewitz, T. Rölle, and G. Walze, “Diffractive optics with high Bragg selectivity: volume holographic optical elements in Bayfol® HX photopolymer film,” Proc. SPIE 9626, 96260T (2015).
[Crossref]

Ozaki, M.

J. Kobashi, Y. Mohri, H. Yoshida, and M. Ozaki, “Circularly-polarized, large-angle reflective deflectors based on periodically patterned cholesteric liquid crystals,” Opt. Data Process. Storage 3(1), 61–66 (2017).
[Crossref]

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

Rasmussen, T.

T. Rasmussen, “Overview of high-efficiency transmission gratings for molecular spectroscopy,” Spectroscopy (Springf.) 29(4), 32–39 (2014).

Rewitz, C.

F. Bruder, T. Fäcke, R. Hagen, D. Hönel, E. Orselli, C. Rewitz, T. Rölle, and G. Walze, “Diffractive optics with high Bragg selectivity: volume holographic optical elements in Bayfol® HX photopolymer film,” Proc. SPIE 9626, 96260T (2015).
[Crossref]

Rölle, T.

F. Bruder, T. Fäcke, R. Hagen, D. Hönel, E. Orselli, C. Rewitz, T. Rölle, and G. Walze, “Diffractive optics with high Bragg selectivity: volume holographic optical elements in Bayfol® HX photopolymer film,” Proc. SPIE 9626, 96260T (2015).
[Crossref]

Rothberg, L. J.

D. Katsis, D. U. Kim, H. P. Chen, L. J. Rothberg, S. H. Chen, and T. Tsutsui, “Circularly polarized photoluminescence from gradient-pitch chiral-nematic films,” Chem. Mater. 13(2), 643–647 (2001).
[Crossref]

Siitonen, S.

Silverstein, L. D.

M. J. Escuti, P. Kossyrev, G. P. Crawford, T. G. Fiske, J. Colegrove, and L. D. Silverstein, “Expanded viewing-angle reflection from diffuse holographic-polymer dispersed liquid crystal films,” Appl. Phys. Lett. 77(26), 4262–4264 (2000).
[Crossref]

Takeshi, E.

I. Kasai, Y. Tanijiri, E. Takeshi, and U. Hiroaki, “A practical see-through head mounted display using a holographic optical element,” Opt. Rev. 8(4), 241–244 (2001).
[Crossref]

Tan, G.

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(2), 64–70 (2018).
[Crossref]

Tanijiri, Y.

I. Kasai, Y. Tanijiri, E. Takeshi, and U. Hiroaki, “A practical see-through head mounted display using a holographic optical element,” Opt. Rev. 8(4), 241–244 (2001).
[Crossref]

Tsutsui, T.

D. Katsis, D. U. Kim, H. P. Chen, L. J. Rothberg, S. H. Chen, and T. Tsutsui, “Circularly polarized photoluminescence from gradient-pitch chiral-nematic films,” Chem. Mater. 13(2), 643–647 (2001).
[Crossref]

Walze, G.

F. Bruder, T. Fäcke, R. Hagen, D. Hönel, E. Orselli, C. Rewitz, T. Rölle, and G. Walze, “Diffractive optics with high Bragg selectivity: volume holographic optical elements in Bayfol® HX photopolymer film,” Proc. SPIE 9626, 96260T (2015).
[Crossref]

Wang, X.

Wang, Y.

Weng, Y.

Wu, S. T

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(2), 64–70 (2018).
[Crossref]

Wu, S. T.

Wu, T. X.

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(3), 367–375 (2003).
[Crossref]

Xiang, X.

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]

Xu, D.

Yang, F.

Yin, K.

Yoshida, H.

J. Kobashi, Y. Mohri, H. Yoshida, and M. Ozaki, “Circularly-polarized, large-angle reflective deflectors based on periodically patterned cholesteric liquid crystals,” Opt. Data Process. Storage 3(1), 61–66 (2017).
[Crossref]

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

Yoshida, T.

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

Zhan, T.

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(2), 64–70 (2018).
[Crossref]

Zhang, N.

Zhang, Y.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

M. J. Escuti, P. Kossyrev, G. P. Crawford, T. G. Fiske, J. Colegrove, and L. D. Silverstein, “Expanded viewing-angle reflection from diffuse holographic-polymer dispersed liquid crystal films,” Appl. Phys. Lett. 77(26), 4262–4264 (2000).
[Crossref]

Chem. Mater. (1)

D. Katsis, D. U. Kim, H. P. Chen, L. J. Rothberg, S. H. Chen, and T. Tsutsui, “Circularly polarized photoluminescence from gradient-pitch chiral-nematic films,” Chem. Mater. 13(2), 643–647 (2001).
[Crossref]

Dig. Tech. Pap. - Soc. Inf. Disp. Int. Symp. (1)

B. C. Kress and W. J. Cummings, “Towards the ultimate mixed reality experience: HoloLens display architecture choices,” Dig. Tech. Pap. - Soc. Inf. Disp. Int. Symp. 48(1), 127–131 (2017).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Soc. Inf. Disp. (2)

H. Mukawa, K. Akutsu, I. Matsumura, S. Nakano, T. Yoshida, M. Kuwahara, and K. Aiki, “A full-color eyewear display using planar waveguides with reflection volume holograms,” J. Soc. Inf. Disp. 17(3), 185–193 (2009).
[Crossref]

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(2), 64–70 (2018).
[Crossref]

Liq. Cryst. (1)

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(3), 367–375 (2003).
[Crossref]

Nat. Photonics (1)

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

Nature (1)

D. J. Broer, J. Lub, and G. N. Mol, “Wide-band reflective polarizers from cholesteric polymer networks with a pitch gradient,” Nature 378(6556), 467–469 (1995).
[Crossref]

Opt. Data Process. Storage (1)

J. Kobashi, Y. Mohri, H. Yoshida, and M. Ozaki, “Circularly-polarized, large-angle reflective deflectors based on periodically patterned cholesteric liquid crystals,” Opt. Data Process. Storage 3(1), 61–66 (2017).
[Crossref]

Opt. Express (4)

Opt. Rev. (1)

I. Kasai, Y. Tanijiri, E. Takeshi, and U. Hiroaki, “A practical see-through head mounted display using a holographic optical element,” Opt. Rev. 8(4), 241–244 (2001).
[Crossref]

Proc. SPIE (1)

F. Bruder, T. Fäcke, R. Hagen, D. Hönel, E. Orselli, C. Rewitz, T. Rölle, and G. Walze, “Diffractive optics with high Bragg selectivity: volume holographic optical elements in Bayfol® HX photopolymer film,” Proc. SPIE 9626, 96260T (2015).
[Crossref]

Sci. Rep. (1)

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]

Spectroscopy (Springf.) (1)

T. Rasmussen, “Overview of high-efficiency transmission gratings for molecular spectroscopy,” Spectroscopy (Springf.) 29(4), 32–39 (2014).

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Figures (5)

Fig. 1.
Fig. 1. LC director profile of the uniform PVGs and CPVGs. (a) the horizontal period is Λx, the vertical period is Λy, and the Bragg period is ΛB. (b) The horizontal periodicity is Λx, the vertical periodicities are Λy1 and Λy2 at the bottom and top, respectively, and the Bragg period are ΛB1 and ΛB2 at the bottom and top, respectively.
Fig. 2.
Fig. 2. Simulated first-order diffraction efficiency: (a) angular response at λ = 532 nm of both gradient pitch CPVGs (red line) and uniform pitch PVG (black line); and (b) simulated angular and spectral responses of the CPVGs. The green dashed lines indicate λ = 532 nm.
Fig. 3.
Fig. 3. (a) Angular behavior of optical efficiency. The red dots denote the measured results of CPVG sample. Inset: a CPVG sample viewed from an oblique angle with the CPVG region circled by the blue line. (b) A photo taken through the CPVG sample. CPVG region is circled in the blue line. The distance between PVG to camera was 1 cm, and the target was 10 cm away.
Fig. 4.
Fig. 4. (a) LC director profile of a multi-layer PVG. The horizontal period is Λx, the number of layers is N, the vertical period is Λy1 to ΛyN, respectively. (b) The horizontal periodicity is Λx, the vertical periodicity is Λy1 for the bottom layer and Λy2 for the top layer. The gray dashed lines show the top surface of the bottom layer.
Fig. 5.
Fig. 5. (a) Simulated and measured angular behavior of two-layer PVG. The red dots denote the experimental results; (b) Simulated first-order diffraction efficiency and angular response at λ = 532 nm of uniform PVG (red line), two-layer PVG (black line), and three-layer PVG (blue line).

Equations (5)

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1 Λ x 2 + 1 Λ y 2 = 1 Λ B 2 .
1 Λ B = 1 Λ B 1 + ( 1 Λ B 2 1 Λ B 1 ) s t ,
1 Λ y = 1 Λ y 1 + ( 1 Λ y 2 1 Λ y 1 ) y d + o ( ( Λ y 1 Λ y 2 ) 2 Λ y 1 3 ) ,
Φ g r a d i e n t , C P V G = π Λ x x + π Λ y 1 y + ( π Λ y 2 π Λ y 1 ) y 2 d ,
Φ i , m u l t i l a y e r , P V G = π Λ x x + π Λ y i y d i + Φ i ,

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