Abstract

The operational bandwidth of a cholesteric liquid crystal deflector based on the Bragg-Berry effect is analyzed using the two-dimensional finite-difference time-domain method. Despite its similarity in structure with a conventional cholesteric mirror under oblique incidence, the bandwidths of selective reflection and selective diffraction are different. The selective reflection wavelength from the cholesteric mirror has a cosine dependence on the Bragg angle, while that of selective diffraction from the cholesteric deflector has a cosine-squared dependence on the slant angle. We also propose equations that approximate the selective diffraction bandwidth of the deflector. The equations can be used to find the helical pitch required to achieve a deflector with a specified deflection angle and operational wavelength, thereby facilitating the development of cholesteric liquid crustal based diffractive optical elements.

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

Full Article  |  PDF Article
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References

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2019 (4)

K. Yin, Y. Lee, Z. He, and S. T. Wu, “Stretchable, flexible, rollable, and adherable polarization volume grating film,” Opt. Express 27(4), 5814–5823 (2019).
[Crossref]

Z. He, F. Gou, R. Chen, K. Yin, T. Zhan, and S. T. Wu, “Liquid Crystal Beam Steering Devices: Principles, Recent Advances, and Future Developments,” Crystals 9(6), 292 (2019).
[Crossref]

I. Nys, M. Stebryte, Y. Y. Ussembayev, J. Beeckman, and K. Neyts, “Tilted Chiral Liquid Crystal Gratings for Efficient Large-Angle Diffraction,” Adv. Opt. Mater. 7(22), 1901364 (2019).
[Crossref]

R. Ozaki, “Simple model for estimating band edge wavelengths of selective reflection from cholesteric liquid crystals for oblique incidence,” Phys. Rev. E 100(1), 012708 (2019).
[Crossref]

2018 (4)

V. Cazac, A. Meshalkin, E. Achimova, V. Abashkin, V. Katkovnik, I. Shevkunov, D. Claus, and G. Pedrini, “Surface relief and refractive index gratings patterned in chalcogenide glasses and studied by off-axis digital holography,” Appl. Opt. 57(3), 507–513 (2018).
[Crossref]

M. Rafayelyan and E. Brasselet, “Spin-to-Orbital Angular Momentum Mapping of Polychromatic Light,” Phys. Rev. Lett. 120(21), 213903 (2018).
[Crossref]

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

M. G. Nassiri, S. Y. Cho, H. Yoshida, M. Ozaki, and E. Brasselet, “High-order Laguerre-Gauss polychromatic beams from Bragg-Berry flat-optics,” Phys. Rev. A 98(6), 063834 (2018).
[Crossref]

2017 (6)

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]

J. Kobashi, H. Yoshida, and M. Ozaki, “Circularly-polarized, semitransparent and double-sided holograms based on helical photonic structures,” Sci. Rep. 7(1), 16470 (2017).
[Crossref]

Y. Mohri, J. Kobashi, H. Yoshida, and M. Ozaki, “Morpho-Butterfly-Inspired Patterning of Helical Photonic Structures for Circular-Polarization-Sensitive, Wide-Angle Diffuse Reflection,” Adv. Opt. Mater. 5(7), 1601071 (2017).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Broadband optical vortex generation from patterned cholesteric liquid crystals,” Mol. Cryst. Liq. Cryst. 646(1), 116–124 (2017).
[Crossref]

M. Rafayelyan, G. Agez, and E. Brasselet, “Ultrabroadband gradient-pitch Bragg-Berry mirrors,” Phys. Rev. A 96(4), 043862 (2017).
[Crossref]

2016 (5)

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

M. Rafayelyan, G. Tkachenko, and E. Brasselet, “Reflective Spin-Orbit Geometric Phase from Chiral Anisotropic Optical Media,” Phys. Rev. Lett. 116(25), 253902 (2016).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic Optical Vortex Generation from Patterned Cholesteric Liquid Crystals,” Phys. Rev. Lett. 116(25), 253903 (2016).
[Crossref]

M. Rafayelyan and E. Brasselet, “Bragg-Berry mirrors: reflective broadband q-plates,” Opt. Lett. 41(17), 3972–3975 (2016).
[Crossref]

K. Wakunami, P. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y. P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7(1), 12954 (2016).
[Crossref]

2015 (2)

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatiall resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref]

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

2014 (2)

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

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light: Sci. Appl. 3(9), e203 (2014).
[Crossref]

2012 (1)

2010 (1)

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 3, 40–45 (2010).
[Crossref]

2008 (1)

2006 (1)

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(22), 221102 (2006).
[Crossref]

1984 (1)

1983 (1)

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental Studies on Reflection Spectra in Monodomain Cholesteric Liquid Crystal Cells: Total Reflection, Subsidiary Oscillation and Its Beat or Swell Structure,” Jpn. J. Appl. Phys. 22(Part 1, No. 7), 1080–1091 (1983).
[Crossref]

1971 (1)

R. Dreher, G. Meier, and A. Saupe, “Selective Reflection by Cholesteric Liquid Crystals,” Mol. Cryst. Liq. Cryst. 13(1), 17–26 (1971).
[Crossref]

1970 (1)

D. W. Berreman and T. J. Scheffer, “Bragg Reflection of Light from Single-Domain Cholesteric Liquid-Crystal Films,” Phys. Rev. Lett. 25(9), 577–581 (1970).
[Crossref]

1951 (1)

H. de Vries, “Rotatory power and other optical properties of certain liquid crystals,” Acta Crystallogr. 4(3), 219–226 (1951).
[Crossref]

Abashkin, V.

Achimova, E.

Agez, G.

M. Rafayelyan, G. Agez, and E. Brasselet, “Ultrabroadband gradient-pitch Bragg-Berry mirrors,” Phys. Rev. A 96(4), 043862 (2017).
[Crossref]

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatiall resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref]

Babin, S.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light: Sci. Appl. 3(9), e203 (2014).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatiall resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref]

Beeckman, J.

I. Nys, M. Stebryte, Y. Y. Ussembayev, J. Beeckman, and K. Neyts, “Tilted Chiral Liquid Crystal Gratings for Efficient Large-Angle Diffraction,” Adv. Opt. Mater. 7(22), 1901364 (2019).
[Crossref]

Berreman, D. W.

D. W. Berreman and T. J. Scheffer, “Bragg Reflection of Light from Single-Domain Cholesteric Liquid-Crystal Films,” Phys. Rev. Lett. 25(9), 577–581 (1970).
[Crossref]

Brasselet, E.

M. G. Nassiri, S. Y. Cho, H. Yoshida, M. Ozaki, and E. Brasselet, “High-order Laguerre-Gauss polychromatic beams from Bragg-Berry flat-optics,” Phys. Rev. A 98(6), 063834 (2018).
[Crossref]

M. Rafayelyan and E. Brasselet, “Spin-to-Orbital Angular Momentum Mapping of Polychromatic Light,” Phys. Rev. Lett. 120(21), 213903 (2018).
[Crossref]

M. Rafayelyan, G. Agez, and E. Brasselet, “Ultrabroadband gradient-pitch Bragg-Berry mirrors,” Phys. Rev. A 96(4), 043862 (2017).
[Crossref]

M. Rafayelyan and E. Brasselet, “Bragg-Berry mirrors: reflective broadband q-plates,” Opt. Lett. 41(17), 3972–3975 (2016).
[Crossref]

M. Rafayelyan, G. Tkachenko, and E. Brasselet, “Reflective Spin-Orbit Geometric Phase from Chiral Anisotropic Optical Media,” Phys. Rev. Lett. 116(25), 253902 (2016).
[Crossref]

Cabrini, S.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light: Sci. Appl. 3(9), e203 (2014).
[Crossref]

Calafiore, G.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light: Sci. Appl. 3(9), e203 (2014).
[Crossref]

Capasso, F.

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

Cazac, V.

Chen, J.

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

Chen, P.

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

Chen, R.

Z. He, F. Gou, R. Chen, K. Yin, T. Zhan, and S. T. Wu, “Liquid Crystal Beam Steering Devices: Principles, Recent Advances, and Future Developments,” Crystals 9(6), 292 (2019).
[Crossref]

Cho, S. Y.

M. G. Nassiri, S. Y. Cho, H. Yoshida, M. Ozaki, and E. Brasselet, “High-order Laguerre-Gauss polychromatic beams from Bragg-Berry flat-optics,” Phys. Rev. A 98(6), 063834 (2018).
[Crossref]

Claus, D.

de Vries, H.

H. de Vries, “Rotatory power and other optical properties of certain liquid crystals,” Acta Crystallogr. 4(3), 219–226 (1951).
[Crossref]

Dhuey, S.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light: Sci. Appl. 3(9), e203 (2014).
[Crossref]

Dreher, R.

R. Dreher, G. Meier, and A. Saupe, “Selective Reflection by Cholesteric Liquid Crystals,” Mol. Cryst. Liq. Cryst. 13(1), 17–26 (1971).
[Crossref]

Duan, W.

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

Escuti, M. J.

Faraon, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatiall resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref]

Fukuda, A.

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental Studies on Reflection Spectra in Monodomain Cholesteric Liquid Crystal Cells: Total Reflection, Subsidiary Oscillation and Its Beat or Swell Structure,” Jpn. J. Appl. Phys. 22(Part 1, No. 7), 1080–1091 (1983).
[Crossref]

Gao, W.

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

Ge, S.

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

Goltsov, A.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light: Sci. Appl. 3(9), e203 (2014).
[Crossref]

Gou, F.

Z. He, F. Gou, R. Chen, K. Yin, T. Zhan, and S. T. Wu, “Liquid Crystal Beam Steering Devices: Principles, Recent Advances, and Future Developments,” Crystals 9(6), 292 (2019).
[Crossref]

Hara, M.

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental Studies on Reflection Spectra in Monodomain Cholesteric Liquid Crystal Cells: Total Reflection, Subsidiary Oscillation and Its Beat or Swell Structure,” Jpn. J. Appl. Phys. 22(Part 1, No. 7), 1080–1091 (1983).
[Crossref]

He, Z.

Z. He, F. Gou, R. Chen, K. Yin, T. Zhan, and S. T. Wu, “Liquid Crystal Beam Steering Devices: Principles, Recent Advances, and Future Developments,” Crystals 9(6), 292 (2019).
[Crossref]

K. Yin, Y. Lee, Z. He, and S. T. Wu, “Stretchable, flexible, rollable, and adherable polarization volume grating film,” Opt. Express 27(4), 5814–5823 (2019).
[Crossref]

Horie, Y.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatiall resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref]

Hsieh, P.

K. Wakunami, P. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y. P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7(1), 12954 (2016).
[Crossref]

Hu, W.

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

Huang, Y. P.

K. Wakunami, P. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y. P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7(1), 12954 (2016).
[Crossref]

Ichihashi, Y.

K. Wakunami, P. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y. P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7(1), 12954 (2016).
[Crossref]

Katkovnik, V.

Kenney, M.

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

Kimball, B. R.

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 3, 40–45 (2010).
[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, “Circularly-polarized, semitransparent and double-sided holograms based on helical photonic structures,” Sci. Rep. 7(1), 16470 (2017).
[Crossref]

Y. Mohri, J. Kobashi, H. Yoshida, and M. Ozaki, “Morpho-Butterfly-Inspired Patterning of Helical Photonic Structures for Circular-Polarization-Sensitive, Wide-Angle Diffuse Reflection,” Adv. Opt. Mater. 5(7), 1601071 (2017).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Broadband optical vortex generation from patterned cholesteric liquid crystals,” Mol. Cryst. Liq. Cryst. 646(1), 116–124 (2017).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic Optical Vortex Generation from Patterned Cholesteric Liquid Crystals,” Phys. Rev. Lett. 116(25), 253903 (2016).
[Crossref]

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

Koshelev, A.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light: Sci. Appl. 3(9), e203 (2014).
[Crossref]

Kuze, E.

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental Studies on Reflection Spectra in Monodomain Cholesteric Liquid Crystal Cells: Total Reflection, Subsidiary Oscillation and Its Beat or Swell Structure,” Jpn. J. Appl. Phys. 22(Part 1, No. 7), 1080–1091 (1983).
[Crossref]

Lee, Y.

Lee, Y. H.

Li, G.

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

Li, T.

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

Lu, Y.

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

Ma, L.

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

Manzo, C.

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(22), 221102 (2006).
[Crossref]

Marrucci, L.

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(22), 221102 (2006).
[Crossref]

Meier, G.

R. Dreher, G. Meier, and A. Saupe, “Selective Reflection by Cholesteric Liquid Crystals,” Mol. Cryst. Liq. Cryst. 13(1), 17–26 (1971).
[Crossref]

Meshalkin, A.

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]

Y. Mohri, J. Kobashi, H. Yoshida, and M. Ozaki, “Morpho-Butterfly-Inspired Patterning of Helical Photonic Structures for Circular-Polarization-Sensitive, Wide-Angle Diffuse Reflection,” Adv. Opt. Mater. 5(7), 1601071 (2017).
[Crossref]

Moritake, H.

Muhlenbernd, H.

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

Nassiri, M. G.

M. G. Nassiri, S. Y. Cho, H. Yoshida, M. Ozaki, and E. Brasselet, “High-order Laguerre-Gauss polychromatic beams from Bragg-Berry flat-optics,” Phys. Rev. A 98(6), 063834 (2018).
[Crossref]

Nersisyan, S. R.

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 3, 40–45 (2010).
[Crossref]

Neyts, K.

I. Nys, M. Stebryte, Y. Y. Ussembayev, J. Beeckman, and K. Neyts, “Tilted Chiral Liquid Crystal Gratings for Efficient Large-Angle Diffraction,” Adv. Opt. Mater. 7(22), 1901364 (2019).
[Crossref]

Nikolova, L.

Nys, I.

I. Nys, M. Stebryte, Y. Y. Ussembayev, J. Beeckman, and K. Neyts, “Tilted Chiral Liquid Crystal Gratings for Efficient Large-Angle Diffraction,” Adv. Opt. Mater. 7(22), 1901364 (2019).
[Crossref]

Oh, C.

Oi, R.

K. Wakunami, P. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y. P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7(1), 12954 (2016).
[Crossref]

Okui, M.

K. Wakunami, P. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y. P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7(1), 12954 (2016).
[Crossref]

Ouchi, Y.

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental Studies on Reflection Spectra in Monodomain Cholesteric Liquid Crystal Cells: Total Reflection, Subsidiary Oscillation and Its Beat or Swell Structure,” Jpn. J. Appl. Phys. 22(Part 1, No. 7), 1080–1091 (1983).
[Crossref]

Ozaki, M.

M. G. Nassiri, S. Y. Cho, H. Yoshida, M. Ozaki, and E. Brasselet, “High-order Laguerre-Gauss polychromatic beams from Bragg-Berry flat-optics,” Phys. Rev. A 98(6), 063834 (2018).
[Crossref]

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, “Circularly-polarized, semitransparent and double-sided holograms based on helical photonic structures,” Sci. Rep. 7(1), 16470 (2017).
[Crossref]

Y. Mohri, J. Kobashi, H. Yoshida, and M. Ozaki, “Morpho-Butterfly-Inspired Patterning of Helical Photonic Structures for Circular-Polarization-Sensitive, Wide-Angle Diffuse Reflection,” Adv. Opt. Mater. 5(7), 1601071 (2017).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Broadband optical vortex generation from patterned cholesteric liquid crystals,” Mol. Cryst. Liq. Cryst. 646(1), 116–124 (2017).
[Crossref]

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

J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic Optical Vortex Generation from Patterned Cholesteric Liquid Crystals,” Phys. Rev. Lett. 116(25), 253903 (2016).
[Crossref]

Ozaki, R.

R. Ozaki, “Simple model for estimating band edge wavelengths of selective reflection from cholesteric liquid crystals for oblique incidence,” Phys. Rev. E 100(1), 012708 (2019).
[Crossref]

R. Ozaki and H. Moritake, “Wavelength and bandwidth tunable photonic stopband of ferroelectric liquid crystals,” Opt. Express 20(6), 6191–6196 (2012).
[Crossref]

Paparo, D.

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(22), 221102 (2006).
[Crossref]

Pedrini, G.

Peroz, C.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light: Sci. Appl. 3(9), e203 (2014).
[Crossref]

Rafayelyan, M.

M. Rafayelyan and E. Brasselet, “Spin-to-Orbital Angular Momentum Mapping of Polychromatic Light,” Phys. Rev. Lett. 120(21), 213903 (2018).
[Crossref]

M. Rafayelyan, G. Agez, and E. Brasselet, “Ultrabroadband gradient-pitch Bragg-Berry mirrors,” Phys. Rev. A 96(4), 043862 (2017).
[Crossref]

M. Rafayelyan and E. Brasselet, “Bragg-Berry mirrors: reflective broadband q-plates,” Opt. Lett. 41(17), 3972–3975 (2016).
[Crossref]

M. Rafayelyan, G. Tkachenko, and E. Brasselet, “Reflective Spin-Orbit Geometric Phase from Chiral Anisotropic Optical Media,” Phys. Rev. Lett. 116(25), 253902 (2016).
[Crossref]

Sasaki, H.

K. Wakunami, P. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y. P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7(1), 12954 (2016).
[Crossref]

Sasorov, P.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light: Sci. Appl. 3(9), e203 (2014).
[Crossref]

Saupe, A.

R. Dreher, G. Meier, and A. Saupe, “Selective Reflection by Cholesteric Liquid Crystals,” Mol. Cryst. Liq. Cryst. 13(1), 17–26 (1971).
[Crossref]

Scheffer, T. J.

D. W. Berreman and T. J. Scheffer, “Bragg Reflection of Light from Single-Domain Cholesteric Liquid-Crystal Films,” Phys. Rev. Lett. 25(9), 577–581 (1970).
[Crossref]

Senoh, T.

K. Wakunami, P. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y. P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7(1), 12954 (2016).
[Crossref]

Shevkunov, I.

Stebryte, M.

I. Nys, M. Stebryte, Y. Y. Ussembayev, J. Beeckman, and K. Neyts, “Tilted Chiral Liquid Crystal Gratings for Efficient Large-Angle Diffraction,” Adv. Opt. Mater. 7(22), 1901364 (2019).
[Crossref]

Steeves, D. M.

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 3, 40–45 (2010).
[Crossref]

Tabiryan, N. V.

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 3, 40–45 (2010).
[Crossref]

Takezoe, H.

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental Studies on Reflection Spectra in Monodomain Cholesteric Liquid Crystal Cells: Total Reflection, Subsidiary Oscillation and Its Beat or Swell Structure,” Jpn. J. Appl. Phys. 22(Part 1, No. 7), 1080–1091 (1983).
[Crossref]

Tang, M.

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

Tkachenko, G.

M. Rafayelyan, G. Tkachenko, and E. Brasselet, “Reflective Spin-Orbit Geometric Phase from Chiral Anisotropic Optical Media,” Phys. Rev. Lett. 116(25), 253902 (2016).
[Crossref]

Todorov, T.

Tomova, N.

Ussembayev, Y. Y.

I. Nys, M. Stebryte, Y. Y. Ussembayev, J. Beeckman, and K. Neyts, “Tilted Chiral Liquid Crystal Gratings for Efficient Large-Angle Diffraction,” Adv. Opt. Mater. 7(22), 1901364 (2019).
[Crossref]

Wakunami, K.

K. Wakunami, P. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y. P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7(1), 12954 (2016).
[Crossref]

Wu, S. T.

Xu, R.

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

Yamamoto, K.

K. Wakunami, P. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y. P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7(1), 12954 (2016).
[Crossref]

Yankov, V.

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light: Sci. Appl. 3(9), e203 (2014).
[Crossref]

Yin, K.

Yoshida, H.

M. G. Nassiri, S. Y. Cho, H. Yoshida, M. Ozaki, and E. Brasselet, “High-order Laguerre-Gauss polychromatic beams from Bragg-Berry flat-optics,” Phys. Rev. A 98(6), 063834 (2018).
[Crossref]

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. Mohri, J. Kobashi, H. Yoshida, and M. Ozaki, “Morpho-Butterfly-Inspired Patterning of Helical Photonic Structures for Circular-Polarization-Sensitive, Wide-Angle Diffuse Reflection,” Adv. Opt. Mater. 5(7), 1601071 (2017).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Circularly-polarized, semitransparent and double-sided holograms based on helical photonic structures,” Sci. Rep. 7(1), 16470 (2017).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Broadband optical vortex generation from patterned cholesteric liquid crystals,” Mol. Cryst. Liq. Cryst. 646(1), 116–124 (2017).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic Optical Vortex Generation from Patterned Cholesteric Liquid Crystals,” Phys. Rev. Lett. 116(25), 253903 (2016).
[Crossref]

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

Yu, N.

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

Zentgraf, T.

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

Zhan, T.

Z. He, F. Gou, R. Chen, K. Yin, T. Zhan, and S. T. Wu, “Liquid Crystal Beam Steering Devices: Principles, Recent Advances, and Future Developments,” Crystals 9(6), 292 (2019).
[Crossref]

Zhang, S.

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

Zheng, G.

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

Zhu, Z.

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

Acta Crystallogr. (1)

H. de Vries, “Rotatory power and other optical properties of certain liquid crystals,” Acta Crystallogr. 4(3), 219–226 (1951).
[Crossref]

Adv. Mater. (1)

P. Chen, L. Ma, W. Duan, J. Chen, S. Ge, Z. Zhu, M. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Lu, “Digitalizing Self-Assembled Chiral Superstructures for Optical Vortex Processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref]

Adv. Opt. Mater. (2)

I. Nys, M. Stebryte, Y. Y. Ussembayev, J. Beeckman, and K. Neyts, “Tilted Chiral Liquid Crystal Gratings for Efficient Large-Angle Diffraction,” Adv. Opt. Mater. 7(22), 1901364 (2019).
[Crossref]

Y. Mohri, J. Kobashi, H. Yoshida, and M. Ozaki, “Morpho-Butterfly-Inspired Patterning of Helical Photonic Structures for Circular-Polarization-Sensitive, Wide-Angle Diffuse Reflection,” Adv. Opt. Mater. 5(7), 1601071 (2017).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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(22), 221102 (2006).
[Crossref]

Crystals (1)

Z. He, F. Gou, R. Chen, K. Yin, T. Zhan, and S. T. Wu, “Liquid Crystal Beam Steering Devices: Principles, Recent Advances, and Future Developments,” Crystals 9(6), 292 (2019).
[Crossref]

Jpn. J. Appl. Phys. (1)

H. Takezoe, Y. Ouchi, M. Hara, A. Fukuda, and E. Kuze, “Experimental Studies on Reflection Spectra in Monodomain Cholesteric Liquid Crystal Cells: Total Reflection, Subsidiary Oscillation and Its Beat or Swell Structure,” Jpn. J. Appl. Phys. 22(Part 1, No. 7), 1080–1091 (1983).
[Crossref]

Light: Sci. Appl. (1)

G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light: Sci. Appl. 3(9), e203 (2014).
[Crossref]

Mol. Cryst. Liq. Cryst. (2)

R. Dreher, G. Meier, and A. Saupe, “Selective Reflection by Cholesteric Liquid Crystals,” Mol. Cryst. Liq. Cryst. 13(1), 17–26 (1971).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Broadband optical vortex generation from patterned cholesteric liquid crystals,” Mol. Cryst. Liq. Cryst. 646(1), 116–124 (2017).
[Crossref]

Nat. Commun. (1)

K. Wakunami, P. Hsieh, R. Oi, T. Senoh, H. Sasaki, Y. Ichihashi, M. Okui, Y. P. Huang, and K. Yamamoto, “Projection-type see-through holographic three-dimensional display,” Nat. Commun. 7(1), 12954 (2016).
[Crossref]

Nat. Mater. (1)

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

Nat. Nanotechnol. (2)

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatiall resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref]

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

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 (3)

Opt. Lett. (2)

Opt. Photonics News (1)

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 3, 40–45 (2010).
[Crossref]

Phys. Rev. A (2)

M. G. Nassiri, S. Y. Cho, H. Yoshida, M. Ozaki, and E. Brasselet, “High-order Laguerre-Gauss polychromatic beams from Bragg-Berry flat-optics,” Phys. Rev. A 98(6), 063834 (2018).
[Crossref]

M. Rafayelyan, G. Agez, and E. Brasselet, “Ultrabroadband gradient-pitch Bragg-Berry mirrors,” Phys. Rev. A 96(4), 043862 (2017).
[Crossref]

Phys. Rev. E (1)

R. Ozaki, “Simple model for estimating band edge wavelengths of selective reflection from cholesteric liquid crystals for oblique incidence,” Phys. Rev. E 100(1), 012708 (2019).
[Crossref]

Phys. Rev. Lett. (4)

D. W. Berreman and T. J. Scheffer, “Bragg Reflection of Light from Single-Domain Cholesteric Liquid-Crystal Films,” Phys. Rev. Lett. 25(9), 577–581 (1970).
[Crossref]

M. Rafayelyan and E. Brasselet, “Spin-to-Orbital Angular Momentum Mapping of Polychromatic Light,” Phys. Rev. Lett. 120(21), 213903 (2018).
[Crossref]

M. Rafayelyan, G. Tkachenko, and E. Brasselet, “Reflective Spin-Orbit Geometric Phase from Chiral Anisotropic Optical Media,” Phys. Rev. Lett. 116(25), 253902 (2016).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic Optical Vortex Generation from Patterned Cholesteric Liquid Crystals,” Phys. Rev. Lett. 116(25), 253903 (2016).
[Crossref]

Sci. Rep. (1)

J. Kobashi, H. Yoshida, and M. Ozaki, “Circularly-polarized, semitransparent and double-sided holograms based on helical photonic structures,” Sci. Rep. 7(1), 16470 (2017).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. (a) Schematic of a conventional cholesteric mirror and its selective diffraction effect under oblique incidence. (b) Schematic of a cholesteric deflector and its selective diffraction effect at normal incidence.
Fig. 2.
Fig. 2. Calculated electric field distributions of light on selective reflection from the conventional cholesteric mirror: (a) λ = 750 nm and θi = 20° and (b) λ = 700 nm and θi = 30°. Calculated electric field distributions of light on selective diffraction from the cholesteric deflector: (c) λ = 700 nm and α = 20° and (d) λ = 600 nm and α = 30°.
Fig. 3.
Fig. 3. (a) Schematic of the director configuration and propagating light in the cholesteric mirror for oblique incidence and the ChLC molecules seen from the light’s point of view. (b) Schematic of the director configuration and propagating light in the cholesteric deflector for normal incidence and the ChLC molecules seen from the light’s point of view. (c) Relationship between ChLC molecules and traveling light before and after reflection in the cholesteric deflector
Fig. 4.
Fig. 4. (a) Calculated transmission spectra of the cholesteric mirror for θi = 0°, 10°, 20°, and 30°. (b) Calculated transmission spectra of the cholesteric deflector for α = 0°, 10°, 20°, and 30°.
Fig. 5.
Fig. 5. Angular dependence of the band-edge wavelengths of the cholesteric mirror and deflector. Blue and red markers are obtained by the FDTD method. The blue and red lines are calculated using Eqs. (1), (2), (5), and (6). Dark and light gray areas are the reflection band of the mirror and the diffraction band of the deflector, respectively.
Fig. 6.
Fig. 6. (a) Wavelength dependence of θd for α = 10°, 20°, 30°, and 40°, in which solid lines are theoretical curves calculated from Eq. (4), and broken lines are the theoretical center wavelengths of diffraction given by Eq. (9). Results for the same α value are represented using the same color. (b) Dependence of θd,c on α which is calculated from Eq. (14).

Equations (15)

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

λ r , o = n ¯ o P cos θ o ,
λ r , e = n ¯ e P cos θ e ,
α = tan 1 P 2 Λ .
sin θ d = λ n i Λ = 2 λ tan α n i P .
λ d , o = n o P cos 2 α ,
λ d , e = n e + n ¯ α 2 P cos 2 α = n e P cos 2 α ,
n ¯ α = 1 2 π 0 2 π { n e 2 cos 2 ϕ + [ n ( α ) ] 2 sin 2 ϕ ] } d ϕ = n e 2 + [ n ( α ) ] 2 2 ,
n ( α ) = n e n o n e 2 sin 2 ( 90 2 α ) + n o 2 cos 2 ( 90 2 α ) .
λ d , c = λ d , o + λ d , e 2 = n o + n e 2 P cos 2 α .
Δ λ d = ( n e n o ) P cos 2 α = Δ n eff P cos 2 α .
λ d = n P cos 2 α ,
n sin 2 α = n i sin θ d .
sin θ d = λ d sin 2 α n i P cos 2 α = 2 λ d tan α n i P .
sin θ d , c = n o + n e 2 n i sin 2 α .
α c r = 1 2 sin 1 ( 2 n i n o + n e ) .

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