Abstract

In this paper, we analyze a few aspects of Pancharatnam–Berry (PB) phase optical lenses. First, we provide theoretical formulas on how the optical efficiency, focal length, and point spread function depend on wavelength and validate them with numerical calculations based on Fresnel diffraction theory. Second, we perform numerical studies on how optical efficiency is affected by discretization of the PB phase. We find that phase discretization significantly lowers the optical efficiency for low f-number PB lenses.

© 2019 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2018 (5)

2017 (3)

C. Peng, Y. Guo, T. Turiv, M. Jiang, Q.-H. Wei, and O. D. Lavrentovich, “Patterning of lyotropic chromonic liquid crystals by photoalignment with photonic metamasks,” Adv. Mater. 29, 1606112 (2017).
[Crossref]

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).
[Crossref]

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. B 34, B56–B63 (2017).
[Crossref]

2016 (5)

M. J. Escuti, J. Kim, and M. W. Kudenov, “Controlling light with geometric-phase holograms,” Opt. Photon. News 27(2), 22–29 (2016).
[Crossref]

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).
[Crossref]

Y. Guo, M. Jiang, C. Peng, K. Sun, O. Yaroshchuk, O. Lavrentovich, and Q.-H. Wei, “High-resolution and high-throughput plasmonic photopatterning of complex molecular orientations in liquid crystals,” Adv. Mater. 28, 2353–2358 (2016).
[Crossref]

Y. Guo, M. Jiang, C. Peng, K. Sun, O. Yaroshchuk, O. Lavrentovich, and Q.-H. Wei, “Designs of plasmonic metamasks for photopatterning molecular orientations in liquid crystals,” Crystals 7, 8 (2016).
[Crossref]

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).
[Crossref]

2015 (5)

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).
[Crossref]

K. Gao, H. Cheng, A. Bhowmik, C. McGinty, and P. Bos, “61.3: ultra-compact non-mechanical zoom lens for enhanced machine vision and computer input applications,” SID Symp. Dig. Tech. Pap. 46, 911–914 (2015).
[Crossref]

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear Pancharatnam-Berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
[Crossref]

J. Zeng, J. Gao, T. S. Luk, N. M. Litchinitser, and X. Yang, “Structuring light by concentric-ring patterned magnetic metamaterial cavities,” Nano Lett. 15, 5363–5368 (2015).
[Crossref]

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

2014 (2)

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref]

M. N. Miskiewicz and M. J. Escuti, “Direct-writing of complex liquid crystal patterns,” Opt. Express 22, 12691–12706 (2014).
[Crossref]

2012 (1)

A. Krasnaberski, Y. Miklyaev, D. Pikhulya, L. Kleinschmidt, W. Imgrunt, M. Ivanenko, and V. Lissotschenko, “Efficient beam splitting with continuous relief DOEs and microlens arrays,” Proc. SPIE 8236, 823609 (2012).
[Crossref]

2010 (3)

K. Huang, P. Shi, X. Kang, X. Zhang, and Y. Li, “Design of DOE for generating a needle of a strong longitudinally polarized field,” Opt. Lett. 35, 965–967 (2010).
[Crossref]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photon. News 21(3), 40–45 (2010).
[Crossref]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The principles of laser beam control with polarization gratings introduced as diffractive waveplates,” Proc. SPIE 7775, 77750U (2010).
[Crossref]

2008 (1)

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).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

2004 (1)

2002 (1)

2001 (1)

1999 (2)

C. Kopp, L. Ravel, and P. Meyrueis, “Efficient beamshaper homogenizer design combining diffractive optical elements, microlens array and random phase plate,” J. Opt. A 1, 398–403 (1999).
[Crossref]

H. Martinsson, J. Bengtsson, M. Ghisoni, and A. Larsson, “Monolithic integration of vertical-cavity surface-emitting laser and diffractive optical element for advanced beam shaping,” IEEE Photon. Technol. Lett. 11, 503–505 (1999).
[Crossref]

1998 (1)

1995 (2)

W. Däschner, P. Long, M. Larsson, and S. H. Lee, “Fabrication of diffractive optical elements using a single optical exposure with a gray level mask,” J. Vac. Sci. Technol. B 13, 2729–2731 (1995).
[Crossref]

T. J. Suleski and D. C. O’Shea, “Gray-scale masks for diffractive-optics fabrication: I. Commercial slide imagers,” Appl. Opt. 34, 7507–7517 (1995).
[Crossref]

1994 (1)

M. T. Gale, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[Crossref]

1992 (1)

M. B. Stern and S. S. Medeiros, “Deep three-dimensional microstructure fabrication for infrared binary optics,” J. Vac. Sci. Technol. B 10, 2520–2525 (1992).
[Crossref]

1991 (1)

M. B. Stern, M. Holz, S. S. Medeiros, and R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[Crossref]

1990 (1)

1989 (1)

G. J. Swanson and W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 286605 (1989).
[Crossref]

1987 (1)

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[Crossref]

1972 (1)

L. d’Auria, J. P. Huignard, A. M. Roy, and E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972).
[Crossref]

1956 (1)

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

Alù, A.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear Pancharatnam-Berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
[Crossref]

Belkin, M. A.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear Pancharatnam-Berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
[Crossref]

Bengtsson, J.

H. Martinsson, J. Bengtsson, M. Ghisoni, and A. Larsson, “Monolithic integration of vertical-cavity surface-emitting laser and diffractive optical element for advanced beam shaping,” IEEE Photon. Technol. Lett. 11, 503–505 (1999).
[Crossref]

Berry, M. V.

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[Crossref]

Bhowmik, A.

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).
[Crossref]

K. Gao, H. Cheng, A. Bhowmik, C. McGinty, and P. Bos, “61.3: ultra-compact non-mechanical zoom lens for enhanced machine vision and computer input applications,” SID Symp. Dig. Tech. Pap. 46, 911–914 (2015).
[Crossref]

Biener, G.

Bomzon, Z.

Bos, P.

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).
[Crossref]

K. Gao, H. Cheng, A. Bhowmik, C. McGinty, and P. Bos, “61.3: ultra-compact non-mechanical zoom lens for enhanced machine vision and computer input applications,” SID Symp. Dig. Tech. Pap. 46, 911–914 (2015).
[Crossref]

Bos, P. J.

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref]

Bunning, T. J.

Chaganava, I.

M. Jiang, H. Yu, X. Feng, Y. Guo, I. Chaganava, T. Turiv, O. D. Lavrentovich, and Q.-H. Wei, “Liquid crystal Pancharatnam-Berry micro-optical elements for laser beam shaping,” Adv. Opt. Mater. 6, 1800961 (2018).
[Crossref]

Chanda, D.

Chen, R.

Cheng, H.

K. Gao, H. Cheng, A. Bhowmik, C. McGinty, and P. Bos, “61.3: ultra-compact non-mechanical zoom lens for enhanced machine vision and computer input applications,” SID Symp. Dig. Tech. Pap. 46, 911–914 (2015).
[Crossref]

Cheng, H.-H.

d’Auria, L.

L. d’Auria, J. P. Huignard, A. M. Roy, and E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972).
[Crossref]

Däschner, W.

W. Däschner, P. Long, M. Larsson, and S. H. Lee, “Fabrication of diffractive optical elements using a single optical exposure with a gray level mask,” J. Vac. Sci. Technol. B 13, 2729–2731 (1995).
[Crossref]

De Sio, L.

Escuti, M. J.

Fan, P.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
[Crossref]

Feng, X.

M. Jiang, H. Yu, X. Feng, Y. Guo, I. Chaganava, T. Turiv, O. D. Lavrentovich, and Q.-H. Wei, “Liquid crystal Pancharatnam-Berry micro-optical elements for laser beam shaping,” Adv. Opt. Mater. 6, 1800961 (2018).
[Crossref]

Flores, A.

Gale, M. T.

M. T. Gale, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. 33, 3556–3566 (1994).
[Crossref]

Gao, J.

J. Zeng, J. Gao, T. S. Luk, N. M. Litchinitser, and X. Yang, “Structuring light by concentric-ring patterned magnetic metamaterial cavities,” Nano Lett. 15, 5363–5368 (2015).
[Crossref]

Gao, K.

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).
[Crossref]

K. Gao, H. Cheng, A. Bhowmik, C. McGinty, and P. Bos, “61.3: ultra-compact non-mechanical zoom lens for enhanced machine vision and computer input applications,” SID Symp. Dig. Tech. Pap. 46, 911–914 (2015).
[Crossref]

Gauza, S.

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).
[Crossref]

Ghisoni, M.

H. Martinsson, J. Bengtsson, M. Ghisoni, and A. Larsson, “Monolithic integration of vertical-cavity surface-emitting laser and diffractive optical element for advanced beam shaping,” IEEE Photon. Technol. Lett. 11, 503–505 (1999).
[Crossref]

Gomez-Diaz, J. S.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear Pancharatnam-Berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
[Crossref]

Gou, F.

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).
[Crossref]

Guo, Y.

M. Jiang, H. Yu, X. Feng, Y. Guo, I. Chaganava, T. Turiv, O. D. Lavrentovich, and Q.-H. Wei, “Liquid crystal Pancharatnam-Berry micro-optical elements for laser beam shaping,” Adv. Opt. Mater. 6, 1800961 (2018).
[Crossref]

C. Peng, Y. Guo, T. Turiv, M. Jiang, Q.-H. Wei, and O. D. Lavrentovich, “Patterning of lyotropic chromonic liquid crystals by photoalignment with photonic metamasks,” Adv. Mater. 29, 1606112 (2017).
[Crossref]

Y. Guo, M. Jiang, C. Peng, K. Sun, O. Yaroshchuk, O. Lavrentovich, and Q.-H. Wei, “High-resolution and high-throughput plasmonic photopatterning of complex molecular orientations in liquid crystals,” Adv. Mater. 28, 2353–2358 (2016).
[Crossref]

Y. Guo, M. Jiang, C. Peng, K. Sun, O. Yaroshchuk, O. Lavrentovich, and Q.-H. Wei, “Designs of plasmonic metamasks for photopatterning molecular orientations in liquid crystals,” Crystals 7, 8 (2016).
[Crossref]

M. Jiang, Y. Guo, H. Yu, Z. Zhou, T. Turiv, O. D. Lavrentovich, and Q.-H. Wei, “Low F-number diffraction-limited Pancharatnam-Berry microlenses enabled by plasmonic photopatterning of liquid crystal polymers,” Adv. Mater., submitted for publication.

Halldórsson, T.

Hasman, E.

He, Z.

Holz, M.

M. B. Stern, M. Holz, S. S. Medeiros, and R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[Crossref]

Huang, K.

Huignard, J. P.

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M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear Pancharatnam-Berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
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Lee, Y.-H.

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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J. Zeng, J. Gao, T. S. Luk, N. M. Litchinitser, and X. Yang, “Structuring light by concentric-ring patterned magnetic metamaterial cavities,” Nano Lett. 15, 5363–5368 (2015).
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Liu, G.

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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J. Zeng, J. Gao, T. S. Luk, N. M. Litchinitser, and X. Yang, “Structuring light by concentric-ring patterned magnetic metamaterial cavities,” Nano Lett. 15, 5363–5368 (2015).
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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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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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L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
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[Crossref]

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C. Kopp, L. Ravel, and P. Meyrueis, “Efficient beamshaper homogenizer design combining diffractive optical elements, microlens array and random phase plate,” J. Opt. A 1, 398–403 (1999).
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Mühlenbernd, H.

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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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S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The principles of laser beam control with polarization gratings introduced as diffractive waveplates,” Proc. SPIE 7775, 77750U (2010).
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S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photon. News 21(3), 40–45 (2010).
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O’Shea, D. D.

D. D. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Praather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).

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L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

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).
[Crossref]

Peng, C.

C. Peng, Y. Guo, T. Turiv, M. Jiang, Q.-H. Wei, and O. D. Lavrentovich, “Patterning of lyotropic chromonic liquid crystals by photoalignment with photonic metamasks,” Adv. Mater. 29, 1606112 (2017).
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Y. Guo, M. Jiang, C. Peng, K. Sun, O. Yaroshchuk, O. Lavrentovich, and Q.-H. Wei, “High-resolution and high-throughput plasmonic photopatterning of complex molecular orientations in liquid crystals,” Adv. Mater. 28, 2353–2358 (2016).
[Crossref]

Y. Guo, M. Jiang, C. Peng, K. Sun, O. Yaroshchuk, O. Lavrentovich, and Q.-H. Wei, “Designs of plasmonic metamasks for photopatterning molecular orientations in liquid crystals,” Crystals 7, 8 (2016).
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Pikhulya, D.

A. Krasnaberski, Y. Miklyaev, D. Pikhulya, L. Kleinschmidt, W. Imgrunt, M. Ivanenko, and V. Lissotschenko, “Efficient beam splitting with continuous relief DOEs and microlens arrays,” Proc. SPIE 8236, 823609 (2012).
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D. D. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Praather, Diffractive Optics: Design, Fabrication, and Test (SPIE, 2003).

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C. Kopp, L. Ravel, and P. Meyrueis, “Efficient beamshaper homogenizer design combining diffractive optical elements, microlens array and random phase plate,” J. Opt. A 1, 398–403 (1999).
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Roberts, D. E.

Roy, A. M.

L. d’Auria, J. P. Huignard, A. M. Roy, and E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972).
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Shi, P.

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L. d’Auria, J. P. Huignard, A. M. Roy, and E. Spitz, “Photolithographic fabrication of thin film lenses,” Opt. Commun. 5, 232–235 (1972).
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M. B. Stern and S. S. Medeiros, “Deep three-dimensional microstructure fabrication for infrared binary optics,” J. Vac. Sci. Technol. B 10, 2520–2525 (1992).
[Crossref]

M. B. Stern, M. Holz, S. S. Medeiros, and R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
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Y. Guo, M. Jiang, C. Peng, K. Sun, O. Yaroshchuk, O. Lavrentovich, and Q.-H. Wei, “Designs of plasmonic metamasks for photopatterning molecular orientations in liquid crystals,” Crystals 7, 8 (2016).
[Crossref]

Y. Guo, M. Jiang, C. Peng, K. Sun, O. Yaroshchuk, O. Lavrentovich, and Q.-H. Wei, “High-resolution and high-throughput plasmonic photopatterning of complex molecular orientations in liquid crystals,” Adv. Mater. 28, 2353–2358 (2016).
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Tabiryan, N. V.

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. B 34, B56–B63 (2017).
[Crossref]

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).
[Crossref]

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).
[Crossref]

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).
[Crossref]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photon. News 21(3), 40–45 (2010).
[Crossref]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The principles of laser beam control with polarization gratings introduced as diffractive waveplates,” Proc. SPIE 7775, 77750U (2010).
[Crossref]

Tan, G.

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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Turiv, T.

M. Jiang, H. Yu, X. Feng, Y. Guo, I. Chaganava, T. Turiv, O. D. Lavrentovich, and Q.-H. Wei, “Liquid crystal Pancharatnam-Berry micro-optical elements for laser beam shaping,” Adv. Opt. Mater. 6, 1800961 (2018).
[Crossref]

C. Peng, Y. Guo, T. Turiv, M. Jiang, Q.-H. Wei, and O. D. Lavrentovich, “Patterning of lyotropic chromonic liquid crystals by photoalignment with photonic metamasks,” Adv. Mater. 29, 1606112 (2017).
[Crossref]

M. Jiang, Y. Guo, H. Yu, Z. Zhou, T. Turiv, O. D. Lavrentovich, and Q.-H. Wei, “Low F-number diffraction-limited Pancharatnam-Berry microlenses enabled by plasmonic photopatterning of liquid crystal polymers,” Adv. Mater., submitted for publication.

Tymchenko, M.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, N. Nookala, M. A. Belkin, and A. Alù, “Gradient nonlinear Pancharatnam-Berry metasurfaces,” Phys. Rev. Lett. 115, 207403 (2015).
[Crossref]

Veldkamp, W. B.

G. J. Swanson and W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 286605 (1989).
[Crossref]

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Wang, L.

Wang, M. R.

Wei, Q.-H.

M. Jiang, H. Yu, X. Feng, Y. Guo, I. Chaganava, T. Turiv, O. D. Lavrentovich, and Q.-H. Wei, “Liquid crystal Pancharatnam-Berry micro-optical elements for laser beam shaping,” Adv. Opt. Mater. 6, 1800961 (2018).
[Crossref]

C. Peng, Y. Guo, T. Turiv, M. Jiang, Q.-H. Wei, and O. D. Lavrentovich, “Patterning of lyotropic chromonic liquid crystals by photoalignment with photonic metamasks,” Adv. Mater. 29, 1606112 (2017).
[Crossref]

Y. Guo, M. Jiang, C. Peng, K. Sun, O. Yaroshchuk, O. Lavrentovich, and Q.-H. Wei, “Designs of plasmonic metamasks for photopatterning molecular orientations in liquid crystals,” Crystals 7, 8 (2016).
[Crossref]

Y. Guo, M. Jiang, C. Peng, K. Sun, O. Yaroshchuk, O. Lavrentovich, and Q.-H. Wei, “High-resolution and high-throughput plasmonic photopatterning of complex molecular orientations in liquid crystals,” Adv. Mater. 28, 2353–2358 (2016).
[Crossref]

M. Jiang, Y. Guo, H. Yu, Z. Zhou, T. Turiv, O. D. Lavrentovich, and Q.-H. Wei, “Low F-number diffraction-limited Pancharatnam-Berry microlenses enabled by plasmonic photopatterning of liquid crystal polymers,” Adv. Mater., submitted for publication.

Weng, Y.

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).
[Crossref]

Wu, S.

Wu, S.-T.

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).
[Crossref]

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).
[Crossref]

Yang, J. J.

Yang, X.

J. Zeng, J. Gao, T. S. Luk, N. M. Litchinitser, and X. Yang, “Structuring light by concentric-ring patterned magnetic metamaterial cavities,” Nano Lett. 15, 5363–5368 (2015).
[Crossref]

Yaroshchuk, O.

Y. Guo, M. Jiang, C. Peng, K. Sun, O. Yaroshchuk, O. Lavrentovich, and Q.-H. Wei, “High-resolution and high-throughput plasmonic photopatterning of complex molecular orientations in liquid crystals,” Adv. Mater. 28, 2353–2358 (2016).
[Crossref]

Y. Guo, M. Jiang, C. Peng, K. Sun, O. Yaroshchuk, O. Lavrentovich, and Q.-H. Wei, “Designs of plasmonic metamasks for photopatterning molecular orientations in liquid crystals,” Crystals 7, 8 (2016).
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Yousefzadeh, C.

Yu, H.

M. Jiang, H. Yu, X. Feng, Y. Guo, I. Chaganava, T. Turiv, O. D. Lavrentovich, and Q.-H. Wei, “Liquid crystal Pancharatnam-Berry micro-optical elements for laser beam shaping,” Adv. Opt. Mater. 6, 1800961 (2018).
[Crossref]

M. Jiang, Y. Guo, H. Yu, Z. Zhou, T. Turiv, O. D. Lavrentovich, and Q.-H. Wei, “Low F-number diffraction-limited Pancharatnam-Berry microlenses enabled by plasmonic photopatterning of liquid crystal polymers,” Adv. Mater., submitted for publication.

Zeldovich, B. Y.

Zeng, J.

J. Zeng, J. Gao, T. S. Luk, N. M. Litchinitser, and X. Yang, “Structuring light by concentric-ring patterned magnetic metamaterial cavities,” Nano Lett. 15, 5363–5368 (2015).
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Zentgraf, T.

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

Zhan, T.

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).
[Crossref]

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).
[Crossref]

Zhang, S.

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

Zheng, G.

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

Zhou, Z.

M. Jiang, Y. Guo, H. Yu, Z. Zhou, T. Turiv, O. D. Lavrentovich, and Q.-H. Wei, “Low F-number diffraction-limited Pancharatnam-Berry microlenses enabled by plasmonic photopatterning of liquid crystal polymers,” Adv. Mater., submitted for publication.

Adv. Mater. (2)

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M. Jiang, Y. Guo, H. Yu, Z. Zhou, T. Turiv, O. D. Lavrentovich, and Q.-H. Wei, “Low F-number diffraction-limited Pancharatnam-Berry microlenses enabled by plasmonic photopatterning of liquid crystal polymers,” Adv. Mater., submitted for publication.

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Figures (5)

Fig. 1.
Fig. 1. Schematic of a PBOE, where the red lines represent light of the same handedness, and the blue lines represent light with the opposite handedness and the additional PB phase.
Fig. 2.
Fig. 2. Conversion efficiency of a PBOE as a function of (a) wavelength λ and (b) film thickness t . The designed working wavelength is at 500 nm, and the hypothetical material is 5CB, a commonly used liquid crystal material.
Fig. 3.
Fig. 3. Numerical results of the PSF for PB lenses with different f number: (a)–(c)  N f = 2 ; (d)–(f)  N f = 10 ; (g)–(i)  N f = 30 . Squares and red lines in the graphs are the calculated PSFs at the focal planes and numerical fittings of Eq. (9) to the data. Insets are intensity distributions at the y z planes (upper left corners) and the x y planes at z = f (upper right corners).
Fig. 4.
Fig. 4. Focal length f as a function of the working wavelength λ at three representative f -numbers: N f = 30 (blue triangle and line), 10 (red circle and line), 2 (black square and line). The data points are from the numerical calculations shown in Fig. 3; the solid lines are fittings to Eq. (8).
Fig. 5.
Fig. 5. Dependence of the calculated optical efficiency on the pixel size p / λ 0 . The blue squares and red circles are numerical results for two different f -numbers, N f = 2 and N f = 10 , respectively. The solid lines are parabola polynomial fittings.

Equations (10)

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T = 1 e i Δ Γ 2 [ 1 0 0 1 ] + 1 + e i Δ Γ 2 [ cos ( 2 θ ) sin ( 2 θ ) sin ( 2 θ ) cos ( 2 θ ) ] .
J ± = T · ( 1 ± i ) = 1 2 [ ( 1 e i Δ Γ ) ( 1 ± i ) + ( 1 + e i Δ Γ ) e ± i 2 θ ( 1 i ) ] .
η ( λ ) = cos 2 Δ Γ 2 .
sin ( θ t ) sin ( θ i ) = λ 2 π n d ϕ d x .
d ϕ d x = 2 π λ 0 r r 2 + f 2 .
ϕ = 2 θ = 2 π λ 0 ( f 2 + r 2 f ) .
sin ( θ t ) = r r 2 + f 0 2 · λ λ 0 .
f ( λ ) f 0 1 2 Δ λ λ 0 .
I ( x , y ) = I 0 ( sin α x α x sin α y α y ) 2 ,
E ( x , y , z ) = 1 i λ E ( x , y ) · e i k r r K ( χ ) d x d y ,

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