Abstract

The conventional liquid crystal-based Pancharatnam-Berry (PB) phase lens exhibits distinct polarization selectivity, manifesting opposite optical power to circularly polarized light with opposite handedness. Here, a polarization-independent liquid crystal PB lens system is theoretically predicted and experimentally verified. Such a lens system consists of at least four PB lenses, with specific distances in between them. This enables the PB lens to be applied in polarization-independent optical systems.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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  19. N. V. Tabirian, D. E. Roberts, D. M. Steeves, and B. R. Kimball, “Diffractive Waveplate Lenses for Correcting Aberrations and Polarization-Independent Functionality,” U.S. Patent Application No. 14/688,256.

2018 (5)

2017 (4)

2016 (3)

2015 (2)

2014 (1)

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

2010 (1)

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 21(3), 41–45 (2010).

2009 (1)

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[Crossref]

2008 (1)

Bhowmik, A.

Bos, P.

Capasso, F.

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

Chanda, D.

Chen, H.

Chen, R.

Cheng, H. H.

De Sio, L.

Escuti, M. J.

Gao, K.

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(1), 79–88 (2017).
[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(1), 79–88 (2017).
[Crossref]

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(19), 22404–22410 (2017).
[Crossref] [PubMed]

He, Z.

Hwang, J. Y.

D. Roberts, Z. Liao, J. Y. Hwang, S. R. Nersisyan, and N. Tabirian, “Chromatic aberration corrected switchable optical systems,” Proc. SPIE 10735, 107350Q (2018).

Kim, J.

Kimball, B. R.

Komanduri, R.

Kudenov, M. W.

Lee, Y. H.

Li, Y.

Liao, Z.

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(1), 79–88 (2017).
[Crossref]

Liu, S.

McGinty, C.

Miskiewicz, M. N.

Nersisyan, S.

Nersisyan, S. R.

D. Roberts, Z. Liao, J. Y. Hwang, S. R. Nersisyan, and N. Tabirian, “Chromatic aberration corrected switchable optical systems,” Proc. SPIE 10735, 107350Q (2018).

N. V. Tabiryan, S. V. Serak, S. R. Nersisyan, D. E. Roberts, B. Ya. Zeldovich, D. M. Steeves, and B. R. Kimball, “Broadband waveplate lenses,” Opt. Express 24(7), 7091–7102 (2016).
[Crossref] [PubMed]

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 21(3), 41–45 (2010).

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[Crossref]

Oh, C.

Peng, 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(1), 79–88 (2017).
[Crossref]

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(19), 22404–22410 (2017).
[Crossref] [PubMed]

Roberts, D.

D. Roberts, Z. Liao, J. Y. Hwang, S. R. Nersisyan, and N. Tabirian, “Chromatic aberration corrected switchable optical systems,” Proc. SPIE 10735, 107350Q (2018).

Roberts, D. E.

Ru, Q.

Serak, S. V.

Steeves, D. M.

Tabirian, N.

D. Roberts, Z. Liao, J. Y. Hwang, S. R. Nersisyan, and N. Tabirian, “Chromatic aberration corrected switchable optical systems,” Proc. SPIE 10735, 107350Q (2018).

Tabiryan, N.

Tabiryan, N. V.

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(1), 79–88 (2017).
[Crossref]

N. V. Tabiryan, S. V. Serak, S. R. Nersisyan, D. E. Roberts, B. Ya. Zeldovich, D. M. Steeves, and B. R. Kimball, “Broadband waveplate lenses,” Opt. Express 24(7), 7091–7102 (2016).
[Crossref] [PubMed]

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(20), 25783–25794 (2015).
[Crossref] [PubMed]

N. V. Tabiryan, S. R. Nersisyan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photonics News 21(3), 41–45 (2010).

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[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]

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(19), 25076–25085 (2018).
[Crossref] [PubMed]

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(1), 79–88 (2017).
[Crossref]

Uskova, O.

Vodopyanov, K. L.

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(1), 79–88 (2017).
[Crossref]

Wickboldt, L.

Wu, S. T.

Xiang, X.

Yang, J.

Yin, K.

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]

Yu, N.

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

Zeldovich, B. Ya.

Zhan, T.

Zhao, D.

Appl. Opt. (1)

J. Nonlinear Opt. Phys. Mater. (1)

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[Crossref]

J. Soc. Inf. Disp. (1)

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]

Nat. Mater. (1)

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

Opt. Data Process. Storage (1)

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(1), 79–88 (2017).
[Crossref]

Opt. Express (7)

X. Xiang, J. Kim, R. Komanduri, and M. J. Escuti, “Nanoscale liquid crystal polymer Bragg polarization gratings,” Opt. Express 25(16), 19298–19308 (2017).
[Crossref] [PubMed]

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(4), 4863–4872 (2018).
[Crossref] [PubMed]

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(19), 25076–25085 (2018).
[Crossref] [PubMed]

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(19), 22404–22410 (2017).
[Crossref] [PubMed]

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

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(20), 25783–25794 (2015).
[Crossref] [PubMed]

N. V. Tabiryan, S. V. Serak, S. R. Nersisyan, D. E. Roberts, B. Ya. Zeldovich, D. M. Steeves, and B. R. Kimball, “Broadband waveplate lenses,” Opt. Express 24(7), 7091–7102 (2016).
[Crossref] [PubMed]

Opt. Lett. (3)

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 21(3), 41–45 (2010).

Optica (1)

Proc. SPIE (1)

D. Roberts, Z. Liao, J. Y. Hwang, S. R. Nersisyan, and N. Tabirian, “Chromatic aberration corrected switchable optical systems,” Proc. SPIE 10735, 107350Q (2018).

Other (1)

N. V. Tabirian, D. E. Roberts, D. M. Steeves, and B. R. Kimball, “Diffractive Waveplate Lenses for Correcting Aberrations and Polarization-Independent Functionality,” U.S. Patent Application No. 14/688,256.

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Figures (4)

Fig. 1
Fig. 1 (a) Top view of the distribution of LC anisotropy axis orientation. (b) phase profile of a PBL with opposite optical power for RCP and LCP, respectively (c) PBL functions as a diverging lens for LCP light but a converging lens for RCP light (d) Notation of PBL system.
Fig. 2
Fig. 2 Simulated system optical power for the solutions of Eq. (15): (a) for ( + , −), (b) for (−, + ), and Eq. (16): (c) for ( + , −), (d) for (−, + ).
Fig. 3
Fig. 3 The optical setup of exposure procedure in the PBL fabrication process.
Fig. 4
Fig. 4 (a) The optical setup to test PBL’s polarization dependency. (b) Normalized intensity versus the relative angle between polarizer and fast-axis of quarter-wave plate. (c) Photos taken through a single PBL (upper) and a polarization independent 4-PBL system (lower).

Equations (16)

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

K=( 1 0 ( 1 ) S 3 +1 2 k 1 ),
M i, S 3 =( A i, S 3 B i, S 3 C i, S 3 D i, S 3 )= K 1 D 1 K 2 D 2 K i1 D i1 K i ,
  K i =( 1 0 ( 1 ) i+ S 3 1 2 k i 1 ),
D i =( 1 d i 0 1 ).
M 2, S 3 =( A 2, S 3 B 2, S 3 C 2, S 3 D 2, S 3 )=( 1+ ( 1 ) S 3 +3 2 k 2 d 1 d 1 ( 1 ) S 3 +1 2 k 1 + ( 1 ) S 3 +3 2 k 2 k 1 k 2 d 1 1+ ( 1 ) S 3 +1 2 k 1 d 1 ).
M 2,+1 = M 2,1 .
{ 1+ k 2 d 1 =1 k 2 d 1 d 1 = d 1 k 1 + k 2 k 1 k 2 d 1 = k 1 k 2 k 1 k 2 d 1 1 k 1 d 1 =1+ k 1 d 1 .
BFL= A 2,+1 C 2,+1 = A 2,1 C 2,1 ,
d 1 = 1 k 2 2 1 k 1 k 2 .
M 3,+1 = M 3,1 .
{ d 1 k 2 d 1 k 3 d 2 k 3 =0 d 1 d 2 k 2 =0 k 2 k 1 k 3 + d 1 d 2 k 1 k 2 k 3 =0 d 2 k 2 d 2 k 1 d 1 k 1 =0 .
M 4,+1 = M 4,1 ,
{ d 1 k 2 d 1 k 3 + d 1 k 4 d 2 k 3 + d 2 k 4 + d 3 k 4 d 1 d 2 d 3 k 2 k 3 k 4 =0 d 1 d 2 k 2 + d 1 d 3 k 2 d 1 d 3 k 3 d 2 d 3 k 3 =0 k 2 k 1 k 3 + k 4 + d 1 d 2 k 1 k 2 k 3 d 1 d 2 k 1 k 2 k 4 d 1 d 3 k 1 k 2 k 4 + d 1 d 3 k 1 k 3 k 4 + d 2 d 3 k 1 k 3 k 4 d 2 d 3 k 2 k 3 k 4 =0 d 2 k 2 d 2 k 1 d 1 k 1 d 3 k 1 + d 3 k 2 d 3 k 3 + d 1 d 2 d 3 k 1 k 2 k 3 =0 .
{ k 1 = d 3 ( d 2 + d 3 ) d 1 ( d 1 + d 2 ) k 2 =± ( d 1 d 3 + d 2 d 3 ) 2 d 3 2 ( d 1 d 2 + d 2 d 3 ) × ( 4 d 3 2 d 3 2 + d 2 2 +8 d 2 d 3 2 +4 d 1 d 2 d 3 2 + d 1 d 2 +4 d 3 4 +4 d 1 d 3 3 ±1 ). k 3 =± 1 2 d 3 2 ( 4 d 2 2 d 3 2 + d 2 2 +8 d 2 d 3 2 +4 d 1 d 2 d 3 2 + d 1 d 2 +4 d 3 4 +4 d 1 d 3 3 d 2 ( d 1 + d 2 ) ±1 ) k 4 =1
{ k 1 = k 4 =1 k 2 = k 3 =± 1+12 d 2 ±1 2 d 2 .
{ k 1 = k 4 =1 k 2 = k 3 =± 1+4 d 1 2 +8 d 1 3 / d 2 ±1 2 d 1 2 .

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