Abstract

We proposed an analytically designed non-iterative dartboard phase filter (DPF) to achieve multifocal arrays by cylindrical vector beams. The DPF is composed of sectors, which is two-dimensionally divided in polar coordinates, along the radial and azimuthal directions. Meanwhile, a modulation factor was first proposed and introduced into the DPF to improve the intensity uniformity of the generated multifocal array. By the proposed DPF, the one-dimensional, two-dimensional and three-dimensional multifocal arrays are generated, which have intensity uniformities larger than 92.5%. The focal position and polarization of these generated multifocal arrays can be controlled, while the transverse sizes of each focal spot are subwavelength. The proposed DPF and the generated multifocal arrays have potential applications in the fields of polarization-multiplexed data storage, polarization-sensitive nanophotonic devices and parallel direct laser writing.

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

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References

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2018 (1)

Y. Z. Yu, H. Huang, M. M. Zhou, and Q. W. Zhan, “Engineering of multi-segmented light tunnel and flattop focus with designed axial lengths and gaps,” Opt. Commun. 407, 398–401 (2018).
[Crossref]

2017 (4)

J. Guan, J. Lin, C. Chen, Y. Ma, J. B. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

L. Zhu, R. Yang, D. Zhang, J. Yu, and J. Chen, “Dynamic three-dimensional multifocal spots in high numerical-aperture objectives,” Opt. Express 25(20), 24756–24766 (2017).
[Crossref] [PubMed]

J. Guan, J. Lin, Y. Ma, J. Tan, and P. Jin, “A subwavelength spot and a three-dimensional optical trap formed by a single planar element with azimuthal light,” Sci. Rep. 7(1), 7380 (2017).
[Crossref] [PubMed]

C. C. Ping, C. H. Liang, F. Wang, and Y. J. Cai, “Radially polarized multi-Gaussian Schell-model beam and its tight focusing properties,” Opt. Express 25(26), 32475–32490 (2017).
[Crossref]

2016 (2)

P. Wozniak, P. Banzer, F. Bouchard, E. Karimi, G. Leuchs, and R. W. Boyd, “Tighter spots of light with superposed orbital-angular-momentum beams,” Phys. Rev. A 94(2), 021803 (2016).
[Crossref]

T. Mu, Z. Chen, S. Pacheco, R. Wu, C. Zhang, and R. Liang, “Generation of a controllable multifocal array from a modulated azimuthally polarized beam,” Opt. Lett. 41(2), 261–264 (2016).
[Crossref] [PubMed]

2015 (3)

2014 (1)

2013 (2)

2012 (2)

2011 (5)

2010 (4)

2009 (1)

T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining Light to Deep Subwavelength Dimensions to Enable Optical Nanopatterning,” Science 324(5929), 917–921 (2009).
[Crossref] [PubMed]

2008 (1)

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

2006 (2)

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[Crossref] [PubMed]

M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, “Fast focus field calculations,” Opt. Express 14, 11277–11291 (2006).

2005 (1)

R. Menon, A. Patel, D. Gil, and H. I. Smith, “Maskless lithography,” Mater. Today 8(2), 26–33 (2005).
[Crossref]

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

2000 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Andrew, T. L.

T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining Light to Deep Subwavelength Dimensions to Enable Optical Nanopatterning,” Science 324(5929), 917–921 (2009).
[Crossref] [PubMed]

April, A.

Banzer, P.

P. Wozniak, P. Banzer, F. Bouchard, E. Karimi, G. Leuchs, and R. W. Boyd, “Tighter spots of light with superposed orbital-angular-momentum beams,” Phys. Rev. A 94(2), 021803 (2016).
[Crossref]

Bouchard, F.

P. Wozniak, P. Banzer, F. Bouchard, E. Karimi, G. Leuchs, and R. W. Boyd, “Tighter spots of light with superposed orbital-angular-momentum beams,” Phys. Rev. A 94(2), 021803 (2016).
[Crossref]

Boyd, R. W.

P. Wozniak, P. Banzer, F. Bouchard, E. Karimi, G. Leuchs, and R. W. Boyd, “Tighter spots of light with superposed orbital-angular-momentum beams,” Phys. Rev. A 94(2), 021803 (2016).
[Crossref]

Brown, T.

Cai, Y. J.

Cao, Y.

Chen, C.

J. Guan, J. Lin, C. Chen, Y. Ma, J. B. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

Chen, J.

Chen, W.

Chen, Z.

Chong, C. T.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Davies, G.

Dehez, H.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Gan, X.

Gil, D.

R. Menon, A. Patel, D. Gil, and H. I. Smith, “Maskless lithography,” Mater. Today 8(2), 26–33 (2005).
[Crossref]

Gu, M.

Guan, J.

J. Guan, J. Lin, C. Chen, Y. Ma, J. B. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

J. Guan, J. Lin, Y. Ma, J. Tan, and P. Jin, “A subwavelength spot and a three-dimensional optical trap formed by a single planar element with azimuthal light,” Sci. Rep. 7(1), 7380 (2017).
[Crossref] [PubMed]

Guo, H.

Hao, X.

Hashimoto, N.

Hell, S. W.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[Crossref] [PubMed]

Hibi, T.

Hong, M.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Horanai, H.

Hu, Q.

Huang, H.

Y. Z. Yu, H. Huang, M. M. Zhou, and Q. W. Zhan, “Engineering of multi-segmented light tunnel and flattop focus with designed axial lengths and gaps,” Opt. Commun. 407, 398–401 (2018).
[Crossref]

Huang, K.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

K. Huang, P. Shi, X. L. Kang, X. Zhang, and Y. P. Li, “Design of DOE for generating a needle of a strong longitudinally polarized field,” Opt. Lett. 35(7), 965–967 (2010).
[Crossref] [PubMed]

Jahn, R.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[Crossref] [PubMed]

Jia, B.

Jiang, M.

Jiao, J.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Jiao, X.

Jin, P.

J. Guan, J. Lin, Y. Ma, J. Tan, and P. Jin, “A subwavelength spot and a three-dimensional optical trap formed by a single planar element with azimuthal light,” Sci. Rep. 7(1), 7380 (2017).
[Crossref] [PubMed]

J. Guan, J. Lin, C. Chen, Y. Ma, J. B. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

J. Lin, Y. Ma, P. Jin, G. Davies, and J. Tan, “Longitudinal polarized focusing of radially polarized sinh-Gaussian beam,” Opt. Express 21(11), 13193–13198 (2013).
[Crossref] [PubMed]

Kang, X. L.

Karimi, E.

P. Wozniak, P. Banzer, F. Bouchard, E. Karimi, G. Leuchs, and R. W. Boyd, “Tighter spots of light with superposed orbital-angular-momentum beams,” Phys. Rev. A 94(2), 021803 (2016).
[Crossref]

Kitamura, K.

Kozawa, Y.

Kuang, C.

Kurihara, M.

Lasser, T.

Leitgeb, R. A.

Leuchs, G.

P. Wozniak, P. Banzer, F. Bouchard, E. Karimi, G. Leuchs, and R. W. Boyd, “Tighter spots of light with superposed orbital-angular-momentum beams,” Phys. Rev. A 94(2), 021803 (2016).
[Crossref]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Leutenegger, M.

Li, P.

Li, X.

Li, Y.

Li, Y. P.

Liang, C. H.

Liang, R.

Lin, H.

Lin, J.

J. Guan, J. Lin, C. Chen, Y. Ma, J. B. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

J. Guan, J. Lin, Y. Ma, J. Tan, and P. Jin, “A subwavelength spot and a three-dimensional optical trap formed by a single planar element with azimuthal light,” Sci. Rep. 7(1), 7380 (2017).
[Crossref] [PubMed]

J. Lin, Y. Ma, P. Jin, G. Davies, and J. Tan, “Longitudinal polarized focusing of radially polarized sinh-Gaussian beam,” Opt. Express 21(11), 13193–13198 (2013).
[Crossref] [PubMed]

J. Lin, K. Yin, Y. Li, and J. Tan, “Achievement of longitudinally polarized focusing with long focal depth by amplitude modulation,” Opt. Lett. 36(7), 1185–1187 (2011).
[Crossref] [PubMed]

Liu, S.

Liu, X.

Lukyanchuk, B.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Luo, X.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Ma, Y.

J. Guan, J. Lin, Y. Ma, J. Tan, and P. Jin, “A subwavelength spot and a three-dimensional optical trap formed by a single planar element with azimuthal light,” Sci. Rep. 7(1), 7380 (2017).
[Crossref] [PubMed]

J. Guan, J. Lin, C. Chen, Y. Ma, J. B. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

J. Lin, Y. Ma, P. Jin, G. Davies, and J. Tan, “Longitudinal polarized focusing of radially polarized sinh-Gaussian beam,” Opt. Express 21(11), 13193–13198 (2013).
[Crossref] [PubMed]

Menon, R.

T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining Light to Deep Subwavelength Dimensions to Enable Optical Nanopatterning,” Science 324(5929), 917–921 (2009).
[Crossref] [PubMed]

R. Menon, A. Patel, D. Gil, and H. I. Smith, “Maskless lithography,” Mater. Today 8(2), 26–33 (2005).
[Crossref]

Mu, T.

Nemoto, T.

Noda, S.

Pacheco, S.

Patel, A.

R. Menon, A. Patel, D. Gil, and H. I. Smith, “Maskless lithography,” Mater. Today 8(2), 26–33 (2005).
[Crossref]

Piché, M.

Ping, C. C.

Qin, F.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Qiu, C.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Rao, R.

Ren, H.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Rizzoli, S. O.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[Crossref] [PubMed]

Sakai, K.

Sato, A.

Sato, S.

Sheppard, C.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Shi, L. P.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Shi, P.

Smith, H. I.

R. Menon, A. Patel, D. Gil, and H. I. Smith, “Maskless lithography,” Mater. Today 8(2), 26–33 (2005).
[Crossref]

Sui, G.

Sun, M.

Tan, J.

Tan, J. B.

J. Guan, J. Lin, C. Chen, Y. Ma, J. B. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

Toussaint, K. C.

Tsai, H. Y.

T. L. Andrew, H. Y. Tsai, and R. Menon, “Confining Light to Deep Subwavelength Dimensions to Enable Optical Nanopatterning,” Science 324(5929), 917–921 (2009).
[Crossref] [PubMed]

Wang, F.

Wang, H. F.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Wang, J.

Wang, Q.

Wang, T.

Wang, Y.

Wei, S. B.

Wen, J.

Weng, X.

Westphal, V.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[Crossref] [PubMed]

Willig, K. I.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
[Crossref] [PubMed]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Wozniak, P.

P. Wozniak, P. Banzer, F. Bouchard, E. Karimi, G. Leuchs, and R. W. Boyd, “Tighter spots of light with superposed orbital-angular-momentum beams,” Phys. Rev. A 94(2), 021803 (2016).
[Crossref]

Wu, J.

F. Qin, K. Huang, J. Wu, J. Jiao, X. Luo, C. Qiu, and M. Hong, “Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light,” Sci. Rep. 5(1), 9977 (2015).
[Crossref] [PubMed]

Wu, R.

Xia, X.

Yang, R.

Yin, K.

Yokoyama, H.

You, S.

Youngworth, K.

Yu, J.

Yu, Y. Z.

Y. Z. Yu, H. Huang, M. M. Zhou, and Q. W. Zhan, “Engineering of multi-segmented light tunnel and flattop focus with designed axial lengths and gaps,” Opt. Commun. 407, 398–401 (2018).
[Crossref]

Yuan, G. H.

Yuan, X. C.

Zhan, Q.

Zhan, Q. W.

Y. Z. Yu, H. Huang, M. M. Zhou, and Q. W. Zhan, “Engineering of multi-segmented light tunnel and flattop focus with designed axial lengths and gaps,” Opt. Commun. 407, 398–401 (2018).
[Crossref]

Zhang, C.

Zhang, D.

Zhang, X.

Zhao, J.

Zhao, Y.

Zhou, M. M.

Y. Z. Yu, H. Huang, M. M. Zhou, and Q. W. Zhan, “Engineering of multi-segmented light tunnel and flattop focus with designed axial lengths and gaps,” Opt. Commun. 407, 398–401 (2018).
[Crossref]

Zhou, R.

Zhu, L.

Zhuang, S.

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Nat. Photonics (1)

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
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Nature (1)

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440(7086), 935–939 (2006).
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Opt. Commun. (2)

Y. Z. Yu, H. Huang, M. M. Zhou, and Q. W. Zhan, “Engineering of multi-segmented light tunnel and flattop focus with designed axial lengths and gaps,” Opt. Commun. 407, 398–401 (2018).
[Crossref]

J. Guan, J. Lin, C. Chen, Y. Ma, J. B. Tan, and P. Jin, “Transversely polarized sub-diffraction optical needle with ultra-long depth of focus,” Opt. Commun. 404, 118–123 (2017).
[Crossref]

Opt. Express (11)

L. Zhu, R. Yang, D. Zhang, J. Yu, and J. Chen, “Dynamic three-dimensional multifocal spots in high numerical-aperture objectives,” Opt. Express 25(20), 24756–24766 (2017).
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L. Zhu, M. Sun, D. Zhang, J. Yu, J. Wen, and J. Chen, “Multifocal array with controllable polarization in each focal spot,” Opt. Express 23(19), 24688–24698 (2015).
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J. Lin, Y. Ma, P. Jin, G. Davies, and J. Tan, “Longitudinal polarized focusing of radially polarized sinh-Gaussian beam,” Opt. Express 21(11), 13193–13198 (2013).
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H. Guo, X. Weng, M. Jiang, Y. Zhao, G. Sui, Q. Hu, Y. Wang, and S. Zhuang, “Tight focusing of a higher-order radially polarized beam transmitting through multi-zone binary phase pupil filters,” Opt. Express 21(5), 5363–5372 (2013).
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C. C. Ping, C. H. Liang, F. Wang, and Y. J. Cai, “Radially polarized multi-Gaussian Schell-model beam and its tight focusing properties,” Opt. Express 25(26), 32475–32490 (2017).
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Opt. Lett. (10)

X. Jiao, S. Liu, Q. Wang, X. Gan, P. Li, and J. Zhao, “Redistributing energy flow and polarization of a focused azimuthally polarized beam with rotationally symmetric sector-shaped obstacles,” Opt. Lett. 37(6), 1041–1043 (2012).
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J. Lin, K. Yin, Y. Li, and J. Tan, “Achievement of longitudinally polarized focusing with long focal depth by amplitude modulation,” Opt. Lett. 36(7), 1185–1187 (2011).
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X. Hao, C. Kuang, T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35(23), 3928–3930 (2010).
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Figures (7)

Fig. 1
Fig. 1 Schematic of achieving a multifocal array by a DPF. (a) Schematic for the calculation of the focal field. (b) Configuration of the proposed DPF and two examples of the cell zone distribution in a DPF.
Fig. 2
Fig. 2 Axial multifocal array generated by a RP beam. (a) Phase distribution of the DPF with M = 3 and N = 44. (b) Lateral normalized intensity for each focal spot of the multifocal array generated by the DPF in (a). (c) and (d) Normalized intensity distribution and profile of the generated multifocal array in the yoz plane and on the z-axis, respectively.
Fig. 3
Fig. 3 Generated 2D multifocal arrays with M = 4 in the focal plane. (a1) Phase distribution of the DPF with N = 16. (a2) Multifocal array generated by a RP beam and the DPF in (a1). (a3) Normalized intensity profiles along x- and y-directions denoted by dotted lines in (a2). (b1) Phase distribution of the DPF with N = 26. (b2) Multifocal array with the controllable polarization in each focal spot generated by an AP beam and the DPF in (b1). Double arrows indicate the polarization direction in each spot. (b3) Normalized intensity profiles along x- and y-directions denoted by dotted lines in (b2).
Fig. 4
Fig. 4 Transversal 2D multifocal arrays in the focal plane. (a1)-(c1) Phase distributions of the DPFs for achieving multifocal arrays with M = 5, 6 and 7 generated by RP beam, respectively. (a2)-(c2) Multifocal arrays generated by RP beam and the DPFs in (a1)-(c1), respectively. (d1)-(f1) Phase distributions of the DPFs for achieving multifocal arrays with M = 5, 6 and 7 generated by AP beam, respectively. (d2)-(f2) Multifocal arrays with controllable polarization in each focal spot generated by AP beam and the DPFs in (e1)-(f1), respectively. Double arrows indicate the polarization direction of each spot. The ranges of x- and y-coordinates in (a2)-(c2) and (d2)-(f2) are from −3λ0 to 3λ0. Scale bar is λ0.
Fig. 5
Fig. 5 Generated 3D multifocal arrays forming the letter pattern of HIT. (a1) and (a2) Phase distribution of the DPF and the corresponding 3D multifocal array generated by a RP beam. (b1) and (b2) Phase distribution of the DPF and the corresponding 3D multifocal array with the controllable polarization in each focal spot generated by an AP beam. Double arrows indicate the polarization direction in each spot.
Fig. 6
Fig. 6 Uniformities as functions of the parameter N for three filters. (a) and (b) Uniformities of the generated multifocal arrays with M = 6 and 7, respectively. The designed 3D position shifts and linear polarization directions for the multifocal arrays with M = 6 and 7 are shown in Table 1.
Fig. 7
Fig. 7 Uniformities of the multifocal array with M = 7 for different modulation factors. (a) Uniformities of the multifocal array generated by RP beam and the ordinal number j of the modulation factor Fj. (b) Uniformities of the multifocal array generated by AP beam and the ordinal number j of the modulation factor Fj. The designed 3D position shifts and linear polarization directions are shown in the last row of Table 1.

Tables (2)

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Table 1 Design Parameters and Uniformities of the Generated Multifocal Arrays

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Table 2 Design Parameters for 3D Multifocal Arrays Forming the Letter Pattern of HIT

Equations (7)

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E (x,y,z)=iA r R max P(θ,φ) E T (θ,φ) e ikzcosθ cosθ e i2π(xξ+yη) dξdη =iAFT[ P(θ,φ) E T (θ,φ) e ikzcosθ cosθ ] =iAFT[G(ξ,η)],
L(θ)=exp[ β 2 ( sinθ sinα ) 2 ] J 1 ( 2β sinθ sinα ),
E T (θ,φ)=[ sin 2 φ+cosθ cos 2 φ (cosθ1)cosφsinφ sinθcosφ (cosθ1)sinφcosφ cos 2 φ+cosθ sin 2 φ sinθsinφ cosφsinθ sinφsinθ cosθ ][ p x e x p y e y p z e z ],
E (xΔx,yΔy,zΔz)=iAFT[G(ξ,η) e i2π(Δxξ+Δyη) e ikΔzcosθ ],
Φ(Δx,Δy,Δz)=k(Δxsinθcosφ+Δysinθsinφ+Δzcosθ).
S(p,q)=Γ(qp+1,M),p=1,2,...,N;q=1,2,...,M
Γ(x,M)={ mod(x,M)for mod(x,M)0, Motherwise.

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