Abstract

We propose a method for producing multifocal spot arrays (MSAs) capable of controlling the position and polarization orientation of each focal spot with radially polarized Bessel-Gaussian beam. Based on a simple analytical equation that can be used to manipulate the position of the focal spot, we design a type of multi-zone plate (MZP) composed of many fan-shaped subareas which accordingly generate lateral position-controllable multifocal spots. By adding a π-phase difference between a division line passing through the center of the back aperture with different orientations to corresponding subareas of the MZP, we realize MSAs in which orientations of the linear polarization in each focal spot can be arbitrarily manipulated. Such position and polarization controllable MSAs may potentially have applications in many fields.

© 2015 Optical Society of America

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2015 (1)

L. Lermusiaux, V. Maillard, and S. Bidault, “Widefield spectral monitoring of nanometer distance changes in DNA-templated plasmon rulers,” ACS Nano 9(1), 978–990 (2015).
[Crossref] [PubMed]

2014 (9)

M. Gu, X. Li, and Y. Cao, “Optical storage arrays: a perspective for future big data storage,” Light Sci. Appl. 3(5), e177 (2014).
[Crossref]

M. P. Busson and S. Bidault, “Selective excitation of single molecules coupled to the bright mode of a plasmonic cavity,” Nano Lett. 14(1), 284–288 (2014).
[Crossref] [PubMed]

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2014).
[Crossref]

P. R. Dolan, X. Li, J. Storteboom, and M. Gu, “Complete determination of the orientation of NV centers with radially polarized beams,” Opt. Express 22(4), 4379–4387 (2014).
[Crossref] [PubMed]

C. Macias-Romero, P. R. T. Munro, and P. Török, “Polarization-multiplexed encoding at nanometer scales,” Opt. Express 22(21), 26240–26245 (2014).
[Crossref] [PubMed]

H. Ren, H. Lin, X. Li, and M. Gu, “Three-dimensional parallel recording with a Debye diffraction-limited and aberration-free volumetric multifocal array,” Opt. Lett. 39(6), 1621–1624 (2014).
[Crossref] [PubMed]

L. Zhu, J. Yu, D. Zhang, M. Sun, and J. Chen, “Multifocal spot array generated by fractional Talbot effect phase-only modulation,” Opt. Express 22(8), 9798–9808 (2014).
[Crossref] [PubMed]

L. Zhu, M. Sun, M. Zhu, J. Chen, X. Gao, W. Ma, and D. Zhang, “Three-dimensional shape-controllable focal spot array created by focusing vortex beams modulated by multi-value pure-phase grating,” Opt. Express 22(18), 21354–21367 (2014).
[Crossref] [PubMed]

H. Ren, X. Li, and M. Gu, “Polarization-multiplexed multifocal arrays by a π-phase-step-modulated azimuthally polarized beam,” Opt. Lett. 39(24), 6771–6774 (2014).
[Crossref] [PubMed]

2013 (9)

S. Hasegawa and Y. Hayasaki, “Polarization distribution control of parallel femtosecond pulses with spatial light modulators,” Opt. Express 21(11), 12987–12995 (2013).
[Crossref] [PubMed]

J. H. Clegg and M. A. A. Neil, “Double pass, common path method for arbitrary polarization control using a ferroelectric liquid crystal spatial light modulator,” Opt. Lett. 38(7), 1043–1045 (2013).
[Crossref] [PubMed]

E. H. Waller and G. von Freymann, “Multi foci with diffraction limited resolution,” Opt. Express 21(18), 21708–21713 (2013).
[Crossref] [PubMed]

K. Lou, S.-X. Qian, Z. C. Ren, C. Tu, Y. Li, and H. T. Wang, “Femtosecond laser processing by using patterned vector optical fields,” Sci. Rep. 3, 2281 (2013).
[Crossref] [PubMed]

H. Lin and M. Gu, “Creation of diffraction-limited non-Airy multifocal arrays using a spatially shifted vortex beam,” Appl. Phys. Lett. 102(8), 084103 (2013).
[Crossref]

M. Cai, C. Tu, H. Zhang, S. Qian, K. Lou, Y. Li, and H. T. Wang, “Subwavelength multiple focal spots produced by tight focusing the patterned vector optical fields,” Opt. Express 21(25), 31469–31482 (2013).
[Crossref] [PubMed]

M. Gu, H. Lin, and X. Li, “Parallel multiphoton microscopy with cylindrically polarized multifocal arrays,” Opt. Lett. 38(18), 3627–3630 (2013).
[Crossref] [PubMed]

F. Shafiei, C. Wu, Y. Wu, A. B. Khanikaev, P. Putzke, A. Singh, X. Li, and G. Shvets, “Plasmonic nano-protractor based on polarization spectro-tomography,” Nat. Photonics 7(5), 367–372 (2013).
[Crossref]

B. van den Broek, B. Ashcroft, T. H. Oosterkamp, and J. van Noort, “Parallel nanometric 3D tracking of intracellular gold nanorods using multifocal two-photon microscopy,” Nano Lett. 13(3), 980–986 (2013).
[Crossref] [PubMed]

2012 (3)

2011 (5)

2010 (4)

2009 (3)

D. Engström, A. Frank, J. Backsten, M. Goksör, and J. Bengtsson, “Grid-free 3D multiple spot generation with an efficient single-plane FFT-based algorithm,” Opt. Express 17(12), 9989–10000 (2009).
[Crossref] [PubMed]

Q. W. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

2008 (3)

2007 (2)

R. Di Leonardo, F. Ianni, and G. Ruocco, “Computer generation of optimal holograms for optical trap arrays,” Opt. Express 15(4), 1913–1922 (2007).
[Crossref] [PubMed]

K. Lindfors, A. Priimagi, T. Setala, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1(4), 228–231 (2007).
[Crossref]

2006 (2)

A. F. Abouraddy and K. C. Toussaint., “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96(15), 153901 (2006).
[Crossref] [PubMed]

M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, “Fast focus field calculations,” Opt. Express 14(23), 11277–11291 (2006).
[Crossref] [PubMed]

2005 (3)

E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial light modulator,” Opt. Express 13(10), 3777–3786 (2005).
[Crossref] [PubMed]

J. Ellis and A. Dogariu, “Optical polarimetry of random fields,” Phys. Rev. Lett. 95(20), 203905 (2005).
[Crossref] [PubMed]

C. Sönnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5(2), 301–304 (2005).
[Crossref] [PubMed]

2003 (2)

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

J. N. Forkey, M. E. Quinlan, M. A. Shaw, J. E. Corrie, and Y. E. Goldman, “Three-dimensional structural dynamics of myosin V by single-molecule fluorescence polarization,” Nature 422(6930), 399–404 (2003).
[Crossref] [PubMed]

2002 (1)

J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2(4), 279–283 (2002).
[Crossref]

2001 (2)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless scanning near-field optical microscopy,” J. Microsc. 202(1), 72–76 (2001).
[Crossref] [PubMed]

2000 (1)

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
[Crossref] [PubMed]

1999 (1)

S. A. Empedocles, R. Neuhauser, and M. G. Bawendi, “Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy,” Nature 399(6732), 126–130 (1999).
[Crossref]

1998 (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
[Crossref]

1959 (2)

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
[Crossref]

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(1247), 358–379 (1959).
[Crossref]

Abouraddy, A. F.

A. F. Abouraddy and K. C. Toussaint., “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96(15), 153901 (2006).
[Crossref] [PubMed]

Alivisatos, A. P.

C. Sönnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5(2), 301–304 (2005).
[Crossref] [PubMed]

Ashcroft, B.

B. van den Broek, B. Ashcroft, T. H. Oosterkamp, and J. van Noort, “Parallel nanometric 3D tracking of intracellular gold nanorods using multifocal two-photon microscopy,” Nano Lett. 13(3), 980–986 (2013).
[Crossref] [PubMed]

Backsten, J.

Banzer, P.

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2014).
[Crossref]

Bauer, T.

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2014).
[Crossref]

Bawendi, M. G.

S. A. Empedocles, R. Neuhauser, and M. G. Bawendi, “Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy,” Nature 399(6732), 126–130 (1999).
[Crossref]

Bengtsson, J.

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Bidault, S.

L. Lermusiaux, V. Maillard, and S. Bidault, “Widefield spectral monitoring of nanometer distance changes in DNA-templated plasmon rulers,” ACS Nano 9(1), 978–990 (2015).
[Crossref] [PubMed]

M. P. Busson and S. Bidault, “Selective excitation of single molecules coupled to the bright mode of a plasmonic cavity,” Nano Lett. 14(1), 284–288 (2014).
[Crossref] [PubMed]

Botvinick, E.

Bowman, R.

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Burnham, D. R.

Busson, M. P.

M. P. Busson and S. Bidault, “Selective excitation of single molecules coupled to the bright mode of a plasmonic cavity,” Nano Lett. 14(1), 284–288 (2014).
[Crossref] [PubMed]

Cai, M.

Cao, H.

Cao, W.

Cao, Y.

M. Gu, X. Li, and Y. Cao, “Optical storage arrays: a perspective for future big data storage,” Light Sci. Appl. 3(5), e177 (2014).
[Crossref]

Chen, J.

Chen, W.

W. Chen and Q. Zhan, “Three dimensional polarization control in 4Pi microscopy,” Opt. Commun. 284(1), 52–56 (2011).
[Crossref]

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[Crossref]

Chichkov, B. N.

Chiu, D. T.

Chon, J. W. M.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

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]

Clark, R. L.

Clegg, J. H.

Cole, D. G.

Cooper, J.

Corrie, J. E.

J. N. Forkey, M. E. Quinlan, M. A. Shaw, J. E. Corrie, and Y. E. Goldman, “Three-dimensional structural dynamics of myosin V by single-molecule fluorescence polarization,” Nature 422(6930), 399–404 (2003).
[Crossref] [PubMed]

Courtial, J.

Dainty, C.

Di Leonardo, R.

Dogariu, A.

J. Ellis and A. Dogariu, “Optical polarimetry of random fields,” Phys. Rev. Lett. 95(20), 203905 (2005).
[Crossref] [PubMed]

Dolan, P. R.

Dorn, R.

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J. N. Forkey, M. E. Quinlan, M. A. Shaw, J. E. Corrie, and Y. E. Goldman, “Three-dimensional structural dynamics of myosin V by single-molecule fluorescence polarization,” Nature 422(6930), 399–404 (2003).
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Friberg, A. T.

K. Lindfors, A. Priimagi, T. Setala, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1(4), 228–231 (2007).
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M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
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Li, X.

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Neil, M. A. A.

Neuhauser, R.

S. A. Empedocles, R. Neuhauser, and M. G. Bawendi, “Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy,” Nature 399(6732), 126–130 (1999).
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M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
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Nordlander, P.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
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L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
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B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
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Obata, K.

Oosterkamp, T. H.

B. van den Broek, B. Ashcroft, T. H. Oosterkamp, and J. van Noort, “Parallel nanometric 3D tracking of intracellular gold nanorods using multifocal two-photon microscopy,” Nano Lett. 13(3), 980–986 (2013).
[Crossref] [PubMed]

Orlov, S.

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2014).
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Padgett, M. J.

Peschel, U.

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2014).
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Petersen, P. B.

J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2(4), 279–283 (2002).
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Preece, D.

Priimagi, A.

K. Lindfors, A. Priimagi, T. Setala, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1(4), 228–231 (2007).
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Putzke, P.

F. Shafiei, C. Wu, Y. Wu, A. B. Khanikaev, P. Putzke, A. Singh, X. Li, and G. Shvets, “Plasmonic nano-protractor based on polarization spectro-tomography,” Nat. Photonics 7(5), 367–372 (2013).
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Qian, S.-X.

K. Lou, S.-X. Qian, Z. C. Ren, C. Tu, Y. Li, and H. T. Wang, “Femtosecond laser processing by using patterned vector optical fields,” Sci. Rep. 3, 2281 (2013).
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Quabis, S.

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

J. N. Forkey, M. E. Quinlan, M. A. Shaw, J. E. Corrie, and Y. E. Goldman, “Three-dimensional structural dynamics of myosin V by single-molecule fluorescence polarization,” Nature 422(6930), 399–404 (2003).
[Crossref] [PubMed]

Ramstein, M.

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless scanning near-field optical microscopy,” J. Microsc. 202(1), 72–76 (2001).
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Rao, R.

Ren, H.

Ren, Z. C.

K. Lou, S.-X. Qian, Z. C. Ren, C. Tu, Y. Li, and H. T. Wang, “Femtosecond laser processing by using patterned vector optical fields,” Sci. Rep. 3, 2281 (2013).
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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(1247), 358–379 (1959).
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Rodríguez-Herrera, O. G.

Rubinsztein-Dunlop, H.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
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Ruocco, G.

Sandoghdar, V.

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless scanning near-field optical microscopy,” J. Microsc. 202(1), 72–76 (2001).
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Saykally, R. J.

J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2(4), 279–283 (2002).
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Schaller, R. D.

J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2(4), 279–283 (2002).
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Schonbrun, E.

Setala, T.

K. Lindfors, A. Priimagi, T. Setala, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1(4), 228–231 (2007).
[Crossref]

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F. Shafiei, C. Wu, Y. Wu, A. B. Khanikaev, P. Putzke, A. Singh, X. Li, and G. Shvets, “Plasmonic nano-protractor based on polarization spectro-tomography,” Nat. Photonics 7(5), 367–372 (2013).
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J. N. Forkey, M. E. Quinlan, M. A. Shaw, J. E. Corrie, and Y. E. Goldman, “Three-dimensional structural dynamics of myosin V by single-molecule fluorescence polarization,” Nature 422(6930), 399–404 (2003).
[Crossref] [PubMed]

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]

Shevchenko, A.

K. Lindfors, A. Priimagi, T. Setala, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1(4), 228–231 (2007).
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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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Shvets, G.

F. Shafiei, C. Wu, Y. Wu, A. B. Khanikaev, P. Putzke, A. Singh, X. Li, and G. Shvets, “Plasmonic nano-protractor based on polarization spectro-tomography,” Nat. Photonics 7(5), 367–372 (2013).
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B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85(21), 4482–4485 (2000).
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Singh, A.

F. Shafiei, C. Wu, Y. Wu, A. B. Khanikaev, P. Putzke, A. Singh, X. Li, and G. Shvets, “Plasmonic nano-protractor based on polarization spectro-tomography,” Nat. Photonics 7(5), 367–372 (2013).
[Crossref]

Sobhani, H.

M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332(6030), 702–704 (2011).
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C. Sönnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5(2), 301–304 (2005).
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Storteboom, J.

Sun, M.

Tien, C. H.

X. Li, T. H. Lan, C. H. Tien, and M. Gu, “Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam,” Nat. Commun. 3, 998 (2012).
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van den Broek, B.

B. van den Broek, B. Ashcroft, T. H. Oosterkamp, and J. van Noort, “Parallel nanometric 3D tracking of intracellular gold nanorods using multifocal two-photon microscopy,” Nano Lett. 13(3), 980–986 (2013).
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van Noort, J.

B. van den Broek, B. Ashcroft, T. H. Oosterkamp, and J. van Noort, “Parallel nanometric 3D tracking of intracellular gold nanorods using multifocal two-photon microscopy,” Nano Lett. 13(3), 980–986 (2013).
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Waller, E. H.

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).
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Wang, H. T.

Wang, S.

Wolf, E.

E. Wolf, “Electromagnetic diffraction in optical systems I. An integral representation of the image field,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 349–357 (1959).
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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(1247), 358–379 (1959).
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Wu, C.

F. Shafiei, C. Wu, Y. Wu, A. B. Khanikaev, P. Putzke, A. Singh, X. Li, and G. Shvets, “Plasmonic nano-protractor based on polarization spectro-tomography,” Nat. Photonics 7(5), 367–372 (2013).
[Crossref]

Wu, Y.

F. Shafiei, C. Wu, Y. Wu, A. B. Khanikaev, P. Putzke, A. Singh, X. Li, and G. Shvets, “Plasmonic nano-protractor based on polarization spectro-tomography,” Nat. Photonics 7(5), 367–372 (2013).
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Wulff, K.

Wulff, K. D.

Yan, H.

J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2(4), 279–283 (2002).
[Crossref]

Yang, P.

J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2(4), 279–283 (2002).
[Crossref]

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
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Yu, J.

Zalevsky, Z.

Zhan, Q.

W. Chen and Q. Zhan, “Three dimensional polarization control in 4Pi microscopy,” Opt. Commun. 284(1), 52–56 (2011).
[Crossref]

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
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Zhan, Q. W.

Q. W. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
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Zhang, D.

Zhang, H.

Zhou, C.

Zhu, L.

Zhu, M.

Zijlstra, P.

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

ACS Nano (1)

L. Lermusiaux, V. Maillard, and S. Bidault, “Widefield spectral monitoring of nanometer distance changes in DNA-templated plasmon rulers,” ACS Nano 9(1), 978–990 (2015).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

Q. W. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

H. Lin and M. Gu, “Creation of diffraction-limited non-Airy multifocal arrays using a spatially shifted vortex beam,” Appl. Phys. Lett. 102(8), 084103 (2013).
[Crossref]

J. Microsc. (1)

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless scanning near-field optical microscopy,” J. Microsc. 202(1), 72–76 (2001).
[Crossref] [PubMed]

J. Opt. (1)

W. Chen and Q. Zhan, “Diffraction limited focusing with controllable arbitrary three-dimensional polarization,” J. Opt. 12(4), 045707 (2010).
[Crossref]

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

Light Sci. Appl. (1)

M. Gu, X. Li, and Y. Cao, “Optical storage arrays: a perspective for future big data storage,” Light Sci. Appl. 3(5), e177 (2014).
[Crossref]

Nano Lett. (4)

B. van den Broek, B. Ashcroft, T. H. Oosterkamp, and J. van Noort, “Parallel nanometric 3D tracking of intracellular gold nanorods using multifocal two-photon microscopy,” Nano Lett. 13(3), 980–986 (2013).
[Crossref] [PubMed]

C. Sönnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5(2), 301–304 (2005).
[Crossref] [PubMed]

M. P. Busson and S. Bidault, “Selective excitation of single molecules coupled to the bright mode of a plasmonic cavity,” Nano Lett. 14(1), 284–288 (2014).
[Crossref] [PubMed]

J. C. Johnson, H. Yan, R. D. Schaller, P. B. Petersen, P. Yang, and R. J. Saykally, “Near-field imaging of nonlinear optical mixing in single zinc oxide nanowires,” Nano Lett. 2(4), 279–283 (2002).
[Crossref]

Nat. Commun. (1)

X. Li, T. H. Lan, C. H. Tien, and M. Gu, “Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam,” Nat. Commun. 3, 998 (2012).
[Crossref] [PubMed]

Nat. Photonics (4)

F. Shafiei, C. Wu, Y. Wu, A. B. Khanikaev, P. Putzke, A. Singh, X. Li, and G. Shvets, “Plasmonic nano-protractor based on polarization spectro-tomography,” Nat. Photonics 7(5), 367–372 (2013).
[Crossref]

T. Bauer, S. Orlov, U. Peschel, P. Banzer, and G. Leuchs, “Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams,” Nat. Photonics 8(1), 23–27 (2014).
[Crossref]

K. Lindfors, A. Priimagi, T. Setala, A. Shevchenko, A. T. Friberg, and M. Kaivola, “Local polarization of tightly focused unpolarized light,” Nat. Photonics 1(4), 228–231 (2007).
[Crossref]

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]

Nature (4)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998).
[Crossref]

J. N. Forkey, M. E. Quinlan, M. A. Shaw, J. E. Corrie, and Y. E. Goldman, “Three-dimensional structural dynamics of myosin V by single-molecule fluorescence polarization,” Nature 422(6930), 399–404 (2003).
[Crossref] [PubMed]

P. Zijlstra, J. W. M. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009).
[Crossref] [PubMed]

S. A. Empedocles, R. Neuhauser, and M. G. Bawendi, “Three-dimensional orientation measurements of symmetric single chromophores using polarization microscopy,” Nature 399(6732), 126–130 (1999).
[Crossref]

Opt. Commun. (1)

W. Chen and Q. Zhan, “Three dimensional polarization control in 4Pi microscopy,” Opt. Commun. 284(1), 52–56 (2011).
[Crossref]

Opt. Express (18)

F. Kenny, D. Lara, O. G. Rodríguez-Herrera, and C. Dainty, “Complete polarization and phase control for focus-shaping in high-NA microscopy,” Opt. Express 20(13), 14015–14029 (2012).
[Crossref] [PubMed]

H. Kang, B. Jia, and M. Gu, “Polarization characterization in the focal volume of high numerical aperture objectives,” Opt. Express 18(10), 10813–10821 (2010).
[Crossref] [PubMed]

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Supplementary Material (2)

NameDescription
» Visualization 1: MP4 (723 KB)      Video 1
» Visualization 2: MP4 (609 KB)      Video 2

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram showing the geometry for the calculation of the focused field distribution and the variables involved.
Fig. 2
Fig. 2 Schematic diagram showing the multi-zone phase distributions used to generate the MSA. (a) The back aperture plane of the objective. (b) A single fan-shaped area with multiple subareas, where the blue line denotes one fan-shaped area as shown in (a), and red lines denote smaller fan-shaped subarea.
Fig. 3
Fig. 3 MZP patterns (N = 50) filled with phase-only distribution as described by Eq. (7) when (a) M = 4, (b) M = 5 and (c) M = 7. (d), (e) and (f) are the corresponding intensity distribution in the focal plane when the high NA objective are modulated by the phase shown in (a), (b) and (c), respectively. Dynamic MSAs with individually controllable position can be created easily using that MZPs (see Visualization 1).
Fig. 4
Fig. 4 The intensity distributions of four spots array in the focal plane when the high NA objective are modulated by the MZPs with the same parameters used in the Fig. 3(a), except the numbers of N: (a) N = 4 and (b) N = 40. (c) and (d) are the corresponding 3D iso-intensity surfaces of single spot shown in Figs. 4(a) and 4(b), respectively. (e) shows the 3D iso-intensity surface of single spot in the square array when N = 50 (as shown in Fig. 3(d)). (f) and (g) show the intensity cross-section profiles of Fig. 4(b). (h) The uniformity changes as a function of the number N.
Fig. 5
Fig. 5 (a) Amplitude and polarization distribution of a radially polarized Bessel-Gaussian beam. The corresponding intensity and polarization distributions in the focal plane is shown in (f). (b) - (e) show the π-phase shift modulations with different diametric directions. (g) - (j) are the corresponding intensity and polarization distributions of the focal spot when the high NA objective modulated by the adding π-phase shift as show in (b) - (e), respectively.
Fig. 6
Fig. 6 (a) Phase distribution of a MZP with different π-phase shift in each subarea. (b) The corresponding intensity and polarization distributions of the MSA in the focal plane. Dynamic MSAs with controllable polarization in each focal spot can be realized. (see Visualization 2)
Fig. 7
Fig. 7 Comparison of intensity plots of single focal spot illuminated by the RPBG with or without π-MZP modulation along the (a) x and (b) y directions. (c) The uniformity of seven spots and the maximum intensity of the central spot in hexagonal MSAs as a function of the radial shifting distances.

Equations (8)

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E ( x , y , z ) = A 0 α 0 2 π P ( θ ) E t ( θ , ϕ ) × exp { i k x 2 + y 2 sin θ cos [ tan 1 ( y / x ) ϕ ] } e x p ( i k z cos θ ) sin θ d ϕ d θ ,
E ( x , y , z ) = 0 α 0 2 π P ( θ ) E t ( θ , ϕ ) e x p [ i ( k z z k x x k y y ) ] sin θ d ϕ d θ ,
E ( x , y , z ) = P ( θ ) E t ( θ , ϕ ) / cos θ × e x p ( i k z z ) e x p [ i 2 π ( ξ x + η y ) ] d ξ d η ,
E z ( x , y ) = F { G ( ξ , η ) } ,
G ( ξ , η ) = P ( θ ) E t ( θ , ϕ ) / cos θ × e x p ( i k z z ) .
E z ( x Δ x , y Δ y ) = F { exp [ i 2 π ( ξ Δ x + η Δ y ) ] G ( ξ , η ) } ,
ψ ( x 0 , y 0 ) = 2 π λ N A R n t ( x 0 Δ x + y 0 Δ y ) ,
P ( θ ) = exp [ β 2 ( sin θ sin α ) 2 ] J 1 ( 2 β sin θ sin α ) ,

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