Abstract

We propose an approach for generating a multifocal spot array (MSA) with a high numerical aperture (NA) objective. The MSA is generated by using a special designed phase-only modulation at the back aperture of an objective. Without using any iteration algorithm, the modulated phase pattern is directly obtained by the simple analytical expressions based on the fractional Talbot effect. It is shown that the number of the spots in the focal region depends solely on the fractional Talbot parameter. By engineering the phase pattern with a large fractional Talbot parameter, a large number of focal spots can be created. Furthermore, the intensity distribution of each focal spot can be manipulated by introducing a composite spatially shifted vortex beam (CSSVB) as the incident field, leading to creation of various kinds of specific shaped spots. Consequently, the MSA composed of multiple individual spots with specific shape is created by focusing the CSSVB combined with the multifocal phase-only modulation. These kinds of MSAs may be found applications in parallel optical micromanipulation, multifocal multiphoton microscopic imaging, and parallel laser printing nanofabrication.

© 2014 Optical Society of America

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    [Crossref]

2014 (1)

J. Chen, X. Gao, L. Zhu, Q. Xu, and W. Ma, “The generation of a complete spiral spot and multi split rings by focusing three circularly polarized vortex beams,” Opt. Commun. 318, 100–104 (2014).
[Crossref]

2013 (6)

2012 (4)

J. Chen, Q. Xu, and G. Wang, “A four-quadrant phase filter for creating two focusing spots,” Opt. Commun. 285(6), 900–904 (2012).
[Crossref]

J. Yu, C. Zhou, W. Jia, W. Cao, S. Wang, J. Ma, and H. Cao, “Three-dimensional Dammann array,” Appl. Opt. 51(10), 1619–1630 (2012).
[Crossref] [PubMed]

J. Yu, C. Zhou, W. Jia, A. Hu, W. Cao, J. Wu, and S. Wang, “Three-dimensional Dammann vortex array with tunable topological charge,” Appl. Opt. 51(13), 2485–2490 (2012).
[Crossref] [PubMed]

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100(12), 121101 (2012).
[Crossref]

2011 (7)

2010 (5)

2009 (3)

2008 (2)

2007 (3)

2006 (2)

2005 (2)

J. Kato, N. Takeyasu, Y. Adachi, H. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. D. 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]

2004 (1)

2003 (2)

2002 (2)

R. L. Eriksen, V. R. Daria, and J. Gluckstad, “Fully dynamic multiple-beam optical tweezers,” Opt. Express 10(14), 597–602 (2002).
[Crossref] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

2001 (1)

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(3), 368–376 (2001).
[Crossref] [PubMed]

2000 (2)

1999 (1)

1995 (1)

C. Zhou and L. Liu, “Simple equations for the calculation of a multilevel phase grating for Talbot array illumination,” Opt. Commun. 115(1–2), 40–44 (1995).
[Crossref]

1990 (1)

1971 (1)

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik (Stuttg.) 34(3), 275–284 (1971).

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]

Adachi, Y.

J. Kato, N. Takeyasu, Y. Adachi, H. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

Ahlawat, S.

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100(12), 121101 (2012).
[Crossref]

Andresen, P.

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(3), 368–376 (2001).
[Crossref] [PubMed]

Antolini, R.

Araki, T.

Arisaka, K.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8(2), 139–142 (2011).
[Crossref] [PubMed]

Backsten, J.

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Bahlmann, K.

Bellve, K.

Bengtsson, J.

Booth, M. J.

Burnham, D. R.

Cai, M.

Cao, G. W.

Cao, H.

Cao, W.

Chen, J.

J. Chen, X. Gao, L. Zhu, Q. Xu, and W. Ma, “The generation of a complete spiral spot and multi split rings by focusing three circularly polarized vortex beams,” Opt. Commun. 318, 100–104 (2014).
[Crossref]

J. Chen, Q. Xu, and G. Wang, “A four-quadrant phase filter for creating two focusing spots,” Opt. Commun. 285(6), 900–904 (2012).
[Crossref]

J. Chen and Y. Yu, “The focusing property of vector Bessel–Gauss beams by a high numerical aperture objective,” Opt. Commun. 283(9), 1655–1660 (2010).
[Crossref]

Cheng, A.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8(2), 139–142 (2011).
[Crossref] [PubMed]

Chichkov, B. N.

Chiu, D. T.

Choudhury, A.

Clark, R. L.

Cole, D. G.

Cooper, J.

Cottrell, D. M.

Courtial, J.

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Daria, V. R.

Dasgupta, R.

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100(12), 121101 (2012).
[Crossref]

Davis, J. A.

Decker, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Di Leonardo, R.

Dong, X.

Duadi, H.

Engström, D.

Eriksen, R. L.

Fittinghoff, D. N.

Fournier, J.-M.

Frank, A.

Fricke, M.

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(3), 368–376 (2001).
[Crossref] [PubMed]

Froner, E.

Fujita, K.

Gansel, J. K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Gao, X.

J. Chen, X. Gao, L. Zhu, Q. Xu, and W. Ma, “The generation of a complete spiral spot and multi split rings by focusing three circularly polarized vortex beams,” Opt. Commun. 318, 100–104 (2014).
[Crossref]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik (Stuttg.) 34(3), 275–284 (1971).

Gluckstad, J.

Goksör, M.

Golshani, P.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8(2), 139–142 (2011).
[Crossref] [PubMed]

Gonçalves, J. T.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8(2), 139–142 (2011).
[Crossref] [PubMed]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Gu, M.

Guo, C.-S.

Guo, H.

Gupta, P. K.

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100(12), 121101 (2012).
[Crossref]

Hashimoto, M.

Hellweg, D.

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(3), 368–376 (2001).
[Crossref] [PubMed]

Hernandez, T. J.

Hinze, U.

Hong, Z.

Hu, A.

Hu, Q.

Hu, Y.

J. Zhao, B. Li, H. Zhao, Y. Hu, W. Wang, and Y. Wang, “Tight focusing properties of the azimuthal discrete phase modulated radially polarized LG11 beam,” Opt. Commun. 296, 95–100 (2013).
[Crossref]

Huang, K.

Ianni, F.

Jenness, N. J.

Jesacher, A.

Jia, B.

Jia, W.

Johannes, M. S.

Jordan, P.

Joseph, J.

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100(12), 121101 (2012).
[Crossref]

Kato, J.

J. Kato, N. Takeyasu, Y. Adachi, H. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

Kawata, S.

Kim, P.-S.

Kirber, M.

Koch, J.

Kosicki, B.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Lasser, T.

Lee, G.

Leitgeb, R. A.

Leutenegger, M.

Li, B.

J. Zhao, B. Li, H. Zhao, Y. Hu, W. Wang, and Y. Wang, “Tight focusing properties of the azimuthal discrete phase modulated radially polarized LG11 beam,” Opt. Commun. 296, 95–100 (2013).
[Crossref]

Li, H.

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, “High-speed spectrally resolved multifocal multiphoton microscopy,” Appl. Phys. B 99(4), 633–637 (2010).
[Crossref]

Li, K.

Li, X.

Li, Y.

Li, Y. P.

Lin, H.

Linden, S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

Liu, L.

C. Zhou and L. Liu, “Simple equations for the calculation of a multilevel phase grating for Talbot array illumination,” Opt. Commun. 115(1–2), 40–44 (1995).
[Crossref]

Lohmann, A. W.

Lou, K.

Ma, J.

Ma, W.

J. Chen, X. Gao, L. Zhu, Q. Xu, and W. Ma, “The generation of a complete spiral spot and multi split rings by focusing three circularly polarized vortex beams,” Opt. Commun. 318, 100–104 (2014).
[Crossref]

Martínez, J. L.

McGonagle, W.

Merenda, F.

Minamikawa, T.

Moreno, I.

Morita, R.

Murakami, N.

Nielsen, T.

T. Nielsen, M. Fricke, D. Hellweg, and P. Andresen, “High efficiency beam splitter for multifocal multiphoton microscopy,” J. Microsc. 201(3), 368–376 (2001).
[Crossref] [PubMed]

Niu, H.

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, “High-speed spectrally resolved multifocal multiphoton microscopy,” Appl. Phys. B 99(4), 633–637 (2010).
[Crossref]

Obata, K.

Oh, C.-H.

Oka, K.

Padgett, M.

Padgett, M. J.

Pavone, F. S.

Piestun, R.

Portera-Cailliau, C.

A. Cheng, J. T. Gonçalves, P. Golshani, K. Arisaka, and C. Portera-Cailliau, “Simultaneous two-photon calcium imaging at different depths with spatiotemporal multiplexing,” Nat. Methods 8(2), 139–142 (2011).
[Crossref] [PubMed]

Qi, J.

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, “High-speed spectrally resolved multifocal multiphoton microscopy,” Appl. Phys. B 99(4), 633–637 (2010).
[Crossref]

Qian, S.

Qu, J.

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, “High-speed spectrally resolved multifocal multiphoton microscopy,” Appl. Phys. B 99(4), 633–637 (2010).
[Crossref]

Rao, R.

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Sakamoto, M.

Salathé, R.-P.

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Schneider, T.

Schonbrun, E.

Shao, Y.

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, “High-speed spectrally resolved multifocal multiphoton microscopy,” Appl. Phys. B 99(4), 633–637 (2010).
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[Crossref]

Thiel, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
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Thomas, J. A.

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E. H. Waller and G. von Freymann, “Multi foci with diffraction limited resolution,” Opt. Express 21(18), 21708–21713 (2013).
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J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
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Waller, E. H.

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J. Chen, Q. Xu, and G. Wang, “A four-quadrant phase filter for creating two focusing spots,” Opt. Commun. 285(6), 900–904 (2012).
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J. Zhao, B. Li, H. Zhao, Y. Hu, W. Wang, and Y. Wang, “Tight focusing properties of the azimuthal discrete phase modulated radially polarized LG11 beam,” Opt. Commun. 296, 95–100 (2013).
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Wang, Y.

J. Zhao, B. Li, H. Zhao, Y. Hu, W. Wang, and Y. Wang, “Tight focusing properties of the azimuthal discrete phase modulated radially polarized LG11 beam,” Opt. Commun. 296, 95–100 (2013).
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Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, “High-speed spectrally resolved multifocal multiphoton microscopy,” Appl. Phys. B 99(4), 633–637 (2010).
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Wegener, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
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J. Chen, X. Gao, L. Zhu, Q. Xu, and W. Ma, “The generation of a complete spiral spot and multi split rings by focusing three circularly polarized vortex beams,” Opt. Commun. 318, 100–104 (2014).
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J. Chen, Q. Xu, and G. Wang, “A four-quadrant phase filter for creating two focusing spots,” Opt. Commun. 285(6), 900–904 (2012).
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Yang, N.

Yin, X.

Yu, J.

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J. Chen and Y. Yu, “The focusing property of vector Bessel–Gauss beams by a high numerical aperture objective,” Opt. Commun. 283(9), 1655–1660 (2010).
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Zhan, Q.

Zhang, H.

Zhang, X. B.

Zhao, H.

J. Zhao, B. Li, H. Zhao, Y. Hu, W. Wang, and Y. Wang, “Tight focusing properties of the azimuthal discrete phase modulated radially polarized LG11 beam,” Opt. Commun. 296, 95–100 (2013).
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Zhao, J.

J. Zhao, B. Li, H. Zhao, Y. Hu, W. Wang, and Y. Wang, “Tight focusing properties of the azimuthal discrete phase modulated radially polarized LG11 beam,” Opt. Commun. 296, 95–100 (2013).
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Zhou, C.

Zhu, L.

J. Chen, X. Gao, L. Zhu, Q. Xu, and W. Ma, “The generation of a complete spiral spot and multi split rings by focusing three circularly polarized vortex beams,” Opt. Commun. 318, 100–104 (2014).
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Zhu, L.-W.

Zhuang, S.

Appl. Opt. (5)

Appl. Phys. B (1)

Y. Shao, J. Qu, H. Li, Y. Wang, J. Qi, G. Xu, and H. Niu, “High-speed spectrally resolved multifocal multiphoton microscopy,” Appl. Phys. B 99(4), 633–637 (2010).
[Crossref]

Appl. Phys. Lett. (3)

J. Kato, N. Takeyasu, Y. Adachi, H. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
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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).
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J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100(12), 121101 (2012).
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J. Opt. Soc. Am. A (2)

Nat. Methods (1)

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Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
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Opt. Commun. (6)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

J. Chen, Q. Xu, and G. Wang, “A four-quadrant phase filter for creating two focusing spots,” Opt. Commun. 285(6), 900–904 (2012).
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J. Chen and Y. Yu, “The focusing property of vector Bessel–Gauss beams by a high numerical aperture objective,” Opt. Commun. 283(9), 1655–1660 (2010).
[Crossref]

J. Zhao, B. Li, H. Zhao, Y. Hu, W. Wang, and Y. Wang, “Tight focusing properties of the azimuthal discrete phase modulated radially polarized LG11 beam,” Opt. Commun. 296, 95–100 (2013).
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J. Chen, X. Gao, L. Zhu, Q. Xu, and W. Ma, “The generation of a complete spiral spot and multi split rings by focusing three circularly polarized vortex beams,” Opt. Commun. 318, 100–104 (2014).
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Opt. Express (16)

M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, “Fast focus field calculations,” Opt. Express 14(23), 11277–11291 (2006).
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N. J. Jenness, K. D. Wulff, M. S. Johannes, M. J. Padgett, D. G. Cole, and R. L. Clark, “Three-dimensional parallel holographic micropatterning using a spatial light modulator,” Opt. Express 16(20), 15942–15948 (2008).
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E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial light modulator,” Opt. Express 13(10), 3777–3786 (2005).
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D. R. Burnham, T. Schneider, and D. T. Chiu, “Effects of aliasing on the fidelity of a two dimensional array of foci generated with a kinoform,” Opt. Express 19(18), 17121–17126 (2011).
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H. Guo, G. Sui, X. Weng, X. Dong, Q. Hu, and S. Zhuang, “Control of the multifocal properties of composite vector beams in tightly focusing systems,” Opt. Express 19(24), 24067–24077 (2011).
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K. Obata, J. Koch, U. Hinze, and B. N. Chichkov, “Multi-focus two-photon polymerization technique based on individually controlled phase modulation,” Opt. Express 18(16), 17193–17200 (2010).
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E. H. Waller and G. von Freymann, “Multi foci with diffraction limited resolution,” Opt. Express 21(18), 21708–21713 (2013).
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R. Di Leonardo, F. Ianni, and G. Ruocco, “Computer generation of optimal holograms for optical trap arrays,” Opt. Express 15(4), 1913–1922 (2007).
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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).
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K. Bahlmann, P. T. C. So, M. Kirber, R. Reich, B. Kosicki, W. McGonagle, and K. Bellve, “Multifocal multiphoton microscopy (MMM) at a frame rate beyond 600 Hz,” Opt. Express 15(17), 10991–10998 (2007).
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R. L. Eriksen, V. R. Daria, and J. Gluckstad, “Fully dynamic multiple-beam optical tweezers,” Opt. Express 10(14), 597–602 (2002).
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T. Minamikawa, M. Hashimoto, K. Fujita, S. Kawata, and T. Araki, “Multi-focus excitation coherent anti-Stokes Raman scattering (CARS) microscopy and its applications for real-time imaging,” Opt. Express 17(12), 9526–9536 (2009).
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A. Jesacher and M. J. Booth, “Parallel direct laser writing in three dimensions with spatially dependent aberration correction,” Opt. Express 18(20), 21090–21099 (2010).
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D. N. Fittinghoff, P. W. Wiseman, and J. A. Squier, “Widefield multiphoton and temporally decorrelated multifocal multiphoton microscopy,” Opt. Express 7(8), 273–279 (2000).
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F. Merenda, J. Rohner, J.-M. Fournier, and R.-P. Salathé, “Miniaturized high-NA focusing-mirror multiple optical tweezers,” Opt. Express 15(10), 6075–6086 (2007).
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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).
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Opt. Lett. (9)

H. Guo, X. Dong, X. Weng, G. Sui, N. Yang, and S. Zhuang, “Multifocus with small size, uniform intensity, and nearly circular symmetry,” Opt. Lett. 36(12), 2200–2202 (2011).
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H. Lin, B. Jia, and M. Gu, “Dynamic generation of Debye diffraction-limited multifocal arrays for direct laser printing nanofabrication,” Opt. Lett. 36(3), 406–408 (2011).
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M. Gu, H. Lin, and X. Li, “Parallel multiphoton microscopy with cylindrically polarized multifocal arrays,” Opt. Lett. 38(18), 3627–3630 (2013).
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K. Huang, P. Shi, G. W. Cao, K. Li, X. B. Zhang, and Y. P. Li, “Vector-vortex Bessel-Gauss beams and their tightly focusing properties,” Opt. Lett. 36(6), 888–890 (2011).
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Optik (Stuttg.) (1)

R. W. Gerchberg and W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik (Stuttg.) 34(3), 275–284 (1971).

Proc. R. Soc. Lond. A Math. Phys. Sci. (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]

Science (1)

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) Phase distribution inside the back aperture of a MSA system with fractional Talbot parameter β = 5, and period number inside the objective aperture Nx = Ny = 20. (b) Enlarged phase distribution in one unit cell. (c) Intensity distribution on the focal plane. (d) Enlarged intensity distributions of one focal spot. (e) and (f) are the corresponding intensity cross-section profiles in (c) and (d), respectively. (Ix and Iy are the cross-section profiles in x and y direction, respectively).

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Fig. 2
Fig. 2

(a) 2D intensity distribution (yz plane) in a meridional plane near focus with the same parameters in Fig. 1. (b) Intensity distribution (xy plane) on the plane of z = 1μm. (c) The 3D iso-intensity surfaces of one focal spot (I(x,y,z) = e-1…-4Imax).

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Fig. 3
Fig. 3

Phase patterns inside the objective aperture of fractional Talbot phase-only modulation with (a) β = 5, (b) β = 15. (c) and (d) Corresponding intensity distributions on the focal plane. (e) Intensity cross-section profiles in (c) and (d), respectively.

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Fig. 4
Fig. 4

Phase patterns of (a) a vortex beam with topological charge l = −1, (b) the multifocal phase, and (c) the combined phase. (d) Intensity distribution on the focal plane. (e) Enlarged image of one focal spot. (f) Intensity cross-section profiles of single focal spot generated by vortex beam without multifocal phase modulation (Iv), and with array phase in the arrays Ia1 with Δx = 2.95 μm, Ia2 with Δx = 4.43 μm, respectively

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Fig. 5
Fig. 5

Phase patterns of (a) multifocal phase with β = 9, (b) spatially shifted vortex phase along x direction, (c) spatially shifted vortex phase along x and y directions. (d) and (g) are the intensity distributions on the focal plane with the combined multifocal and shifted vortex phase. (e) and (h) are the enlarged images of one spot. (f) and (i) are the iso-intenstiy surfaces given by the intensity at the half of the peak value, corresponding to (e) and (h), respectively.

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Equations (10)

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A( r )={ 1 r≤R 0 otherwise ,
E → (x,y,z)= ∫ 0 α ∫ 0 2π [ U( θ,φ ) E → t ( θ,φ ) ] ×exp{ik( x 2 + y 2 sinθcos[ tan −1 (y/x)−φ]+zcosθ)}sinθdφdθ,
E → ( x,y,z )= ∬ [ U( r,φ ) E → t ( θ,φ ) exp(i k z z) / cosθ ]exp[ −i( k x x+ k y y) ]d k x d k y =F{ U( k x , k y ) }∗ E → 0 ( x,y,z ),
E → 0 ( x,y,z )=F{ E → t ( θ,φ ) exp( i k z z ) / cosθ }.
Φ ( m , n , β ) = π 2 ( γ − 1 β ) ( m 2 + n 2 ) ,
u ( x 0 , y 0 ) = rect ( x 0 Δ , y 0 Δ ) { ∑ h 1 = 0 β − 1 ∑ h 2 = 0 β − 1 δ ( x 0 − h 1 d , y 0 − h 2 d ) exp [ i ϕ ( h 1 , h 2 , β ) ] } ,
U ( x 0 , y 0 ) = u ( x 0 , y 0 ) ∗ ∑ n 1 ∑ n 2 δ ( x 0 − n 1 Δ , y 0 − n 2 Δ ) ,
| F { U ( k x , k y ) } | 2 = ∑ n 1 ∑ n 2 | c ( n 1 , n 2 , β ) | 2 I ( x − n 1 Δ x , y − n 2 Δ y ) ,
Δ x = N x λ 2 N A ,   Δ y = N y λ 2 N A ,
Φ( x 0 , y 0 )= ∑ n=1 N l n arctan( y 0 − b n R x 0 − a n R ) ,

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