Abstract

We propose a method for creating a three-dimensional (3D) shape-controllable focal spot array by combination of a two-dimensional (2D) pure-phase modulation grating and an additional axial shifting pure-phase modulation composed of four-quadrant phase distribution unit at the back aperture of a high numerical aperture (NA) objective. It is demonstrated that the one-dimensional (1D) grating designed by optimized algorithm of selected number of equally spaced arbitrary phase value in a single period could produce desired number of equally spaced diffraction spot with identical intensity. It is also shown that the 2D pure-phase grating designed with this method could generate 2D diffraction spot array. The number of the spots in the array along each of two dimensions depends solely on the number of divided area with different phase values of the dimension. We also show that, by combining the axial translation phase modulation at the back aperture, we can create 3D focal spot array at the focal volume of the high NA objective. Furthermore, the shape or intensity distribution of each focal spot in the 3D focal array can be manipulated by introducing spatially shifted multi vortex beams as the incident beam. These kinds of 3D shape-controllable focal spot array could be utilized in the fabrication of artificial metamaterials, in parallel optical micromanipulation and multifocal multiphoton microscopic imaging.

© 2014 Optical Society of America

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References

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2014 (2)

2013 (6)

2012 (1)

2011 (5)

2010 (4)

2009 (3)

B. Jia, H. Kang, J. Li, and M. Gu, “Use of radially polarized beams in three-dimensional photonic crystal fabrication with the two-photon polymerization method,” Opt. Lett. 34(13), 1918–1920 (2009).
[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]

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]

2008 (1)

2007 (1)

2006 (3)

2005 (2)

2004 (3)

2003 (3)

2002 (1)

J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

2001 (2)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

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 (2)

C. Zhou, S. Stankovic, and T. Tschudi, “Analytic phase-factor equations for Talbot array illuminations,” Appl. Opt. 38(2), 284–290 (1999).
[Crossref] [PubMed]

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, and H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399(6735), 446–448 (1999).
[Crossref] [PubMed]

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 (3)

J. Turunen, A. Vasara, J. Westerholm, and A. U. Salin, “Arbitrary interconnections with 2D Dammann-type stripe holograms,” Proc. SPIE 1281, 200–206 (1990).
[Crossref]

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

A. W. Lohmann and J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29(29), 4337–4340 (1990).
[Crossref] [PubMed]

1989 (1)

J. Jahns, M. M. Downs, M. E. Prise, N. Streib, and S. J. Walker, “Dammann graitngs for laser-beam shaping,” Opt. Eng. 28(12), 1267–1275 (1989).
[Crossref]

1974 (1)

H. Blume, T. Bader, and F. Luty, “Bi-directional holographic information storage based on the optical reorientation of FA centers in KCl:Na,” Opt. Commun. 12(2), 147–151 (1974).
[Crossref]

1971 (1)

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[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]

Akashi, K.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, and H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399(6735), 446–448 (1999).
[Crossref] [PubMed]

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.

Arai, Y.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, and H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399(6735), 446–448 (1999).
[Crossref] [PubMed]

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]

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

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]

Bader, T.

H. Blume, T. Bader, and F. Luty, “Bi-directional holographic information storage based on the optical reorientation of FA centers in KCl:Na,” Opt. Commun. 12(2), 147–151 (1974).
[Crossref]

Blume, H.

H. Blume, T. Bader, and F. Luty, “Bi-directional holographic information storage based on the optical reorientation of FA centers in KCl:Na,” Opt. Commun. 12(2), 147–151 (1974).
[Crossref]

Botcherby, E. J.

E. J. Botcherby, R. Juskaitis, and T. Wilson, “Scanning two photon fluorescence microscopy with extended depth of field,” Opt. Commun. 268(2), 253–260 (2006).
[Crossref]

Brown, T. G.

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Burnham, D. R.

Cai, M.

Cao, H.

Cao, W.

Cao, Y.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(2061), 2061 (2013).
[PubMed]

Chen, J.

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.

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]

J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

Choudhury, A.

Cooper, I. J.

Dai, E.

Dammann, H.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[Crossref]

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]

Denk, W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

Dholakia, K.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Di, C.

Dong, X.

Downs, M. M.

J. Jahns, M. M. Downs, M. E. Prise, N. Streib, and S. J. Walker, “Dammann graitngs for laser-beam shaping,” Opt. Eng. 28(12), 1267–1275 (1989).
[Crossref]

Duadi, H.

Evans, R. A.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(2061), 2061 (2013).
[PubMed]

Fittinghoff, D. N.

Fournier, J.-M.

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.

Gan, X.

D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11(21), 2747–2752 (2003).
[Crossref] [PubMed]

J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

Gan, Z.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(2061), 2061 (2013).
[PubMed]

Ganic, D.

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]

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]

Görtler, K.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[Crossref]

Gu, M.

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]

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]

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(2061), 2061 (2013).
[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]

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).
[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]

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]

B. Jia, H. Kang, J. Li, and M. Gu, “Use of radially polarized beams in three-dimensional photonic crystal fabrication with the two-photon polymerization method,” Opt. Lett. 34(13), 1918–1920 (2009).
[Crossref] [PubMed]

D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11(21), 2747–2752 (2003).
[Crossref] [PubMed]

J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

Guo, H.

Harada, Y.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, and H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399(6735), 446–448 (1999).
[Crossref] [PubMed]

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]

Hinze, U.

Hu, Q.

Itoh, H.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, and H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399(6735), 446–448 (1999).
[Crossref] [PubMed]

Jahns, J.

J. Jahns, M. M. Downs, M. E. Prise, N. Streib, and S. J. Walker, “Dammann graitngs for laser-beam shaping,” Opt. Eng. 28(12), 1267–1275 (1989).
[Crossref]

Jia, B.

Jia, W.

Juskaitis, R.

E. J. Botcherby, R. Juskaitis, and T. Wilson, “Scanning two photon fluorescence microscopy with extended depth of field,” Opt. Commun. 268(2), 253–260 (2006).
[Crossref]

Kang, H.

Kim, P.-S.

Kinosita, K.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, and H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399(6735), 446–448 (1999).
[Crossref] [PubMed]

Koch, J.

Lasser, T.

Lee, G.

Leitgeb, R. A.

Lerman, G. M.

Leutenegger, M.

Levy, U.

Li, G.

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, J.

Li, X.

Li, Y.

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.

Luty, F.

H. Blume, T. Bader, and F. Luty, “Bi-directional holographic information storage based on the optical reorientation of FA centers in KCl:Na,” Opt. Commun. 12(2), 147–151 (1974).
[Crossref]

Ma, J.

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Merenda, F.

Miyata, H.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, and H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399(6735), 446–448 (1999).
[Crossref] [PubMed]

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.

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Pavone, F. S.

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]

Prise, M. E.

J. Jahns, M. M. Downs, M. E. Prise, N. Streib, and S. J. Walker, “Dammann graitngs for laser-beam shaping,” Opt. Eng. 28(12), 1267–1275 (1989).
[Crossref]

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.

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(1247), 358–379 (1959).
[Crossref]

Rill, M. 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]

Rohner, J.

Roy, M.

Sacconi, L.

Saile, V.

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]

Sakamoto, M.

Salathé, R.-P.

Salin, A. U.

J. Turunen, A. Vasara, J. Westerholm, and A. U. Salin, “Arbitrary interconnections with 2D Dammann-type stripe holograms,” Proc. SPIE 1281, 200–206 (1990).
[Crossref]

Schneider, T.

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).
[Crossref]

Sheppard, C. J. R.

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Song, S. H.

Squier, J. A.

Stankovic, S.

Streib, N.

J. Jahns, M. M. Downs, M. E. Prise, N. Streib, and S. J. Walker, “Dammann graitngs for laser-beam shaping,” Opt. Eng. 28(12), 1267–1275 (1989).
[Crossref]

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

Sui, G.

Sun, M.

Taghizadeh, M. R.

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).
[Crossref] [PubMed]

Thomas, J. A.

Tschudi, T.

Tu, C.

Turunen, J.

J. Turunen, A. Vasara, J. Westerholm, and A. U. Salin, “Arbitrary interconnections with 2D Dammann-type stripe holograms,” Proc. SPIE 1281, 200–206 (1990).
[Crossref]

Vasara, A.

J. Turunen, A. Vasara, J. Westerholm, and A. U. Salin, “Arbitrary interconnections with 2D Dammann-type stripe holograms,” Proc. SPIE 1281, 200–206 (1990).
[Crossref]

von Freymann, G.

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

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]

Walker, S. J.

J. Jahns, M. M. Downs, M. E. Prise, N. Streib, and S. J. Walker, “Dammann graitngs for laser-beam shaping,” Opt. Eng. 28(12), 1267–1275 (1989).
[Crossref]

Waller, E. H.

Wang, H. T.

Wang, S.

Wang, 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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Webb, W. W.

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21(11), 1369–1377 (2003).
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W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Weng, X.

Westerholm, J.

J. Turunen, A. Vasara, J. Westerholm, and A. U. Salin, “Arbitrary interconnections with 2D Dammann-type stripe holograms,” Proc. SPIE 1281, 200–206 (1990).
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Williams, R. M.

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21(11), 1369–1377 (2003).
[Crossref] [PubMed]

Wilson, T.

E. J. Botcherby, R. Juskaitis, and T. Wilson, “Scanning two photon fluorescence microscopy with extended depth of field,” Opt. Commun. 268(2), 253–260 (2006).
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Wiseman, P. W.

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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Xu, G.

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]

Yang, N.

Yasuda, R.

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, and H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399(6735), 446–448 (1999).
[Crossref] [PubMed]

Youngworth, K. S.

Yu, J.

Zalevsky, Z.

Zhang, D.

Zhang, H.

Zhou, C.

Zhu, L.

Zhuang, S.

Zhuang, X.

X. Zhuang, “Molecular biology. Unraveling DNA Condensation with Optical Tweezers,” Science 305(5681), 188–190 (2004).
[Crossref] [PubMed]

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]

Zipfel, W. R.

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21(11), 1369–1377 (2003).
[Crossref] [PubMed]

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. (2)

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. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high numerical-aperture objective in free space,” Appl. Phys. Lett. 81(9), 1576–1578 (2002).
[Crossref]

J. Microsc. (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]

J. Opt. Soc. Am. A (2)

Nat. Biotechnol. (1)

W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21(11), 1369–1377 (2003).
[Crossref] [PubMed]

Nat. Commun. (1)

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(2061), 2061 (2013).
[PubMed]

Nat. Methods (1)

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]

Nature (2)

Y. Arai, R. Yasuda, K. Akashi, Y. Harada, H. Miyata, K. Kinosita, and H. Itoh, “Tying a molecular knot with optical tweezers,” Nature 399(6735), 446–448 (1999).
[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]

Opt. Commun. (4)

E. J. Botcherby, R. Juskaitis, and T. Wilson, “Scanning two photon fluorescence microscopy with extended depth of field,” Opt. Commun. 268(2), 253–260 (2006).
[Crossref]

H. Blume, T. Bader, and F. Luty, “Bi-directional holographic information storage based on the optical reorientation of FA centers in KCl:Na,” Opt. Commun. 12(2), 147–151 (1974).
[Crossref]

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]

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3(5), 312–315 (1971).
[Crossref]

Opt. Eng. (1)

J. Jahns, M. M. Downs, M. E. Prise, N. Streib, and S. J. Walker, “Dammann graitngs for laser-beam shaping,” Opt. Eng. 28(12), 1267–1275 (1989).
[Crossref]

Opt. Express (14)

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000).
[Crossref] [PubMed]

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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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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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).
[Crossref] [PubMed]

G. M. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16(7), 4567–4581 (2008).
[Crossref] [PubMed]

D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11(21), 2747–2752 (2003).
[Crossref] [PubMed]

I. J. Cooper, M. Roy, and C. J. R. Sheppard, “Focusing of pseudoradial polarized beams,” Opt. Express 13(4), 1066–1071 (2005).
[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).
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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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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).
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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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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).
[Crossref] [PubMed]

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

Opt. Lett. (8)

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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M. Sakamoto, K. Oka, R. Morita, and N. Murakami, “Stable and flexible ring-shaped optical-lattice generation by use of axially symmetric polarization elements,” Opt. Lett. 38(18), 3661–3664 (2013).
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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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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. 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).
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B. Jia, H. Kang, J. Li, and M. Gu, “Use of radially polarized beams in three-dimensional photonic crystal fabrication with the two-photon polymerization method,” Opt. Lett. 34(13), 1918–1920 (2009).
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L. Sacconi, E. Froner, R. Antolini, M. R. Taghizadeh, A. Choudhury, and F. S. Pavone, “Multiphoton multifocal microscopy exploiting a diffractive optical element,” Opt. Lett. 28(20), 1918–1920 (2003).
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G. Lee, S. H. Song, C.-H. Oh, and P.-S. Kim, “Arbitrary structuring of two-dimensional photonic crystals by use of phase-only Fourier gratings,” Opt. Lett. 29(21), 2539–2541 (2004).
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Proc. R. Soc. Lond. A Math. Phys. Sci. (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]

Proc. SPIE (1)

J. Turunen, A. Vasara, J. Westerholm, and A. U. Salin, “Arbitrary interconnections with 2D Dammann-type stripe holograms,” Proc. SPIE 1281, 200–206 (1990).
[Crossref]

Science (4)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

X. Zhuang, “Molecular biology. Unraveling DNA Condensation with Optical Tweezers,” Science 305(5681), 188–190 (2004).
[Crossref] [PubMed]

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 (10)

Fig. 1
Fig. 1 The contrast schematic of two pure-phase grating with the period normalized to 1. (a) an ordinary phase grating. (b) The phase distribution of a MVPPG with the period normalized to 1 when N = 5.
Fig. 2
Fig. 2 (a) An example of the simulated 1D phase distribution of the optimized 1D MVPPG for generating equal spacing diffracting orders with equal intensities, in which β = 9. (b) Plot of the optimized 1D MVPPG phase distribution. (c) The 2D diffraction intensity distribution of the optimized 1D MVPPG. (d) Plot of the 1D diffracting intensity distribution .
Fig. 3
Fig. 3 (a) The simulated 2D phase distribution of the optimized 2D MVPPG for generating a 2D equal spacing array with equal intensities when β = 9. (b) The simulated 2D diffraction intensity distribution of the optimized 2D MVPPG in (a).
Fig. 4
Fig. 4 The scheme of four additional phase shifts imposed on the unit cell of optimized 2D MVPPG. The four additional phase shifts on the whole back aperture of objective will produce four layers of identical 2D focusing spot array.
Fig. 5
Fig. 5 (a) the simulated phase distribution for splitting one focusing spot into four equally spaced focusing spots along the optical axis; (b) the enlarged image of a small area in the (a); (c) the focusing spot viewed in xy plane; (d) four focusing spot aligned along the z axis. (e) the 1D normalized intensity distribution of four spots.
Fig. 6
Fig. 6 The axial focusing spot array with different shifting distance (a) Δz1 = −3μm, Δz2 = −1μm, Δz3 = 1μm, Δz4 = 3μm; (b) Δz1 = −2μm, Δz2 = −1μm, Δz3 = 1μm, Δz4 = 2μm; (c) Δz1 = −1μm, Δz2 = −0.5μm, Δz3 = 0.5μm, Δz4 = 1μm. Left: Phase patterns; Middle: 2D intensity distribution in xz plane; Right: 3D iso-intensity surface of the focusing spot array with I = e-1...-2Imax.
Fig. 7
Fig. 7 (a) the phase distribution of the vortex beam with topological charge of 1; (b) shows the status of beam polarization; (c) and (e) are the phase distributions of two optimized one-dimensional MVPPG with β = 5 and β = 9, respectively. (d) and (f) are the combined phase distribution with the phase pattern in (a); (g) and (h) are the focusing intensity distribution when the incident field are modulated by two optimized one-dimensional MVPPG with β = 5 and β = 9, respectively.
Fig. 8
Fig. 8 The generation of the 2D focusing annular spot array with the optimized 2D MVPPG is illustrated. (a) the phase distribution of the optimized 2D MVPPG; (b) the phase distribution of the vortex beam with topological charge of 1; (c) the combination of the phase distributions in (a) and (b). (d) the generated 2D annular focusing spot array.
Fig. 9
Fig. 9 The 3D focusing spot array created by combining the optimized 2D MVPPG with the phase modulation imposed on the incident beam at the back aperture for shifting the focusing spot along the optical axis. The topological charge of the vortex beam is 0. In the optimized 2D MVPPG, the splitting parameter is β = 5. The shifting distance Δz1 = 4μm, Δz2 = −4μm, Δz3 = 12μm, Δz4 = −12μm. The 3D focusing spot array is a 4 × 5 × 5 array. The phase distributions of (a) a 2D MVPPG, (b) axial shift splitting focal spots, and (c) the overall phase modulation. (d) the 3D iso-intensity surface of the focusing spot array with I = Imax/2. (e) and (f) are the cross-section views of the focusing spot array in xy and xz plane, respectively.
Fig. 10
Fig. 10 The 3D shape-controllable focusing spot array created by combining the optimized 2D MVPPG, the axial shifting phase modulation and the spatial shifting vortex beam. (a) the phase distribution of the 2D MVPPG with β = 5; (b) phase of the shifting focusing spot along the optical axis. The shifting distance Δz1 = Δz4 = 7μm, Δz2 = Δz3 = −7μm; (c) the phase distribution of the spatial shifting vortex beam with topological charge of l1 = l2 = l3 = −1; (d) the overall phase modulation; (e) the 3D iso-intensity surface of the focusing spot array with I = Imax/2; (f), (g) and (h) the cross-section views of the focusing spot array; (i) the 3D iso-intensity surface of one focal spot from among the 3D focusing spot array.

Tables (1)

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Table 1 Optimization Results

Equations (12)

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T( x )=comb( x ) n=0 N1 t n ( x ) ,
t n ( x )=exp( i φ n )rect[ x ( 2n+1 ) /2 1/N ],
F{ t n ( x ) }= i 2πξ exp( i φ n ){ exp[ i2πξ( n+1 ) ]exp( i2πξn ) },
A m ={ 1 N n=0 N1 exp( i φ n ),m=0 i 2mπ n=0 N1 [ exp( i2mπ n+1 N )exp( 2mπ n N ) ]exp( i φ n ) ,m0 ,
η= m β I m = m β A m A m * ,
ψ=1- max( I m )min( I m ) max( I m )+min( I m ) .
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]}exp(ikzcosθ)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 ) }F{ E t ( θ,φ ) exp( i k z z ) / cosθ },
φ Δz ( x,y )= 2π λ Δz n t 2 N A 2 R 2 ( x 2 + y 2 ) ,
E i =A( r )exp( ilϕ )( a x +i a y ),
A( r )={ 1rR 0otherwise ,
Φ= l 1 atan( y xa R max )+ l 2 atan( y xb R max )+ l 3 atan( y x ),

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