Abstract

We demonstrate a scheme that can produce a three-dimensional (3D) focus spot array in a 3D lattice structure, called a 3D Dammann array, in focal region of an objective. This 3D Dammann array is generated by using two separate micro-optical elements, a Dammann zone plate (DZP) that produces a series of coaxial focus spots and a conventional two-dimensional (2D) Dammann grating (DG). A simple, fast, and clear method is presented to design this binary pure-phase (0,π) DZP in vectorial Debye theory regime. Based on this kind of DZP, one can always obtain a 3D Dammann array both for low and high numerical aperture (NA) focusing objectives. For experimental demonstration, an arrangement combining a DZP, a 2D DG, and a pair of opposing lenses is proposed to generate a 5×5×5 Dammann array in focal region of an objective with NA=0.127 and another 6×6×7 Dammann array for an objective of NA=0.66. It is shown that this arrangement makes it possible to achieve 3D Dammann arrays with micrometer-sized focus spots and focus spacings of tens of micrometers for various practical applications, such as 3D parallel micro- and nanomachining, 3D simultaneous optical manipulation, 3D optical data storage, and multifocal fluorescence microscope, etc.

© 2012 Optical Society of America

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2011 (2)

2010 (3)

I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X.-C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35, 1536–1538 (2010).
[CrossRef]

M. Thiel, J. Fischer, G. von Freymann, and M. Wegener, “Direct laser writing of three-dimensional submicron structures using a continuous-wave laser at 532 nm,” Appl. Phys. Lett. 97, 221102 (2010).
[CrossRef]

J. Yu, C. Zhou, W. Jia, and A. Hu, “Focal shift and axial dispersion of binary pure-phase filters in focusing systems,” Proc. SPIE 7848, 784815 (2010).
[CrossRef]

2009 (2)

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324, 910–913 (2009).
[CrossRef]

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

2008 (4)

W. Wang, C. Zhou, and W. Jia, “High-fidelity replication of Dammann gratings using soft lithography,” Appl. Opt. 47, 1427–1429 (2008).
[CrossRef]

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photon. 2, 219–225(2008).
[CrossRef]

J. Zheng, C. Zhou, and B. Wang, “Phase interpretation for polarization-dependent near-field images of high-density gratings,” Opt. Commun. 281, 3254–3259 (2008).
[CrossRef]

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

2007 (1)

2006 (4)

2005 (1)

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

2004 (1)

C. Zhou, W. Wang, E. Dai, and L. Liu, “Simple principles of the Talbot effect,” Opt. Photon. News 15(11), 46–50 (2004).
[CrossRef]

2003 (2)

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

C. Zhou, J. Jia, and L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003).
[CrossRef]

2001 (1)

2000 (1)

S. Maruo and K. Ikuta, “Three-dimensional microfabrication by use of single-photon-absorbed polymerization,” Appl. Phys. Lett. 76, 2656–2658 (2000).
[CrossRef]

1999 (1)

1995 (1)

1990 (1)

1977 (1)

H. Dammann and E. Klotz, “Coherent optical generation and inspection of 2-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

1964 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplantic system,” Proc. R. Soc. London Ser. A 253, 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, 044102 (2005).
[CrossRef]

Campos, J.

Chen, G. X.

Y. Lin, M. H. Hong, T. C. Chong, C. S. Lim, G. X. Chen, L. S. Tan, Z. B. Wang, and L. P. Shi, “Ultrafast-laser-induced parallel phase-change nanolithography,” Appl. Phys. Lett. 89, 041108 (2006).
[CrossRef]

Chong, C. T.

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

Chong, T. C.

Y. Lin, M. H. Hong, T. C. Chong, C. S. Lim, G. X. Chen, L. S. Tan, Z. B. Wang, and L. P. Shi, “Ultrafast-laser-induced parallel phase-change nanolithography,” Appl. Phys. Lett. 89, 041108 (2006).
[CrossRef]

Cottrell, D.

Cottrell, D. M.

Dai, E.

C. Zhou, W. Wang, E. Dai, and L. Liu, “Simple principles of the Talbot effect,” Opt. Photon. News 15(11), 46–50 (2004).
[CrossRef]

Dammann, H.

H. Dammann and E. Klotz, “Coherent optical generation and inspection of 2-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Davis, J.

Davis, J. A.

Deubel, M.

Dorn, R.

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

Fischer, J.

M. Thiel, J. Fischer, G. von Freymann, and M. Wegener, “Direct laser writing of three-dimensional submicron structures using a continuous-wave laser at 532 nm,” Appl. Phys. Lett. 97, 221102 (2010).
[CrossRef]

Fourkas, J. T.

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324, 910–913 (2009).
[CrossRef]

Gattass, R. R.

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324, 910–913 (2009).
[CrossRef]

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photon. 2, 219–225(2008).
[CrossRef]

Gershgoren, E.

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324, 910–913 (2009).
[CrossRef]

Gu, M.

Hernandez, T.

Hong, M. H.

Y. Lin, M. H. Hong, T. C. Chong, C. S. Lim, G. X. Chen, L. S. Tan, Z. B. Wang, and L. P. Shi, “Ultrafast-laser-induced parallel phase-change nanolithography,” Appl. Phys. Lett. 89, 041108 (2006).
[CrossRef]

Hu, A.

J. Yu, C. Zhou, W. Jia, and A. Hu, “Focal shift and axial dispersion of binary pure-phase filters in focusing systems,” Proc. SPIE 7848, 784815 (2010).
[CrossRef]

Hwang, H.

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324, 910–913 (2009).
[CrossRef]

Iemmi, C.

Ikuta, K.

S. Maruo and K. Ikuta, “Three-dimensional microfabrication by use of single-photon-absorbed polymerization,” Appl. Phys. Lett. 76, 2656–2658 (2000).
[CrossRef]

Jia, B.

Jia, J.

Jia, W.

J. Yu, C. Zhou, W. Jia, and A. Hu, “Focal shift and axial dispersion of binary pure-phase filters in focusing systems,” Proc. SPIE 7848, 784815 (2010).
[CrossRef]

W. Wang, C. Zhou, and W. Jia, “High-fidelity replication of Dammann gratings using soft lithography,” Appl. Opt. 47, 1427–1429 (2008).
[CrossRef]

John, S.

Kato, J.

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

Kawata, S.

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

Klotz, E.

H. Dammann and E. Klotz, “Coherent optical generation and inspection of 2-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Lasser, T.

Leitgeb, R. A.

Leuchs, G.

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

Leutenegger, M.

Li, L. J.

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324, 910–913 (2009).
[CrossRef]

Lim, C. S.

Y. Lin, M. H. Hong, T. C. Chong, C. S. Lim, G. X. Chen, L. S. Tan, Z. B. Wang, and L. P. Shi, “Ultrafast-laser-induced parallel phase-change nanolithography,” Appl. Phys. Lett. 89, 041108 (2006).
[CrossRef]

Lin, H.

Lin, Y.

Y. Lin, M. H. Hong, T. C. Chong, C. S. Lim, G. X. Chen, L. S. Tan, Z. B. Wang, and L. P. Shi, “Ultrafast-laser-induced parallel phase-change nanolithography,” Appl. Phys. Lett. 89, 041108 (2006).
[CrossRef]

Linden, S.

Liu, L.

Lohmann, A. W.

López-Coronado, O.

Lu, Y.

Lukyanchuk, B.

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

Martínez, J.

Martínez-Corral, M.

Maruo, S.

S. Maruo and K. Ikuta, “Three-dimensional microfabrication by use of single-photon-absorbed polymerization,” Appl. Phys. Lett. 76, 2656–2658 (2000).
[CrossRef]

Mazur, E.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photon. 2, 219–225(2008).
[CrossRef]

McCutchen, C. W.

Moreno, I.

Muñoz-Escrivá, L.

Pons, A.

Quabis, S.

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

Rao, R.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplantic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Sheppard, C.

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

Shi, L.

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

Shi, L. P.

Y. Lin, M. H. Hong, T. C. Chong, C. S. Lim, G. X. Chen, L. S. Tan, Z. B. Wang, and L. P. Shi, “Ultrafast-laser-induced parallel phase-change nanolithography,” Appl. Phys. Lett. 89, 041108 (2006).
[CrossRef]

Stankovic, S.

Sun, H.

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

Takeyasu, N.

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

Tan, L. S.

Y. Lin, M. H. Hong, T. C. Chong, C. S. Lim, G. X. Chen, L. S. Tan, Z. B. Wang, and L. P. Shi, “Ultrafast-laser-induced parallel phase-change nanolithography,” Appl. Phys. Lett. 89, 041108 (2006).
[CrossRef]

Thiel, M.

M. Thiel, J. Fischer, G. von Freymann, and M. Wegener, “Direct laser writing of three-dimensional submicron structures using a continuous-wave laser at 532 nm,” Appl. Phys. Lett. 97, 221102 (2010).
[CrossRef]

Thomas, J. A.

Tschudi, T.

Tuvey, C. S.

von Freymann, G.

M. Thiel, J. Fischer, G. von Freymann, and M. Wegener, “Direct laser writing of three-dimensional submicron structures using a continuous-wave laser at 532 nm,” Appl. Phys. Lett. 97, 221102 (2010).
[CrossRef]

M. Deubel, M. Wegener, S. Linden, G. von Freymann, and S. John, “3D-2D-3D photonic crystal heterostructures fabricated by direct laser writing,” Opt. Lett. 31, 805–807(2006).
[CrossRef]

Wang, B.

J. Zheng, C. Zhou, and B. Wang, “Phase interpretation for polarization-dependent near-field images of high-density gratings,” Opt. Commun. 281, 3254–3259 (2008).
[CrossRef]

Y. Lu, C. Zhou, S. Wang, and B. Wang, “Polarization-dependent Talbot effect,” J. Opt. Soc. Am. A 23, 2154–2160 (2006).
[CrossRef]

Wang, H.

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

Wang, S.

Wang, W.

W. Wang, C. Zhou, and W. Jia, “High-fidelity replication of Dammann gratings using soft lithography,” Appl. Opt. 47, 1427–1429 (2008).
[CrossRef]

C. Zhou, W. Wang, E. Dai, and L. Liu, “Simple principles of the Talbot effect,” Opt. Photon. News 15(11), 46–50 (2004).
[CrossRef]

Wang, Z. B.

Y. Lin, M. H. Hong, T. C. Chong, C. S. Lim, G. X. Chen, L. S. Tan, Z. B. Wang, and L. P. Shi, “Ultrafast-laser-induced parallel phase-change nanolithography,” Appl. Phys. Lett. 89, 041108 (2006).
[CrossRef]

Wegener, M.

M. Thiel, J. Fischer, G. von Freymann, and M. Wegener, “Direct laser writing of three-dimensional submicron structures using a continuous-wave laser at 532 nm,” Appl. Phys. Lett. 97, 221102 (2010).
[CrossRef]

M. Deubel, M. Wegener, S. Linden, G. von Freymann, and S. John, “3D-2D-3D photonic crystal heterostructures fabricated by direct laser writing,” Opt. Lett. 31, 805–807(2006).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplantic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Yu, J.

J. Yu, C. Zhou, W. Jia, and A. Hu, “Focal shift and axial dispersion of binary pure-phase filters in focusing systems,” Proc. SPIE 7848, 784815 (2010).
[CrossRef]

C. Zhou and J. Yu, “Dammann zone plate,” Chinese invention patent, application 201010585480.4 (2010).

Yuan, X.-C.

Yzuel, M. J.

Zhan, Q.

Zhang, N.

Zheng, J.

J. Zheng, C. Zhou, and B. Wang, “Phase interpretation for polarization-dependent near-field images of high-density gratings,” Opt. Commun. 281, 3254–3259 (2008).
[CrossRef]

Zhou, C.

J. Yu, C. Zhou, W. Jia, and A. Hu, “Focal shift and axial dispersion of binary pure-phase filters in focusing systems,” Proc. SPIE 7848, 784815 (2010).
[CrossRef]

J. Zheng, C. Zhou, and B. Wang, “Phase interpretation for polarization-dependent near-field images of high-density gratings,” Opt. Commun. 281, 3254–3259 (2008).
[CrossRef]

W. Wang, C. Zhou, and W. Jia, “High-fidelity replication of Dammann gratings using soft lithography,” Appl. Opt. 47, 1427–1429 (2008).
[CrossRef]

Y. Lu, C. Zhou, S. Wang, and B. Wang, “Polarization-dependent Talbot effect,” J. Opt. Soc. Am. A 23, 2154–2160 (2006).
[CrossRef]

C. Zhou, W. Wang, E. Dai, and L. Liu, “Simple principles of the Talbot effect,” Opt. Photon. News 15(11), 46–50 (2004).
[CrossRef]

C. Zhou, J. Jia, and L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003).
[CrossRef]

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

C. Zhou and L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34, 5961–5969 (1995).
[CrossRef]

C. Zhou and J. Yu, “Dammann zone plate,” Chinese invention patent, application 201010585480.4 (2010).

Adv. Opt. Photon. (1)

Appl. Opt. (6)

Appl. Phys. Lett. (4)

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

Y. Lin, M. H. Hong, T. C. Chong, C. S. Lim, G. X. Chen, L. S. Tan, Z. B. Wang, and L. P. Shi, “Ultrafast-laser-induced parallel phase-change nanolithography,” Appl. Phys. Lett. 89, 041108 (2006).
[CrossRef]

S. Maruo and K. Ikuta, “Three-dimensional microfabrication by use of single-photon-absorbed polymerization,” Appl. Phys. Lett. 76, 2656–2658 (2000).
[CrossRef]

M. Thiel, J. Fischer, G. von Freymann, and M. Wegener, “Direct laser writing of three-dimensional submicron structures using a continuous-wave laser at 532 nm,” Appl. Phys. Lett. 97, 221102 (2010).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Nat. Photon. (2)

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

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photon. 2, 219–225(2008).
[CrossRef]

Opt. Acta (1)

H. Dammann and E. Klotz, “Coherent optical generation and inspection of 2-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Opt. Commun. (1)

J. Zheng, C. Zhou, and B. Wang, “Phase interpretation for polarization-dependent near-field images of high-density gratings,” Opt. Commun. 281, 3254–3259 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (5)

Opt. Photon. News (1)

C. Zhou, W. Wang, E. Dai, and L. Liu, “Simple principles of the Talbot effect,” Opt. Photon. News 15(11), 46–50 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

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

Proc. R. Soc. London Ser. A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplantic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Proc. SPIE (1)

J. Yu, C. Zhou, W. Jia, and A. Hu, “Focal shift and axial dispersion of binary pure-phase filters in focusing systems,” Proc. SPIE 7848, 784815 (2010).
[CrossRef]

Science (1)

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324, 910–913 (2009).
[CrossRef]

Other (1)

C. Zhou and J. Yu, “Dammann zone plate,” Chinese invention patent, application 201010585480.4 (2010).

Supplementary Material (1)

» Media 1: AVI (6972 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

Illustration of a focusing system with a DZP for generating multiple coaxial focus spots with high efficiency and good uniformity. The position of the geometrical focus of the objective is set as the origin of the Cartesian coordinate system, and the z -coordinate is along the optical axis.

Fig. 2.
Fig. 2.

Theoretical results of a 1 × 5 binary pure-phase ( 0 , π ) DZP with 10 periods for NA = 0.1 . (a) Phase transition points of the DZP versus the normalized radial coordinate. (b) 2D intensity distribution on a meridian plane. (c) Transverse intensity profiles of these five focus spots along x -axis compared with that of the Airy pattern.

Fig. 3.
Fig. 3.

Axial intensity profiles of 1 × 5 10-period DZPs focusing by objectives of different NA values ( NA = 0.01 , 0.1, 0.65, and 0.95). (a) The DZP designed for NA = 0.01 . (b) The DZP designed for NA = 0.65 .

Fig. 4.
Fig. 4.

Schematic of a focusing system with a DG and a DZP located before for generating a 3D Dammann array of focus spots. This 3D Dammann array is arranged into the structure of a 3D lattice, and Δ x , Δ y , and Δ z are focus spacings along the x -, y -, and z -axes, respectively.

Fig. 5.
Fig. 5.

Numerical simulations of a 5 × 5 × 5 Dammann array focusing with an objective ( NA = 0.95 ) with different polarized incident fields. In the simulation, N x = N y = 32 and N ξ = 5 . (a), (b), and (c) are 2D intensity distributions on the meridian plane across the geometrical focus under circular, radial, and azimuthal polarization incidence, respectively. (d) and (e) are intensity profiles along transverse and axial directions across the geometrical focus, respectively.

Fig. 6.
Fig. 6.

(a) Experimental setup for verifying the DZP, and (b) schematic of a 3D Dammann array produced by a 2D DG and a DZP. M, Mirror; P 1 , polarizer; P 2 , λ / 4 wave plate; BE, beam expander; L 3 ( f 3 = 6.25 cm ) and L 4 ( f 4 = 10 cm ) are two opposing lenses for adjusting the diffractive angle of the beam from the DG, and it also provides a possibility to tailor the 3D lattice of focus spots by introducing an amplitude filter on the confocal plane. MO 1 , the objective for focusing; MO 2 , the objective for magnifying.

Fig. 7.
Fig. 7.

Experimental results of the 3D intensity distribution of a focusing system with a 1 × 5 DZP. (a) Axial intensity profile of the focusing objective with the 1 × 5 DZP, and the insets are the corresponding transverse 2D intensity distributions of these five coaxial focus spots. (b) Axial intensity profile of the unfiltered objective (without the DZP), and the inset is corresponding transverse 2D intensity at the axial intensity peak. (c) Transverse intensity profiles of these five coaxial focus spots along the x -axis compared with that of the unfiltered objective.

Fig. 8.
Fig. 8.

Experimental results of a 5 × 5 × 5 Dammann array of a focusing system ( NA = 0.127 ) with a 1 × 5 DZP and a 5 × 5 DG. (a), (b), (c), (d) and (e) are 2D intensity distributions at five axial focal planes produced by the 1 × 5 DZP. The bars in all these five figures are a length of 50 μm . (f) Transverse intensity profile across the central five focus spots on the geometrical focal plane ( z = 0 ).

Fig. 9.
Fig. 9.

Experimental results of a 6 × 6 × 7 Dammann array of a focusing system ( NA = 0.66 ) with a 1 × 7 DZP and a 6 × 6 DG (Media 1). (a), (b), (c), (d), (e), (f), and (g) are 2D intensity distributions at seven axial focal planes produced by the 1 × 7 DZP. The bars in all these seven figures are a length of 15 μm .

Equations (11)

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E o ( 0 , z ) = 0 α 0 2 π [ T DZP ( θ ) E t ( θ , φ ) ] × e i k z cos θ sin θ d φ d θ ,
T DZP ( θ ) = 2 n = 1 N all 1 ( 1 ) n circ ( sin θ s n sin α ) + ( 1 ) N all circ ( sin θ s N all sin α ) ,
circ ( s s n ) = { 1 s s n 0 s > s n .
E o ( 0 , z ) = cos α 1 T DZP ( t ) G ( t ) e i k z t d t ,
E o ( 0 , z ) = I { T DZP ( ξ ) } I { G ( ξ ) } ,
G ( ξ ) = { G ( t ) | ξ | ( 1 cos α ) / 2 0 other .
E o ( x , y , z ) = 0 0 { T DZP ( k x , k y ) T DG ( k x , k y ) E t ( k x , k y ) / cos θ } e i ( k x x + k y y ) d k x d k y = I { T DZP ( ξ ) } I { T DG ( k x , k y ) } E Airy ( x , y , z ) ,
I o ( x , y , z ) = m = n = q = C m C n C q × I Airy ( x m Δ x , y n Δ y , z q Δ z ) ,
Δ x = N x 2 sin α λ ,
Δ y = N y 2 sin α λ ,
Δ z = N ξ 1 cos α λ .

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