Abstract

We propose a method based on six-pinhole interferometers to generate vortex arrays with topological charge 2, only with plane wave illumination. The six-pinhole interferometer is composed of two concentric symmetrical three-pinhole interferometers with different radial distances of the pinholes and a relative rotation of 60 deg from each other. In the Fourier domain, the vortices with second-order topological charge are generated when the radial distances of the two three-pinhole interferometers satisfy some certain ratios. Due to the symmetry of the six-pinhole interferometer, such vortices are distributed at the vertices of some symmetrically distributed regular hexagons. The experimental results obtained in a focal-to-focal system show satisfactory coincidence with the calculations.

© 2014 Optical Society of America

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    [Crossref]
  2. O. V. Angelsky, A. P. Maksimyak, P. P. Maksimyak, and S. G. Hanson, “Biaxial crystal-based optical tweezers,” Ukr. J. Phys. Opt. 11, 99–106 (2010).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2013 (1)

2012 (3)

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

B. K. Singh, G. Singh, P. Senthilkumaran, and D. S. Mehta, “Generation of optical vortex arrays using single-element reversed-wavefront folding interferometer,” Int. J. Opt. 2012, 689612 (2012).
[Crossref]

E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108, 087801 (2012).
[Crossref]

2011 (3)

2010 (2)

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref]

O. V. Angelsky, A. P. Maksimyak, P. P. Maksimyak, and S. G. Hanson, “Biaxial crystal-based optical tweezers,” Ukr. J. Phys. Opt. 11, 99–106 (2010).
[Crossref]

2009 (1)

2007 (3)

2006 (1)

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinke, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. vanderVeen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

1992 (2)

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. vanderVeen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Angelsky, O. V.

O. V. Angelsky, A. P. Maksimyak, P. P. Maksimyak, and S. G. Hanson, “Biaxial crystal-based optical tweezers,” Ukr. J. Phys. Opt. 11, 99–106 (2010).
[Crossref]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinke, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

M. W. Beijersbergen, L. Allen, H. E. L. O. vanderVeen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Boguslawski, M.

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84, 013832 (2011).
[Crossref]

Brasselet, E.

E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108, 087801 (2012).
[Crossref]

Cao, W. G.

Chan, C. T.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref]

Chen, X. Y.

Chen, Y. F.

Cheng, C. F.

Chu, S. C.

Coerwinke, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinke, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Dennis, M. R.

Denz, C.

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84, 013832 (2011).
[Crossref]

Hanson, S. G.

O. V. Angelsky, A. P. Maksimyak, P. P. Maksimyak, and S. G. Hanson, “Biaxial crystal-based optical tweezers,” Ukr. J. Phys. Opt. 11, 99–106 (2010).
[Crossref]

Heckenberg, N. R.

Hu, A. D.

Huang, K. F.

Jia, W.

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinke, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Li, X.

Li, Z. H.

Liang, G. T.

Lin, Y. C.

Lin, Z.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref]

Lu, T. H.

Maksimyak, A. P.

O. V. Angelsky, A. P. Maksimyak, P. P. Maksimyak, and S. G. Hanson, “Biaxial crystal-based optical tweezers,” Ukr. J. Phys. Opt. 11, 99–106 (2010).
[Crossref]

Maksimyak, P. P.

O. V. Angelsky, A. P. Maksimyak, P. P. Maksimyak, and S. G. Hanson, “Biaxial crystal-based optical tweezers,” Ukr. J. Phys. Opt. 11, 99–106 (2010).
[Crossref]

McDuff, R.

Mehta, D. S.

B. K. Singh, G. Singh, P. Senthilkumaran, and D. S. Mehta, “Generation of optical vortex arrays using single-element reversed-wavefront folding interferometer,” Int. J. Opt. 2012, 689612 (2012).
[Crossref]

Ng, J.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref]

O’Holleran, K.

Otsuka, K.

Padgett, M. J.

Paganin, D. M.

G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75, 066613 (2007).
[Crossref]

Rose, P.

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84, 013832 (2011).
[Crossref]

Ruben, G.

G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75, 066613 (2007).
[Crossref]

Senthilkumaran, P.

B. K. Singh, G. Singh, P. Senthilkumaran, and D. S. Mehta, “Generation of optical vortex arrays using single-element reversed-wavefront folding interferometer,” Int. J. Opt. 2012, 689612 (2012).
[Crossref]

S. Vyas and P. Senthilkumaran, “Vortex array generation by interference of spherical waves,” Appl. Opt. 46, 7862–7867 (2007).
[Crossref]

S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46, 2893–2898 (2007).
[Crossref]

Singh, B. K.

B. K. Singh, G. Singh, P. Senthilkumaran, and D. S. Mehta, “Generation of optical vortex arrays using single-element reversed-wavefront folding interferometer,” Int. J. Opt. 2012, 689612 (2012).
[Crossref]

Singh, G.

B. K. Singh, G. Singh, P. Senthilkumaran, and D. S. Mehta, “Generation of optical vortex arrays using single-element reversed-wavefront folding interferometer,” Int. J. Opt. 2012, 689612 (2012).
[Crossref]

Smith, C. P.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

vanderVeen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. vanderVeen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

Vyas, S.

Wang, S. Q.

Wang, Z.

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinke, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

M. W. Beijersbergen, L. Allen, H. E. L. O. vanderVeen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Wu, J.

Yu, J. J.

Yuan, X.

Zhang, M. N.

Zhang, N.

Zhou, C. H.

Appl. Opt. (3)

Int. J. Opt. (1)

B. K. Singh, G. Singh, P. Senthilkumaran, and D. S. Mehta, “Generation of optical vortex arrays using single-element reversed-wavefront folding interferometer,” Int. J. Opt. 2012, 689612 (2012).
[Crossref]

Opt. Commun. (2)

M. W. Beijersbergen, L. Allen, H. E. L. O. vanderVeen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[Crossref]

M. W. Beijersbergen, R. P. C. Coerwinke, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. A (2)

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84, 013832 (2011).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Phys. Rev. E (1)

G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75, 066613 (2007).
[Crossref]

Phys. Rev. Lett. (2)

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref]

E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108, 087801 (2012).
[Crossref]

Ukr. J. Phys. Opt. (1)

O. V. Angelsky, A. P. Maksimyak, P. P. Maksimyak, and S. G. Hanson, “Biaxial crystal-based optical tweezers,” Ukr. J. Phys. Opt. 11, 99–106 (2010).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1.

Schematic diagram of the six-pinhole interferometer. The radial distances of the two three-pinhole interferometers are a and b, respectively.

Fig. 2.
Fig. 2.

Calculated wave field after a three-pinhole interferometer. (a) Real part and (b) imaginary part. In both, the negative values are depicted in gray, the positive values are shown in white, and the zero value lines are represented by dashed lines. The line arrows show the orientational difference between two three-pinhole cases, and their different lengths indicate the different scales of the diffracted wave fields.

Fig. 3.
Fig. 3.

Calculated wave distribution after the six-pinhole interferometer with a0/b0=45. (a) Intensity distribution. (b) Zero distributions of the imaginary part (black lines) and the real part (gray lines). (c) Phase distribution. The phase ranging from π to π is represented by eight-interval gray scale. The solid circles in this map indicate the periodically distributed base points. (d) Magnified map of the phase distribution in the white square of (c). The six vortices with topological charge 2 are marked by solid circles.

Fig. 4.
Fig. 4.

Calculated wave fields after six-pinhole interferometers with different a0/b0. The ratios in the maps are (a) 12, (b) 75, (c) 78, (d) 1011, and (e) 1314.

Fig. 5.
Fig. 5.

Schematic diagram of the experimental setup. The six-pinhole interferometer and the CCD are put in the front focal plane and the back focal plane of the lens L1, respectively.

Fig. 6.
Fig. 6.

Experimental results. (a) Direct record of the intensity pattern on the CCD plane. (b) Interferogram on the CCD plane. (c) Expanded map of the square area in (b). (d) Corresponding phase distribution of the wave field in (c). In both (a) and (b), the depicted areas are 8μm×8μm, and in the other two maps such areas are 3.2μm×3.2μm.

Fig. 7.
Fig. 7.

(a) Simulated intensity pattern with pinhole diameter 60 μm. (b) Normalized intensity distribution along the horizontal line passing through the center of (a).

Equations (7)

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U1(x,y)=exp[i2πxa/λf],
U2(x,y)=exp[i2π(xa/2+3ya/2)/λf],
U3(x,y)=exp[i2π(xa/23ya/2)/λf],
Re(x,y)=cos(2u)+cos(u+v)+cos(uv)=cos(2u)+2cos(u)cos(v),
Im(x,y)=sin(2u)+sin(u+v)+sin(uv)=2sin(u)[cos(u)cos(v)],
U(x,y)=m=13{exp{i2πλf{xacos[2(m1)3π]+yasin[2(m1)3π]}}+exp{i2πλf{xbcos[2(m1)+13π]+ybsin[2(m1)+13π]}}},
a0:b0=(3na+1):(3nb1),

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