Abstract

In this paper, we designed a binary phase mask (PM) with specific phase modulation characteristic and analyzed the spatial spectrum of the beam passing through the PM. In the case where the difference of phase modulation between two lattices of the binary PM is not equal to π, we found the spatial spectrum has the central spot (direct current component, DC component) except for the central eight strong symmetrical spots and many outer weak symmetrical spots. Based on the multiple-beam interference, the propagation-invariant vortex with a square array can be realized by interference of the eight plane waves with the same wave vectors along the optical axis from the central eight symmetrical spots via the modulated phase values of the central eight symmetric spots. The vortex arrays have two kinds of vortex with an opposite topological charge of l=±1. The helix can be formed with a square array by the interference of the vortex array and the plane wave along the optical axis from the DC component. The helix with outstanding helical intensity distributions have two screw directions, which coincide with the phase distribution of the optical vortex with the square array. The energy efficiency of this method can reach more than 80%. The simulation results demonstrate the feasibility of this method.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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2019 (3)

2018 (1)

A. Marzo, M. Caleap, and B. W. Drinkwater, “Acoustic Virtual Vortices with Tunable Orbital Angular Momentum for Trapping of Mie Particles,” Phys. Rev. Lett. 120(4), 044301 (2018).
[Crossref]

2017 (1)

2016 (1)

D. Baresch, J.-L. Thomas, and R. Marchiano, “Observation of a Single-Beam Gradient Force Acoustical Trap for Elastic Particles: Acoustical Tweezers,” Phys. Rev. Lett. 116(2), 024301 (2016).
[Crossref]

2015 (1)

Z. Hong, J. Zhang, and B. W. Drinkwater, “Observation of Orbital Angular Momentum Transfer from Bessel-Shaped Acoustic Vortices to Diphasic Liquid-Microparticle Mixtures,” Phys. Rev. Lett. 114(21), 214301 (2015).
[Crossref]

2014 (4)

T. Niermann, J. Verbeeck, and M. Lehmann, “Creating arrays of electron vortices,” Ultramicroscopy 136, 165–170 (2014).
[Crossref]

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of Nondiffracting Electron Bessel Beams,” Phys. Rev. X 4(1), 011013 (2014).
[Crossref]

J. T. Mendonça and J. Vieira, “Donut wakefields generated by intense laser pulses with orbital angular momentum,” Phys. Plasmas 21(3), 033107 (2014).
[Crossref]

J. Vieira and J. T. Mendonça, “Nonlinear Laser Driven Donut Wakefields for Positron and Electron Acceleration,” Phys. Rev. Lett. 112(21), 215001 (2014).
[Crossref]

2013 (1)

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie>, “Generation of electro Airy beams,” Nature 494(7437), 331–335 (2013).
[Crossref]

2011 (4)

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref]

V. Arrizón, D. Sánchez-de-la-Llave, G. Méndez, and U. Ruiz, “Efficient generation of periodic and quasi-periodic non-diffractive optical fields with phase holograms,” Opt. Express 19(11), 10553–10562 (2011).
[Crossref]

Y. Han and C. Liu, “Propagation-invariant hollow beams with hexagonal symmetry,” Opt. Commun. 284(9), 2264–2267 (2011).
[Crossref]

J. Becker, P. Rose, M. Boguslawski, and C. Denz, “Systematic approach to complex periodic vortex and helix lattices,” Opt. Express 19(10), 9848–9862 (2011).
[Crossref]

2010 (3)

A. Jiménez-Ceniceros, M. Trejo-Durán, E. Alvarado-Méndez, and V. M. Castaño, “Extinction zones and scalability in N-beam interference lattices,” Opt. Commun. 283(3), 362–367 (2010).
[Crossref]

C.-S. Guo, Y.-N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun. 283(9), 1889–1893 (2010).
[Crossref]

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref]

2009 (1)

G.-X. Wei, L.-L. Lu, and C.-S. Guo, “Generation of optical vortex array based on the fractional Talbot effect,” Opt. Commun. 282(14), 2665–2669 (2009).
[Crossref]

2008 (1)

G. C. G. Berkhout and M. W. Beijersbergen, “Method for Probing the Orbital Angular Momentum of Optical Vortices in Electromagnetic Waves from Astronomical Objects,” Phys. Rev. Lett. 101(10), 100801 (2008).
[Crossref]

2007 (1)

2006 (1)

C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
[Crossref]

2005 (5)

2004 (1)

2003 (4)

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref]

J. E. Curtis and D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28(11), 872–874 (2003).
[Crossref]

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. 53(7), 537–578 (2003).
[Crossref]

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[Crossref]

2002 (3)

L. Z. Cai, X. L. Yang, and Y. R. Wang, “All fourteen Bravais lattices can be formed by interference of four noncoplanar beams,” Opt. Lett. 27(11), 900–902 (2002).
[Crossref]

X. L. Yang and L. Z. Cai, “Wave design of the interference of three noncoplanar beams for microfiber fabrication,” Opt. Commun. 208(4-6), 293–297 (2002).
[Crossref]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic Holographic Optical Tweezers,” Opt. Commun. 207(1-6), 169–175 (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]

L. Z. Cai, X. L. Yang, and Y. R. Wang, “Formation of a microfiber bundle by interference of three noncoplanar beams,” Opt. Lett. 26(23), 1858–1860 (2001).
[Crossref]

2000 (2)

R. Oron, N. Davidson, A. A. Friesem, and F. Hasman, “Efficient formation of pure helical laser beams,” Opt. Commun. 182(1-3), 205–208 (2000).
[Crossref]

J. A. Davis, D. E. Mc Namra, D. M. Cottrell, and J. Campos, “Image processing with the radial Hilbert transform: theory and experiments,” Opt. Lett. 25(2), 99–101 (2000).
[Crossref]

1996 (1)

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

1994 (2)

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110(5-6), 670–678 (1994).
[Crossref]

M. W. Beijersbergen, R. P. C. Coerwinkel, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5-6), 321–327 (1994).
[Crossref]

1993 (1)

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic Laser Mode Converters and Transfer of Orbital Angular-Momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[Crossref]

1992 (2)

N. R. Heckenberg, R. Mc Duff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A: At., Mol., Opt. Phys. 45(11), 8185–8189 (1992).
[Crossref]

1977 (1)

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24(4), 505–515 (1977).
[Crossref]

Agrawal, A.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref]

Allen, L.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110(5-6), 670–678 (1994).
[Crossref]

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic Laser Mode Converters and Transfer of Orbital Angular-Momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A: At., Mol., Opt. Phys. 45(11), 8185–8189 (1992).
[Crossref]

Alvarado-Méndez, E.

A. Jiménez-Ceniceros, M. Trejo-Durán, E. Alvarado-Méndez, and V. M. Castaño, “Extinction zones and scalability in N-beam interference lattices,” Opt. Commun. 283(3), 362–367 (2010).
[Crossref]

Anderson, I. M.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref]

Arie, A.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie>, “Generation of electro Airy beams,” Nature 494(7437), 331–335 (2013).
[Crossref]

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]

Arrizón, V.

Azizian-Kalandaragh, Y.

A. Porfirev, S. Khonina, Y. Azizian-Kalandaragh, and M. Kirilenko, “Efficient generation of arrays of closed-packed high-quality light rings,” Photonic. Nanostruct. 37, 100736 (2019).
[Crossref]

Baresch, D.

D. Baresch, J.-L. Thomas, and R. Marchiano, “Observation of a Single-Beam Gradient Force Acoustical Trap for Elastic Particles: Acoustical Tweezers,” Phys. Rev. Lett. 116(2), 024301 (2016).
[Crossref]

Barnett, S. M.

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110(5-6), 670–678 (1994).
[Crossref]

Becker, J.

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, “Method for Probing the Orbital Angular Momentum of Optical Vortices in Electromagnetic Waves from Astronomical Objects,” Phys. Rev. Lett. 101(10), 100801 (2008).
[Crossref]

M. W. Beijersbergen, R. P. C. Coerwinkel, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5-6), 321–327 (1994).
[Crossref]

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic Laser Mode Converters and Transfer of Orbital Angular-Momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A: At., Mol., Opt. Phys. 45(11), 8185–8189 (1992).
[Crossref]

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, “Method for Probing the Orbital Angular Momentum of Optical Vortices in Electromagnetic Waves from Astronomical Objects,” Phys. Rev. Lett. 101(10), 100801 (2008).
[Crossref]

Bernet, S.

Boguslawski, M.

Bouchal, Z.

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. 53(7), 537–578 (2003).
[Crossref]

Boyd, R. W.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of Nondiffracting Electron Bessel Beams,” Phys. Rev. X 4(1), 011013 (2014).
[Crossref]

Brett, M. J.

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]

Cai, L. Z.

Caleap, M.

A. Marzo, M. Caleap, and B. W. Drinkwater, “Acoustic Virtual Vortices with Tunable Orbital Angular Momentum for Trapping of Mie Particles,” Phys. Rev. Lett. 120(4), 044301 (2018).
[Crossref]

Campos, J.

Carrada, R.

Castaño, V. M.

A. Jiménez-Ceniceros, M. Trejo-Durán, E. Alvarado-Méndez, and V. M. Castaño, “Extinction zones and scalability in N-beam interference lattices,” Opt. Commun. 283(3), 362–367 (2010).
[Crossref]

Chavez-Cerda, S.

Cheng, X.

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5-6), 321–327 (1994).
[Crossref]

Cottrell, D. M.

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref]

J. E. Curtis and D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28(11), 872–874 (2003).
[Crossref]

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

Dammann, H.

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24(4), 505–515 (1977).
[Crossref]

Davidson, N.

R. Oron, N. Davidson, A. A. Friesem, and F. Hasman, “Efficient formation of pure helical laser beams,” Opt. Commun. 182(1-3), 205–208 (2000).
[Crossref]

Davis, J. A.

Dennis, M. R.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of Nondiffracting Electron Bessel Beams,” Phys. Rev. X 4(1), 011013 (2014).
[Crossref]

Denz, C.

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]

Ding, J. P.

C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
[Crossref]

Ding, J.-P.

Drinkwater, B. W.

A. Marzo, M. Caleap, and B. W. Drinkwater, “Acoustic Virtual Vortices with Tunable Orbital Angular Momentum for Trapping of Mie Particles,” Phys. Rev. Lett. 120(4), 044301 (2018).
[Crossref]

Z. Hong, J. Zhang, and B. W. Drinkwater, “Observation of Orbital Angular Momentum Transfer from Bessel-Shaped Acoustic Vortices to Diphasic Liquid-Microparticle Mixtures,” Phys. Rev. Lett. 114(21), 214301 (2015).
[Crossref]

Foo, G.

Frabboni, S.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of Nondiffracting Electron Bessel Beams,” Phys. Rev. X 4(1), 011013 (2014).
[Crossref]

Friesem, A. A.

R. Oron, N. Davidson, A. A. Friesem, and F. Hasman, “Efficient formation of pure helical laser beams,” Opt. Commun. 182(1-3), 205–208 (2000).
[Crossref]

Fürhapter, S.

Gazzadi, G. C.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of Nondiffracting Electron Bessel Beams,” Phys. Rev. X 4(1), 011013 (2014).
[Crossref]

Gover, A.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie>, “Generation of electro Airy beams,” Nature 494(7437), 331–335 (2013).
[Crossref]

Grier, D. G.

J. E. Curtis and D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28(11), 872–874 (2003).
[Crossref]

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref]

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

Grillo, V.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of Nondiffracting Electron Bessel Beams,” Phys. Rev. X 4(1), 011013 (2014).
[Crossref]

Guo, C. S.

C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
[Crossref]

Guo, C.-S.

C.-S. Guo, Y.-N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun. 283(9), 1889–1893 (2010).
[Crossref]

G.-X. Wei, L.-L. Lu, and C.-S. Guo, “Generation of optical vortex array based on the fractional Talbot effect,” Opt. Commun. 282(14), 2665–2669 (2009).
[Crossref]

C.-S. Guo, X. Cheng, X.-Y. Ren, J.-P. Ding, and H.-T. Wang, “Optical vortex phase-shifting digital holography,” Opt. Express 12(21), 5166–5171 (2004).
[Crossref]

Han, Y.

Y. Han and C. Liu, “Propagation-invariant hollow beams with hexagonal symmetry,” Opt. Commun. 284(9), 2264–2267 (2011).
[Crossref]

Han, Y. J.

C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
[Crossref]

Hasman, F.

R. Oron, N. Davidson, A. A. Friesem, and F. Hasman, “Efficient formation of pure helical laser beams,” Opt. Commun. 182(1-3), 205–208 (2000).
[Crossref]

Hebri, D.

Heckenberg, N. R.

Herzing, A. A.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref]

Hong, Z.

Z. Hong, J. Zhang, and B. W. Drinkwater, “Observation of Orbital Angular Momentum Transfer from Bessel-Shaped Acoustic Vortices to Diphasic Liquid-Microparticle Mixtures,” Phys. Rev. Lett. 114(21), 214301 (2015).
[Crossref]

C.-S. Guo, Y.-N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun. 283(9), 1889–1893 (2010).
[Crossref]

Jensen, M. O.

Jesacher, A.

Jiménez-Ceniceros, A.

A. Jiménez-Ceniceros, M. Trejo-Durán, E. Alvarado-Méndez, and V. M. Castaño, “Extinction zones and scalability in N-beam interference lattices,” Opt. Commun. 283(3), 362–367 (2010).
[Crossref]

Juodkazis, S.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[Crossref]

Karimi, E.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of Nondiffracting Electron Bessel Beams,” Phys. Rev. X 4(1), 011013 (2014).
[Crossref]

Khonina, S.

A. Porfirev, S. Khonina, Y. Azizian-Kalandaragh, and M. Kirilenko, “Efficient generation of arrays of closed-packed high-quality light rings,” Photonic. Nanostruct. 37, 100736 (2019).
[Crossref]

Khonina, S. N.

Kirilenko, M.

A. Porfirev, S. Khonina, Y. Azizian-Kalandaragh, and M. Kirilenko, “Efficient generation of arrays of closed-packed high-quality light rings,” Photonic. Nanostruct. 37, 100736 (2019).
[Crossref]

Klotz, E.

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24(4), 505–515 (1977).
[Crossref]

Kondo, T.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[Crossref]

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]

Lehmann, M.

T. Niermann, J. Verbeeck, and M. Lehmann, “Creating arrays of electron vortices,” Ultramicroscopy 136, 165–170 (2014).
[Crossref]

Lereah, Y.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie>, “Generation of electro Airy beams,” Nature 494(7437), 331–335 (2013).
[Crossref]

Lezec, H. J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref]

Lilach, Y.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie>, “Generation of electro Airy beams,” Nature 494(7437), 331–335 (2013).
[Crossref]

Liu, C.

Y. Han and C. Liu, “Propagation-invariant hollow beams with hexagonal symmetry,” Opt. Commun. 284(9), 2264–2267 (2011).
[Crossref]

Lu, L.-L.

G.-X. Wei, L.-L. Lu, and C.-S. Guo, “Generation of optical vortex array based on the fractional Talbot effect,” Opt. Commun. 282(14), 2665–2669 (2009).
[Crossref]

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]

Marchiano, R.

D. Baresch, J.-L. Thomas, and R. Marchiano, “Observation of a Single-Beam Gradient Force Acoustical Trap for Elastic Particles: Acoustical Tweezers,” Phys. Rev. Lett. 116(2), 024301 (2016).
[Crossref]

Marzo, A.

A. Marzo, M. Caleap, and B. W. Drinkwater, “Acoustic Virtual Vortices with Tunable Orbital Angular Momentum for Trapping of Mie Particles,” Phys. Rev. Lett. 120(4), 044301 (2018).
[Crossref]

Matsuo, S.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[Crossref]

Mc Duff, R.

Mc Namra, D. E.

McClelland, J. J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref]

McMorran, B. J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref]

Méndez, G.

Mendonça, J. T.

J. T. Mendonça and J. Vieira, “Donut wakefields generated by intense laser pulses with orbital angular momentum,” Phys. Plasmas 21(3), 033107 (2014).
[Crossref]

J. Vieira and J. T. Mendonça, “Nonlinear Laser Driven Donut Wakefields for Positron and Electron Acceleration,” Phys. Rev. Lett. 112(21), 215001 (2014).
[Crossref]

Misawa, H.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[Crossref]

Mizeikis, V.

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[Crossref]

Niermann, T.

T. Niermann, J. Verbeeck, and M. Lehmann, “Creating arrays of electron vortices,” Ultramicroscopy 136, 165–170 (2014).
[Crossref]

Oron, R.

R. Oron, N. Davidson, A. A. Friesem, and F. Hasman, “Efficient formation of pure helical laser beams,” Opt. Commun. 182(1-3), 205–208 (2000).
[Crossref]

Padgett, M. J.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

Palacios, D. M.

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]

Porfirev, A.

A. Porfirev, S. Khonina, Y. Azizian-Kalandaragh, and M. Kirilenko, “Efficient generation of arrays of closed-packed high-quality light rings,” Photonic. Nanostruct. 37, 100736 (2019).
[Crossref]

Porfirev, A. P.

Rasouli, S.

Ren, X.-Y.

Ritsch-Marte, M.

Robertson, D. A.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

Rose, P.

Ruiz, U.

Sánchez-de-la-Llave, D.

Schattschneider, P.

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref]

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]

Smith, C. P.

Smith, G. M.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

Spreeuw, R. J.

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A: At., Mol., Opt. Phys. 45(11), 8185–8189 (1992).
[Crossref]

Swartzlander, G. A.

Thomas, J.-L.

D. Baresch, J.-L. Thomas, and R. Marchiano, “Observation of a Single-Beam Gradient Force Acoustical Trap for Elastic Particles: Acoustical Tweezers,” Phys. Rev. Lett. 116(2), 024301 (2016).
[Crossref]

Tian, H.

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref]

Trejo-Durán, M.

A. Jiménez-Ceniceros, M. Trejo-Durán, E. Alvarado-Méndez, and V. M. Castaño, “Extinction zones and scalability in N-beam interference lattices,” Opt. Commun. 283(3), 362–367 (2010).
[Crossref]

Turnbull, G. A.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

Unguris, J.

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref]

Vanderveen, H.

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic Laser Mode Converters and Transfer of Orbital Angular-Momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[Crossref]

Verbeeck, J.

T. Niermann, J. Verbeeck, and M. Lehmann, “Creating arrays of electron vortices,” Ultramicroscopy 136, 165–170 (2014).
[Crossref]

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref]

Vieira, J.

J. T. Mendonça and J. Vieira, “Donut wakefields generated by intense laser pulses with orbital angular momentum,” Phys. Plasmas 21(3), 033107 (2014).
[Crossref]

J. Vieira and J. T. Mendonça, “Nonlinear Laser Driven Donut Wakefields for Positron and Electron Acceleration,” Phys. Rev. Lett. 112(21), 215001 (2014).
[Crossref]

Voloch-Bloch, N.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie>, “Generation of electro Airy beams,” Nature 494(7437), 331–335 (2013).
[Crossref]

Wang, H. T.

C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
[Crossref]

Wang, H.-T.

Wang, Y. R.

Wei, G.-X.

G.-X. Wei, L.-L. Lu, and C.-S. Guo, “Generation of optical vortex array based on the fractional Talbot effect,” Opt. Commun. 282(14), 2665–2669 (2009).
[Crossref]

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5-6), 321–327 (1994).
[Crossref]

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic Laser Mode Converters and Transfer of Orbital Angular-Momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A: At., Mol., Opt. Phys. 45(11), 8185–8189 (1992).
[Crossref]

Yang, X. L.

Yu, Y.-N.

C.-S. Guo, Y.-N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun. 283(9), 1889–1893 (2010).
[Crossref]

Zhang, J.

Z. Hong, J. Zhang, and B. W. Drinkwater, “Observation of Orbital Angular Momentum Transfer from Bessel-Shaped Acoustic Vortices to Diphasic Liquid-Microparticle Mixtures,” Phys. Rev. Lett. 114(21), 214301 (2015).
[Crossref]

Zhang, Y.

C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
[Crossref]

Appl. Phys. Lett. (1)

T. Kondo, S. Matsuo, S. Juodkazis, V. Mizeikis, and H. Misawa, “Multiphoton fabrication of periodic structures by multibeam interference of femtosecond pulses,” Appl. Phys. Lett. 82(17), 2758–2760 (2003).
[Crossref]

Czech. J. Phys. (1)

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. 53(7), 537–578 (2003).
[Crossref]

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

Nature (2)

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, and A. Arie>, “Generation of electro Airy beams,” Nature 494(7437), 331–335 (2013).
[Crossref]

J. Verbeeck, H. Tian, and P. Schattschneider, “Production and application of electron vortex beams,” Nature 467(7313), 301–304 (2010).
[Crossref]

Opt. Acta (1)

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24(4), 505–515 (1977).
[Crossref]

Opt. Commun. (12)

A. Jiménez-Ceniceros, M. Trejo-Durán, E. Alvarado-Méndez, and V. M. Castaño, “Extinction zones and scalability in N-beam interference lattices,” Opt. Commun. 283(3), 362–367 (2010).
[Crossref]

C. S. Guo, Y. Zhang, Y. J. Han, J. P. Ding, and H. T. Wang, “Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering,” Opt. Commun. 259(2), 449–454 (2006).
[Crossref]

G.-X. Wei, L.-L. Lu, and C.-S. Guo, “Generation of optical vortex array based on the fractional Talbot effect,” Opt. Commun. 282(14), 2665–2669 (2009).
[Crossref]

R. Oron, N. Davidson, A. A. Friesem, and F. Hasman, “Efficient formation of pure helical laser beams,” Opt. Commun. 182(1-3), 205–208 (2000).
[Crossref]

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic Laser Mode Converters and Transfer of Orbital Angular-Momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[Crossref]

M. W. Beijersbergen, R. P. C. Coerwinkel, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112(5-6), 321–327 (1994).
[Crossref]

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4-6), 183–188 (1996).
[Crossref]

S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110(5-6), 670–678 (1994).
[Crossref]

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

X. L. Yang and L. Z. Cai, “Wave design of the interference of three noncoplanar beams for microfiber fabrication,” Opt. Commun. 208(4-6), 293–297 (2002).
[Crossref]

C.-S. Guo, Y.-N. Yu, and Z. Hong, “Optical sorting using an array of optical vortices with fractional topological charge,” Opt. Commun. 283(9), 1889–1893 (2010).
[Crossref]

Y. Han and C. Liu, “Propagation-invariant hollow beams with hexagonal symmetry,” Opt. Commun. 284(9), 2264–2267 (2011).
[Crossref]

Opt. Express (7)

Opt. Lett. (7)

Photonic. Nanostruct. (1)

A. Porfirev, S. Khonina, Y. Azizian-Kalandaragh, and M. Kirilenko, “Efficient generation of arrays of closed-packed high-quality light rings,” Photonic. Nanostruct. 37, 100736 (2019).
[Crossref]

Phys. Plasmas (1)

J. T. Mendonça and J. Vieira, “Donut wakefields generated by intense laser pulses with orbital angular momentum,” Phys. Plasmas 21(3), 033107 (2014).
[Crossref]

Phys. Rev. A: At., Mol., Opt. Phys. (1)

L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A: At., Mol., Opt. Phys. 45(11), 8185–8189 (1992).
[Crossref]

Phys. Rev. Lett. (7)

Z. Hong, J. Zhang, and B. W. Drinkwater, “Observation of Orbital Angular Momentum Transfer from Bessel-Shaped Acoustic Vortices to Diphasic Liquid-Microparticle Mixtures,” Phys. Rev. Lett. 114(21), 214301 (2015).
[Crossref]

D. Baresch, J.-L. Thomas, and R. Marchiano, “Observation of a Single-Beam Gradient Force Acoustical Trap for Elastic Particles: Acoustical Tweezers,” Phys. Rev. Lett. 116(2), 024301 (2016).
[Crossref]

A. Marzo, M. Caleap, and B. W. Drinkwater, “Acoustic Virtual Vortices with Tunable Orbital Angular Momentum for Trapping of Mie Particles,” Phys. Rev. Lett. 120(4), 044301 (2018).
[Crossref]

J. Vieira and J. T. Mendonça, “Nonlinear Laser Driven Donut Wakefields for Positron and Electron Acceleration,” Phys. Rev. Lett. 112(21), 215001 (2014).
[Crossref]

G. C. G. Berkhout and M. W. Beijersbergen, “Method for Probing the Orbital Angular Momentum of Optical Vortices in Electromagnetic Waves from Astronomical Objects,” Phys. Rev. Lett. 101(10), 100801 (2008).
[Crossref]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow Effects in Spiral Phase Contrast Microscopy,” Phys. Rev. Lett. 94(23), 233902 (2005).
[Crossref]

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003).
[Crossref]

Phys. Rev. X (1)

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of Nondiffracting Electron Bessel Beams,” Phys. Rev. X 4(1), 011013 (2014).
[Crossref]

Science (2)

B. J. McMorran, A. Agrawal, I. M. Anderson, A. A. Herzing, H. J. Lezec, J. J. McClelland, and J. Unguris, “Electron vortex beams with high quanta of orbital angular momentum,” Science 331(6014), 192–195 (2011).
[Crossref]

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]

Ultramicroscopy (1)

T. Niermann, J. Verbeeck, and M. Lehmann, “Creating arrays of electron vortices,” Ultramicroscopy 136, 165–170 (2014).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Optical system diagram.
Fig. 2.
Fig. 2. The phase modulation characteristics of the binary phase mask with φ=0.25π and the spatial spectrum of the beam passing through the phase mask.
Fig. 3.
Fig. 3. The phase distribution of the eight symmetric spots which can be used for generate the vortex with square array.
Fig. 4.
Fig. 4. The simulation results of the interference pattern of the eight symmetric plane wave from the eight symmetric spots shown in Fig. 3.
Fig. 5.
Fig. 5. The contour of the intensity distribution of the single vortex shown in Fig. 4.
Fig. 6.
Fig. 6. The phase difference between the single vortex shown in Fig. 4 and an ideal optical vortex with l = 1.
Fig. 7.
Fig. 7. The intensity distribution of the helix with square array at different z. (a) z = 110 mm, (b) z = 112 mm, (c) z = 114 mm, (d) z = 116 mm, (e) z = 118 mm, (f) z = 120 mm.

Equations (5)

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u P M ( x , y , 0 ) = A cos ϕ + i A sin ϕ exp { i π [ Int ( k 1 x π ) + Int ( k 1 y π ) + Int ( k 1 x + y π ) + Int ( k 1 x y π ) ] } .
a = A sin ϕ l = + m = + ( 2 π ) 4 1 ( 2 l 2 m + 1 ) ( 1 2 l 2 m ) ( 2 m + 1 ) ( 2 l + 1 ) = 0.2702 A sin ϕ .
u v o r t e x ( x , y , z ) = 4 a { sin [ 2 k r 10 ( x + y ) ] sin [ k r 10 ( x y ) ] + i sin [ k r 10 ( x + y ) ] sin [ 2 k r 10 ( x y ) ] } exp ( i k z z ) .
u h e l i x ( x , y , z ) = A cos ϕ exp ( i k z ) + 1.0808 A sin ϕ { sin [ 2 k r 10 ( x + y ) ] sin [ k r 10 ( x y ) ] + i sin [ k r 10 ( x + y ) ] sin [ 2 k r 10 ( x y ) ] } exp ( i k z z ) .
η = cos 2 ϕ + 8 × ( 0.2702 sin ϕ ) 2 = 82.56 % .

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