Abstract

In this work, we demonstrate experimentally the formation of 10 different structures consisting of bright beams with flat phase fronts in the focus of a lens (i.e., in the artificial far field). The basic structure used is a large, stable, square-shaped optical vortex (OV) array composed of vortices with alternating topological charges (TCs). The TCs of one individual OV, of a subarray of OVs, or of the complete OV lattice were erased/doubled in the cases of perfect superposition (on-site alignment) or are manipulated in phase in the cases of an offset between the vortices (off-site alignment). A dramatic reshaping of the beam is observed in the far field and shown to be in excellent agreement with numerical simulations.

© 2018 Optical Society of America

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References

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2017 (6)

2016 (3)

2015 (1)

L. Stoyanov, S. Topuzoski, I. Stefanov, L. Janicijevic, and A. Dreischuh, “Far field diffraction of an optical vortex beam by a fork-shaped grating,” Opt. Commun. 350, 301–308 (2015).
[Crossref]

2014 (1)

2012 (1)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

2011 (2)

S. Topuzoski and L. Janicijevic, “Fraunhofer diffraction of a Laguerre-Gaussian laser beam by fork-shaped grating,” J. Mod. Opt. 58, 138–145 (2011).
[Crossref]

P. Bingen, M. Reuss, J. Engelhardt, and S. W. Hell, “Parallelized STED fluorescence nanoscopy,” Opt. Express 19, 23716–23726 (2011).
[Crossref]

2010 (2)

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12, 083053 (2010).
[Crossref]

A. Picón, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Photoionization with orbital angular momentum beams,” Opt. Express 18, 3660–3671 (2010).
[Crossref]

2009 (3)

P. Hansinger, A. Dreischuh, and G. G. Paulus, “Optical vortices in self-focusing Kerr nonlinear media,” Opt. Commun. 282, 3349–3355 (2009).
[Crossref]

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[Crossref]

A. Lizana, N. Martin, M. Estapé, E. Fernández, I. Moreno, A. Márquez, C. Iemmi, J. Campoz, and M. J. Yzuel, “Influence of the incident angle in the performance of liquid crystal on silicon displays,” Opt. Express 17, 8491–8505 (2009).
[Crossref]

2008 (1)

2007 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[Crossref]

2006 (1)

2005 (2)

2003 (1)

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

2002 (2)

1999 (1)

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

1998 (1)

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, “Motion control of ensembles of ordered optical vortices generated on finite extent background,” Opt. Commun. 151, 413–421 (1998).
[Crossref]

1997 (2)

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, “Experimental observation of fluid like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
[Crossref]

D. Rozas, C. T. Law, and G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997).
[Crossref]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[Crossref]

Agrawal, G. P.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Ahmed, N.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Anderson, B. P.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

Assa, M.

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, “Motion control of ensembles of ordered optical vortices generated on finite extent background,” Opt. Commun. 151, 413–421 (1998).
[Crossref]

Benseny, A.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12, 083053 (2010).
[Crossref]

Bernet, S.

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[Crossref]

Bingen, P.

Bouchard, F.

Bowman, C. N.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[Crossref]

Boyd, R. W.

Brandt, E. H.

E. H. Brandt, J. Vanacken, and V. V. Moshchalkov, “Vortices in physics,” Physica C 369, 1–9 (2002).
[Crossref]

Calvo, G. F.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12, 083053 (2010).
[Crossref]

A. Picón, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Photoionization with orbital angular momentum beams,” Opt. Express 18, 3660–3671 (2010).
[Crossref]

Campoz, J.

Cesar, J.

Chervenkov, S.

Chipouline, A.

Cornell, E. A.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

Denz, C.

Desyatnikov, A. S.

A. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Träger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Yu. S. Kivshar, “Two-dimensional self-trapped nonlinear photonic lattices,” Opt. Express 14, 2851–2863 (2006).
[Crossref]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” in Progress in Optics, E. Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 291–391.

Dimitrov, N.

Dinev, S.

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, “Motion control of ensembles of ordered optical vortices generated on finite extent background,” Opt. Commun. 151, 413–421 (1998).
[Crossref]

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Dreischuh, A.

L. Stoyanov, N. Dimitrov, I. Stefanov, D. N. Neshev, and A. Dreischuh, “Optical waveguiding by necklace and azimuthon beams in nonlinear media,” J. Opt. Soc. Am. B 34, 801–807 (2017).
[Crossref]

P. Hansinger, G. Maleshkov, I. L. Garanovich, D. V. Skryabin, D. N. Neshev, A. Dreischuh, and G. G. Paulus, “White light generated by femtosecond optical vortex beams,” J. Opt. Soc. Am. B 33, 681–690 (2016).
[Crossref]

L. Stoyanov, S. Topuzoski, I. Stefanov, L. Janicijevic, and A. Dreischuh, “Far field diffraction of an optical vortex beam by a fork-shaped grating,” Opt. Commun. 350, 301–308 (2015).
[Crossref]

P. Hansinger, G. Maleshkov, I. L. Garanovich, D. Skryabin, D. N. Neshev, A. Dreischuh, and G. G. Paulus, “Vortex algebra by multiply cascaded four-wave mixing of femtosecond optical beams,” Opt. Express 22, 11079–11089 (2014).
[Crossref]

P. Hansinger, A. Dreischuh, and G. G. Paulus, “Optical vortices in self-focusing Kerr nonlinear media,” Opt. Commun. 282, 3349–3355 (2009).
[Crossref]

A. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Träger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Yu. S. Kivshar, “Two-dimensional self-trapped nonlinear photonic lattices,” Opt. Express 14, 2851–2863 (2006).
[Crossref]

A. Dreischuh, S. Chervenkov, D. Neshev, G. G. Paulus, and H. Walther, “Generation of lattice structures of optical vortices,” J. Opt. Soc. Am. B 19, 550–556 (2002).
[Crossref]

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, “Motion control of ensembles of ordered optical vortices generated on finite extent background,” Opt. Commun. 151, 413–421 (1998).
[Crossref]

Dudley, A.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
[Crossref]

Engelhardt, J.

Estapé, M.

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Fernández, E.

Fischer, R.

Foo, G.

Forbes, A.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
[Crossref]

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref]

Fürhapter, S.

Gagnon-Bischoff, J.

Garanovich, I. L.

Gregg, P.

Grier, D. G.

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

Grillo, V.

Gurbatov, S. O.

Haidar, M.

Haljan, P. C.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

Hall, D. S.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

Hansinger, P.

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref]

Hell, S. W.

Huang, H.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Iemmi, C.

Janicijevic, L.

L. Stoyanov, S. Topuzoski, I. Stefanov, L. Janicijevic, and A. Dreischuh, “Far field diffraction of an optical vortex beam by a fork-shaped grating,” Opt. Commun. 350, 301–308 (2015).
[Crossref]

S. Topuzoski and L. Janicijevic, “Fraunhofer diffraction of a Laguerre-Gaussian laser beam by fork-shaped grating,” J. Mod. Opt. 58, 138–145 (2011).
[Crossref]

L. Janicijevic and S. Topuzoski, “Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings,” J. Opt. Soc. Am. A 25, 2659–2669 (2008).
[Crossref]

Jesacher, A.

Karimi, E.

Kivshar, Yu. S.

A. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Träger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Yu. S. Kivshar, “Two-dimensional self-trapped nonlinear photonic lattices,” Opt. Express 14, 2851–2863 (2006).
[Crossref]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” in Progress in Optics, E. Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 291–391.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Kowalski, B. A.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[Crossref]

Kristensen, P.

Krolikowski, W.

Küppers, F.

Larocque, H.

Law, C. T.

Li, S.

Lizana, A.

Lyubopytov, V.

Malekizandi, M.

Maleshkov, G.

Márquez, A.

Martin, N.

Matthews, M. R.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

McLeod, R. R.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[Crossref]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[Crossref]

Mompart, J.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12, 083053 (2010).
[Crossref]

A. Picón, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Photoionization with orbital angular momentum beams,” Opt. Express 18, 3660–3671 (2010).
[Crossref]

Moreno, I.

Mortimer, D.

Moshchalkov, V. V.

E. H. Brandt, J. Vanacken, and V. V. Moshchalkov, “Vortices in physics,” Physica C 369, 1–9 (2002).
[Crossref]

Ndagano, B.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
[Crossref]

Neshev, D.

A. Dreischuh, S. Chervenkov, D. Neshev, G. G. Paulus, and H. Walther, “Generation of lattice structures of optical vortices,” J. Opt. Soc. Am. B 19, 550–556 (2002).
[Crossref]

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, “Motion control of ensembles of ordered optical vortices generated on finite extent background,” Opt. Commun. 151, 413–421 (1998).
[Crossref]

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A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12, 083053 (2010).
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A. Picón, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Photoionization with orbital angular momentum beams,” Opt. Express 18, 3660–3671 (2010).
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J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
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Zghal, M.

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
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Zhang, Y.

J. Mod. Opt. (1)

S. Topuzoski and L. Janicijevic, “Fraunhofer diffraction of a Laguerre-Gaussian laser beam by fork-shaped grating,” J. Mod. Opt. 58, 138–145 (2011).
[Crossref]

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

J. Opt. Soc. Am. B (4)

Nat. Photonics (1)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[Crossref]

Nature (1)

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

New J. Phys. (1)

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12, 083053 (2010).
[Crossref]

Opt. Commun. (3)

L. Stoyanov, S. Topuzoski, I. Stefanov, L. Janicijevic, and A. Dreischuh, “Far field diffraction of an optical vortex beam by a fork-shaped grating,” Opt. Commun. 350, 301–308 (2015).
[Crossref]

P. Hansinger, A. Dreischuh, and G. G. Paulus, “Optical vortices in self-focusing Kerr nonlinear media,” Opt. Commun. 282, 3349–3355 (2009).
[Crossref]

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, “Motion control of ensembles of ordered optical vortices generated on finite extent background,” Opt. Commun. 151, 413–421 (1998).
[Crossref]

Opt. Express (11)

P. Gregg, P. Kristensen, and S. Ramachandran, “13.4  km OAM state propagation by recirculating fiber loop,” Opt. Express 24, 18938–18947 (2016).
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A. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Träger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Yu. S. Kivshar, “Two-dimensional self-trapped nonlinear photonic lattices,” Opt. Express 14, 2851–2863 (2006).
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V. Lyubopytov, A. Porfirev, S. O. Gurbatov, S. Paul, M. Schumann, J. Cesar, M. Malekizandi, M. Haidar, M. Wegener, A. Chipouline, and F. Küppers, “Simultaneous wavelength and orbital angular momentum demultiplexing using tunable MEMS-based Fabry–Perot filter,” Opt. Express 25, 9634–9646 (2017).
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M. J. Padgett, “Orbital angular momentum 25 years on,” Opt. Express 25, 11265–11274 (2017).
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H. Larocque, J. Gagnon-Bischoff, D. Mortimer, Y. Zhang, F. Bouchard, J. Upham, V. Grillo, R. W. Boyd, and E. Karimi, “Generalized optical angular momentum sorter and its application to high-dimensional quantum cryptography,” Opt. Express 25, 19832–19843 (2017).
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E. Otte, K. Tekce, and C. Denz, “Tailored intensity landscapes by tight focusing of singular vector beams,” Opt. Express 25, 20194–20200 (2017).
[Crossref]

S. Li and J. Wang, “Experimental demonstration of optical interconnects exploiting orbital angular momentum array,” Opt. Express 25, 21537–21547 (2017).
[Crossref]

A. Lizana, N. Martin, M. Estapé, E. Fernández, I. Moreno, A. Márquez, C. Iemmi, J. Campoz, and M. J. Yzuel, “Influence of the incident angle in the performance of liquid crystal on silicon displays,” Opt. Express 17, 8491–8505 (2009).
[Crossref]

A. Picón, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Photoionization with orbital angular momentum beams,” Opt. Express 18, 3660–3671 (2010).
[Crossref]

P. Bingen, M. Reuss, J. Engelhardt, and S. W. Hell, “Parallelized STED fluorescence nanoscopy,” Opt. Express 19, 23716–23726 (2011).
[Crossref]

P. Hansinger, G. Maleshkov, I. L. Garanovich, D. Skryabin, D. N. Neshev, A. Dreischuh, and G. G. Paulus, “Vortex algebra by multiply cascaded four-wave mixing of femtosecond optical beams,” Opt. Express 22, 11079–11089 (2014).
[Crossref]

Opt. Lett. (2)

Phys. Rev. Lett. (3)

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, “Experimental observation of fluid like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
[Crossref]

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, “Vortices in a Bose–Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[Crossref]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref]

Physica C (1)

E. H. Brandt, J. Vanacken, and V. V. Moshchalkov, “Vortices in physics,” Physica C 369, 1–9 (2002).
[Crossref]

Proc. R. Soc. London A (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[Crossref]

Sci. Rep. (1)

A. Trichili, C. Rosales-Guzmán, A. Dudley, B. Ndagano, A. B. Salem, M. Zghal, and A. Forbes, “Optical communication beyond orbital angular momentum,” Sci. Rep. 6, 27674 (2016).
[Crossref]

Science (1)

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[Crossref]

Other (2)

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” in Progress in Optics, E. Wolf, ed. (North-Holland, 2005), Vol. 47, pp. 291–391.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

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Figures (10)

Fig. 1.
Fig. 1. Experimental setup. Nd:YVO4, continuous-wave frequency-doubled laser emitting at a wavelength λ=532  nm; BS, beam splitters; M, flat silver mirrors; SLM, reflective spatial light modulator (model Pluto, Holoeye Photonics); L, focusing lens (f=100  cm); CCD, charge-coupled device camera. Laser beam power 1.2 mW in front of SLM1 and 0.63 mW behind SLM2 independent of whether the liquid crystal displays are addressed with OV lattices or are switched off.
Fig. 2.
Fig. 2. (a) Amplitude and (b) phase profile of the basic square-shaped vortex lattice. (c) displays the interference pattern numerically generated by interfering the singular beam with a tilted plane wave. Some 22% of the total area of the computational window spanning over 1024×1024 points is shown.
Fig. 3.
Fig. 3. Numerical data. (a) Black curves, intensity profiles of the OV cores in the case of an initial pure phase modulation at the effective position of SLM1 and (b) in the case of both amplitude (tanh) and phase modulation. Blue dashed and red solid curves, beam profiles at the position of the focusing lens (L) and in its focus, respectively (F, artificial far field). The curve corresponding to the far-field (red) was divided by 425 for better visualization.
Fig. 4.
Fig. 4. Numerical data. Far-field intensity distributions (solid curves) of recovered Gaussian beams and their respective phase profiles (dashed curves) when all TCs of large square OV array are erased by a second (oppositely charged) vortex array. The vortex array node spacing is 41 pixels (blue solid/dashed curve) and 21 pixels (black squares/solid curves). The blue solid/dashed curves are horizontal slices of the data shown in Figs. 5(g) and 5(h), respectively.
Fig. 5.
Fig. 5. Numerical simulations for array node spacing 41 pixels. (a) Intensity of the background beam illuminating SLM1; (b) phase distribution sent to this modulator; and (c) resulting intensity distribution just in front of SLM2. (d) After the inverted (in signs) TC phase distribution erases the whole array of square singularities, the phase profile is modulated but does not contain phase discontinuities and (e) in front of the focusing lens, the dark beam contrast gradually decreases. The lens [phase profile just behind it shown in frame (f)] focuses the beam. Intensity (g), (i) and phase profiles (h), (j) of the recovered Gaussian beams in the artificial far field (g), (h) and 6.5LDiff behind it (i), (j). Some 6% of the total computational area is shown in each frame.
Fig. 6.
Fig. 6. Experimental result for an array node spacing of 41 pixels. (a), (c) Far-field intensity distributions, of the Gaussian beams after all TCs of large square OV array are erased. Frames (b), (d) show the recorded respective interference patterns. Frames (c), (d) are the same as frames (a), (b) but with one quadrant processed intentionally by tone adjustment for better visibility of some weak satellite structures.
Fig. 7.
Fig. 7. (a)–(f) Single square OV array theory versus (g), (h) experiment. Far-field intensity (a), (c), (e)–(g) and phase (b), (d) profiles of a square OV array, and (h) respective interference pattern for node spacing 41 pixels.
Fig. 8.
Fig. 8. (a) Far-field intensity profiles (even rows) of large square OV lattices structured by adding an OV with an opposite TC; (b) one-dimensional dark beam; and (c) crossed one-dimensional dark beams. First two rows, numerical results; last two rows, experimental data. In the second row are shown calculated beam phase profiles, whereas in the last row of frames are presented experimentally recorded interferograms. Node spacing 41 pixels.
Fig. 9.
Fig. 9. Numerical results (upper row) and experimental data (lower row) for the far-field intensity distribution in the case of (a), (b) on-site and (c), (d) off-site array alignments. In the on-site case, two large square OV lattices are projected on the modulators, causing an effective doubling of all TCs. In the off-site case, the square OV lattices are shifted by a half of the node spacing in vertical direction. The frames to the right of the intensity distributions are calculated beam phase profiles (upper row) and experimentally recorded interference patterns (lower row). The numerical data refer to 41 pixel lattice node spacing.
Fig. 10.
Fig. 10. Experimentally recorded far-field intensity profiles of bright beams (upper row) and respective interference patterns (lower row) in four different cases. (a) Diffraction of a large square OV lattice from a second lattice shifted both horizontally and vertically at one-half of the lattice node spacing (i.e., off-site diagonal alignment); (b) far-field pattern created from a small 6×6 OV array with alternating TCs. The second SLM is acting as a mirror. (c) Far-field pattern created when small 6×6 OV array with alternating OV TCs is added to a large square OV pattern. The alignment is on-site, so the TCs in the central part of the large OV array are erased. (d) Far-field diffraction of a large hexagonal OV array with alternating TCs from a large square array of OVs with alternating TCs. The lattice node spacing of the square lattice is 2.5 times smaller than that of the hexagonal lattice.

Equations (2)

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iE/(z/LDiff)+(1/2)ΔTE=0.
T(x,y)exp{ik(x2+y2)/(2f)},

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