Abstract

Structured light has been created by a myriad of near-and far-field techniques and has found both classical and quantum applications. In the case of orbital angular momentum (OAM), continuous spiral phase patterns in dynamic or geometric phase are often employed with the phase patterns existing across the entire transverse plane. Here, we exploit the uncertain relationship between OAM and angle in order to create structured OAM fields by using multilevel OAM holograms. We show theoretically and experimentally that only a multilevel angular phase contour in the near-field is needed to create structured OAM light in the far-field, exploiting the reciprocal nature of angular momentum and angle. We use this approach to demonstrate exotic 3D structured light control to show the Poynting vector’s evolution in such fields and to highlight the physics underlying this phenomenon.

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

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References

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2018 (7)

C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20(12), 123001 (2018).
[Crossref]

M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photons: new quantum perspectives in high dimensions,” Light Sci. Appl. 7(3), 17146 (2018).
[Crossref]

B. Ndagano, I. Nape, M. A. Cox, C. Rosales-Guzman, and A. Forbes, “Creation and detection of vector vortex modes for classical and quantum communication,” J. Lit. Technol. 36(2), 292–301 (2018).
[Crossref]

A. H. Dorrah, C. Rosales-Guzman, A. Forbes, and M. Mojahedi, “Evolution of orbital angular momentum in three-dimensional structured light,” Phys. Rev. A (Coll. Park) 98(4), 043846 (2018).
[Crossref]

Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).
[Crossref]

E. Otte, C. Rosales-Guzmán, B. Ndagano, C. Denz, and A. Forbes, “Entanglement beating in free space through spin–orbit coupling,” Light Sci. Appl. 7(5), 18009 (2018).
[Crossref]

N. Bhebhe, C. Rosales-Guzman, and A. Forbes, “Classical and quantum analysis of propagation invariant vector flat-top beams,” Appl. Opt. 57(19), 5451–5458 (2018).
[Crossref] [PubMed]

2017 (5)

J. Webster, C. Rosales-Guzmán, and A. Forbes, “Radially dependent angular acceleration of twisted light,” Opt. Lett. 42(4), 675–678 (2017).
[Crossref] [PubMed]

M. J. Padgett, “Orbital angular momentum 25 years on,” Opt. Express 25(10), 11265–11274 (2017).
[Crossref] [PubMed]

A. Forbes, “Controlling light’s helicity at the source: orbital angular momentum states from lasers,” Philos Trans A Math Phys Eng Sci 375(2087), 20150436 (2017).
[Crossref] [PubMed]

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[Crossref] [PubMed]

2016 (1)

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

2015 (3)

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
[Crossref]

R. Dharmavarapu, A. Vijayakumar, and S. Bhattacharya, “Design and fabrication of holographic optical elements for the generation of tilted and accelerating Airy beams,” Asian J. Phys. 24(10), 1363–1372 (2015).

2013 (3)

2012 (1)

2011 (2)

2010 (3)

S. Vo, K. Fuerschbach, K. P. Thompson, M. A. Alonso, and J. P. Rolland, “Airy beams: a geometric optics perspective,” J. Opt. Soc. Am. A 27(12), 2574–2582 (2010).
[Crossref] [PubMed]

J. M. Hickmann, E. J. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using lights orbital angular momentum,” Phys. Rev. Lett. 105(5), 053904 (2010).
[Crossref] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient Sorting of Orbital Angular Momentum States of Light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

2009 (3)

2008 (2)

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

2004 (2)

2002 (1)

F. Cervera, L. Sanchis, J. V. Sánchez-Pérez, R. Martínez-Sala, C. Rubio, F. Meseguer, C. López, D. Caballero, and J. Sánchez-Dehesa, “Refractive acoustic devices for airborne sound,” Phys. Rev. Lett. 88(2), 023902 (2002).
[Crossref] [PubMed]

2001 (2)

G. Molina-Terriza, E. M. Wright, and L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26(3), 163–165 (2001).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

1997 (2)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
[Crossref]

G.-H. Kim, J.-H. Jeon, K.-H. Ko, H.-J. Moon, J.-H. Lee, and J.-S. Chang, “Optical vortices produced with a nonspiral phase plate,” Appl. Opt. 36(33), 8614–8621 (1997).
[Crossref] [PubMed]

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(3), 221–223 (1992).
[Crossref] [PubMed]

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

1991 (1)

1974 (1)

’t Hooft, G. W.

Ahmed, N.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Allen, L.

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Alonso, M. A.

Alpmann, C.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

Ambrosio, A.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[Crossref] [PubMed]

Anderson, M. E.

Andrews, D. L.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

Ashrafi, N.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Ashrafi, S.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Assanto, G.

Baker, M.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

Banzer, P.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

Bao, C.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Barnett, S. M.

Bauer, T.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

Beijersbergen, M. W.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient Sorting of Orbital Angular Momentum States of Light,” Phys. Rev. Lett. 105(15), 153601 (2010).
[Crossref] [PubMed]

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Belmonte, A.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient Sorting of Orbital Angular Momentum States of Light,” Phys. Rev. Lett. 105(15), 153601 (2010).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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R. Dharmavarapu, A. Vijayakumar, and S. Bhattacharya, “Design and fabrication of holographic optical elements for the generation of tilted and accelerating Airy beams,” Asian J. Phys. 24(10), 1363–1372 (2015).

Bhebhe, N.

Bigelow, N. P.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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Brasselet, E.

E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
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F. Cervera, L. Sanchis, J. V. Sánchez-Pérez, R. Martínez-Sala, C. Rubio, F. Meseguer, C. López, D. Caballero, and J. Sánchez-Dehesa, “Refractive acoustic devices for airborne sound,” Phys. Rev. Lett. 88(2), 023902 (2002).
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Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).
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A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
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R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
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F. Cervera, L. Sanchis, J. V. Sánchez-Pérez, R. Martínez-Sala, C. Rubio, F. Meseguer, C. López, D. Caballero, and J. Sánchez-Dehesa, “Refractive acoustic devices for airborne sound,” Phys. Rev. Lett. 88(2), 023902 (2002).
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Chang, J.-S.

Chávez-Cerda, S.

J. M. Hickmann, E. J. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using lights orbital angular momentum,” Phys. Rev. Lett. 105(5), 053904 (2010).
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Courtial, J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient Sorting of Orbital Angular Momentum States of Light,” Phys. Rev. Lett. 105(15), 153601 (2010).
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Cox, M. A.

B. Ndagano, I. Nape, M. A. Cox, C. Rosales-Guzman, and A. Forbes, “Creation and detection of vector vortex modes for classical and quantum communication,” J. Lit. Technol. 36(2), 292–301 (2018).
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Davidson, N.

de Araujo, L. E. E.

Dennis, M.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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E. Otte, C. Rosales-Guzmán, B. Ndagano, C. Denz, and A. Forbes, “Entanglement beating in free space through spin–orbit coupling,” Light Sci. Appl. 7(5), 18009 (2018).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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Devlin, R. C.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017).
[Crossref] [PubMed]

Dharmavarapu, R.

R. Dharmavarapu, A. Vijayakumar, and S. Bhattacharya, “Design and fabrication of holographic optical elements for the generation of tilted and accelerating Airy beams,” Asian J. Phys. 24(10), 1363–1372 (2015).

Dholakia, K.

Dorrah, A. H.

A. H. Dorrah, C. Rosales-Guzman, A. Forbes, and M. Mojahedi, “Evolution of orbital angular momentum in three-dimensional structured light,” Phys. Rev. A (Coll. Park) 98(4), 043846 (2018).
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A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
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C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
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A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett. 38(17), 3429–3432 (2013).
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C. Schulze, A. Dudley, D. Flamm, M. Duparre, and A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. Phys. 15(7), 073025 (2013).
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I. A. Litvin, A. Dudley, and A. Forbes, “Poynting vector and orbital angular momentum density of superpositions of Bessel beams,” Opt. Express 19(18), 16760–16771 (2011).
[Crossref] [PubMed]

R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, “Generating superpositions of higher-order Bessel beams,” Opt. Express 17(26), 23389–23395 (2009).
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Duparre, M.

C. Schulze, A. Dudley, D. Flamm, M. Duparre, and A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. Phys. 15(7), 073025 (2013).
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Duparré, M.

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
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Erhard, M.

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M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photons: new quantum perspectives in high dimensions,” Light Sci. Appl. 7(3), 17146 (2018).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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C. Schulze, A. Dudley, D. Flamm, M. Duparre, and A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. Phys. 15(7), 073025 (2013).
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Fonseca, E. J.

J. M. Hickmann, E. J. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using lights orbital angular momentum,” Phys. Rev. Lett. 105(5), 053904 (2010).
[Crossref] [PubMed]

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B. Ndagano, I. Nape, M. A. Cox, C. Rosales-Guzman, and A. Forbes, “Creation and detection of vector vortex modes for classical and quantum communication,” J. Lit. Technol. 36(2), 292–301 (2018).
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C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20(12), 123001 (2018).
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A. H. Dorrah, C. Rosales-Guzman, A. Forbes, and M. Mojahedi, “Evolution of orbital angular momentum in three-dimensional structured light,” Phys. Rev. A (Coll. Park) 98(4), 043846 (2018).
[Crossref]

E. Otte, C. Rosales-Guzmán, B. Ndagano, C. Denz, and A. Forbes, “Entanglement beating in free space through spin–orbit coupling,” Light Sci. Appl. 7(5), 18009 (2018).
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N. Bhebhe, C. Rosales-Guzman, and A. Forbes, “Classical and quantum analysis of propagation invariant vector flat-top beams,” Appl. Opt. 57(19), 5451–5458 (2018).
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J. Webster, C. Rosales-Guzmán, and A. Forbes, “Radially dependent angular acceleration of twisted light,” Opt. Lett. 42(4), 675–678 (2017).
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A. Forbes, “Controlling light’s helicity at the source: orbital angular momentum states from lasers,” Philos Trans A Math Phys Eng Sci 375(2087), 20150436 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
[Crossref]

A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett. 38(17), 3429–3432 (2013).
[Crossref] [PubMed]

C. Schulze, A. Dudley, D. Flamm, M. Duparre, and A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. Phys. 15(7), 073025 (2013).
[Crossref]

I. A. Litvin, A. Dudley, and A. Forbes, “Poynting vector and orbital angular momentum density of superpositions of Bessel beams,” Opt. Express 19(18), 16760–16771 (2011).
[Crossref] [PubMed]

R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, “Generating superpositions of higher-order Bessel beams,” Opt. Express 17(26), 23389–23395 (2009).
[Crossref] [PubMed]

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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).
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M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56(5), 4064–4075 (1997).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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F. Cervera, L. Sanchis, J. V. Sánchez-Pérez, R. Martínez-Sala, C. Rubio, F. Meseguer, C. López, D. Caballero, and J. Sánchez-Dehesa, “Refractive acoustic devices for airborne sound,” Phys. Rev. Lett. 88(2), 023902 (2002).
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A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
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A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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A. H. Dorrah, C. Rosales-Guzman, A. Forbes, and M. Mojahedi, “Evolution of orbital angular momentum in three-dimensional structured light,” Phys. Rev. A (Coll. Park) 98(4), 043846 (2018).
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E. Otte, C. Rosales-Guzmán, B. Ndagano, C. Denz, and A. Forbes, “Entanglement beating in free space through spin–orbit coupling,” Light Sci. Appl. 7(5), 18009 (2018).
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C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
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Xie, G.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
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A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
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Zeilinger, A.

M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photons: new quantum perspectives in high dimensions,” Light Sci. Appl. 7(3), 17146 (2018).
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Zeng, J.

Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).
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Zhao, C.

Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).
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Zhao, Z.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
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Zhu, X.

Y. Yang, X. Zhu, J. Zeng, X. Lu, C. Zhao, and Y. Cai, “Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation,” Nanophotonics 7(3), 677–682 (2018).
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Adv. Opt. Photonics (2)

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
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A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
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Appl. Opt. (3)

Asian J. Phys. (1)

R. Dharmavarapu, A. Vijayakumar, and S. Bhattacharya, “Design and fabrication of holographic optical elements for the generation of tilted and accelerating Airy beams,” Asian J. Phys. 24(10), 1363–1372 (2015).

J. Lit. Technol. (1)

B. Ndagano, I. Nape, M. A. Cox, C. Rosales-Guzman, and A. Forbes, “Creation and detection of vector vortex modes for classical and quantum communication,” J. Lit. Technol. 36(2), 292–301 (2018).
[Crossref]

J. Opt. (2)

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).
[Crossref]

C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20(12), 123001 (2018).
[Crossref]

J. Opt. Soc. Am. (1)

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

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

Light Sci. Appl. (2)

E. Otte, C. Rosales-Guzmán, B. Ndagano, C. Denz, and A. Forbes, “Entanglement beating in free space through spin–orbit coupling,” Light Sci. Appl. 7(5), 18009 (2018).
[Crossref]

M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photons: new quantum perspectives in high dimensions,” Light Sci. Appl. 7(3), 17146 (2018).
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Nanophotonics (1)

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Supplementary Material (2)

NameDescription
» Visualization 1       Evolution of the Poynting vector in a structured light beam engineered by a multi-phase approach and propagating along a curved trajectory.
» Visualization 2       Evolution of the Poynting vector in a structured light beam engineered by a multi-phase approach.

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Figures (8)

Fig. 1
Fig. 1 A schematic of the concept. Converting a continuous blazed grating (a) into a multilevel element results in a spectrum of linear momenta, as illustrated in (b) and (c). The insets to the left of each hologram illustrates the phase values (top) and linear momentum spectrum (bottom). Likewise, a continuous azimuthal phase in (d) has a well-defined OAM value, whereas a multilevel approximation in the azimuth, (e) and (f), results in a spectrum of OAM. Again, the insets to the right illustrate the phase values (top) and OAM spectrum (bottom). In (g) the multilevel approach is confined to only a contour in the transverse plane, allowing for the simple generation of controlled OAM superpositions.
Fig. 2
Fig. 2 Example of angular partitioning the transverse plane to create multilevel binary holograms. As the number of phase levels (N) is increased so the azimuthal phase becomes closer to the ideal, in this example a topological charge of m = 1. The black color indicates a 0-phase value, while white indicates a 2π-phase value.
Fig. 3
Fig. 3 Experimental set-up used for generation of beams by a multilevel phase element as well as the subsequent modal decomposition of the beams.
Fig. 4
Fig. 4 Example of the far field intensity of twenty multiplexed modes. (a) Calibration pattern required to identify the (x,y) coordinates where the on-axis intensity is measured. (b) Projection of an min = 4 input mode onto the multiplexed set of modes exp( imϕ ),  m[10,9].
Fig. 5
Fig. 5 OAM spectrum of an input beam (m in = 3) as function of the number of phase levels (N) employed for its generation. Simulation in (a) and experimental results in (b). Notice how our experimental results agree very well with our simulations.
Fig. 6
Fig. 6 Experimentally measured OAM spectrum as function of the number of phase steps (N) employed to generate an input beam with topological charge min. From (a) to (f) the topological charge of the input beams takes the values min = [-4, −3, −2, −1, 1 2 3 4].
Fig. 7
Fig. 7 (a) Simulated intensity at the focal plane of the diffractive lens using Fresnel propagation and Poynting vector plot, (b) experimental intensity recorded at the focal plane.
Fig. 8
Fig. 8 Phase image of (a) DOE1 and (b) DOE2. The simulated (LHS) and experimental (RHS) results at three different planes (z = 45 cm, 48 cm and 51 cm) for (c) DOE1 (Visualization 1) and (b) DOE2 (Visualization 2).

Equations (11)

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m= 1 2π ϕ(x,y)· d s ,
t( ϕ )= n=1 N exp( i ϕ n ) with 2πm( n1 ) N ϕ 2πmn N
ϕ n = 2πm( n1 ) N .
U( ϕ )= m A m exp( imϕ ),
A m = 1 2π 0 2π U( ϕ )exp( imϕ ) dϕ.
A m = exp( iπm/N ) N sinc( πm/N ) sin( πm ) sin[ π( m1 )/N ] .
S= ε 0 ω 4 [ i( U U * U * U )+2k | U | 2 z ^ ],
j z =r× S c 2 ,
J z = j z .dA,
J z W = ( r× E× B z ).dA c E× B z .dA = m eff ω
| A m | 2 ={ N 2 π m 2 , m1 N 0, m1 N }

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