Abstract

Optical vortices (OV) are usually associated to cylindrically symmetric light beams. However, they can have more general geometries that extends their applicability. Since the typical experimental characterization methods are not appropriate for OV with arbitrary shapes, we discuss in this work how the definitions of the classical orbital angular momentum and the topological charge can be used to retrieve these informations in the general case. The concepts discussed are experimentally demonstrated and may be specially useful in areas such as optical tweezers and plasmonics.

© 2014 Optical Society of America

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References

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    [Crossref]

2013 (7)

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, “Quantum orbital angular momentum of elliptically symmetric light,” Phys. Rev. A 87, 033806 (2013).
[Crossref]

A. Rury, “Coherent control of plasmonic spectra using the orbital angular momentum of light,” Phys. Rev. B 88, 205132 (2013).
[Crossref]

Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, “Generating far-field orbital angular momenta from near-field optical chirality,” Phys. Rev. Lett. 110, 203906 (2013).
[Crossref] [PubMed]

E. Brasselet, G. Gervinskas, G. Seniutinas, and S. Juodkazis, “Topological shaping of light by closed-path nanoslits,” Phys. Rev. Lett. 111, 193901 (2013).
[Crossref] [PubMed]

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

A. M. Amaral, E. L. Falcão-Filho, and C. B. de Araújo, “Shaping optical beams with topological charge,” Opt. Lett. 38, 1579–1581 (2013).
[Crossref] [PubMed]

M. Chen, M. Mazilu, Y. Arita, E. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38, 4919–4922 (2013).
[Crossref] [PubMed]

2012 (2)

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12, 3645–3649 (2012).
[Crossref] [PubMed]

J. Wang, J. 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,” Nature Photon. 6, 488–496 (2012).
[Crossref]

2011 (1)

2010 (3)

T. Ando, N. Matsumoto, Y. Ohtake, Y. Takiguchi, and T. Inoue, “Structure of optical singularities in coaxial superpositions of Laguerre-Gaussian modes,” J. Opt. Soc. Am. A 27, 2602–2612 (2010).
[Crossref]

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10, 529–536 (2010).
[Crossref] [PubMed]

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

2009 (1)

M. V. Berry, “Optical currents,” J. Opt. A: Pure Appl. Opt. 11, 094001 (2009).
[Crossref]

2008 (2)

G. Berkhout and M. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[Crossref] [PubMed]

A. Jesacher, C. Maurer, S. Fuerhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Optical tweezers of programmable shape with transverse scattering forces,” Opt. Commun. 281, 2207–2212 (2008).
[Crossref]

2007 (2)

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[Crossref] [PubMed]

K. Ahnert and M. Abel, “Numerical differentiation of experimental data: local versus global methods,” Comput. Phys. Commun. 177, 764–774 (2007).
[Crossref]

2006 (3)

Q. Zhan, “Properties of circularly polarized vortex beams,” Opt. Lett. 31, 867–869 (2006).
[Crossref] [PubMed]

M. Dennis, “Rows of optical vortices from elliptically perturbing a high-order beam,” Opt. Lett. 31, 1325–1327 (2006).
[Crossref] [PubMed]

A. Y. Bekshaev, M. V. Vasnetsov, and M. S. Soskin, “Description of the morphology of optical vortices using the orbital angular momentum and its components,” Opt. Spectrosc. 100, 910–915 (2006).
[Crossref]

2004 (4)

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6, 259–268 (2004).
[Crossref]

J. Leach, E. Yao, and M. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[Crossref]

F. S. Roux, “Distribution of angular momentum and vortex morphology in optical beams,” Opt. Commun. 242, 45–55 (2004).
[Crossref]

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Physics-Uspekhi 47, 1177–1203 (2004).
[Crossref]

2003 (1)

2002 (1)

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum and Semiclass. Opt. 4, S52–S57 (2002).
[Crossref]

2001 (1)

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

1998 (1)

M. V. Berry, “Paraxial beams of spinning light,” Proc. SPIE 3487, 6 (1998).
[Crossref]

1997 (1)

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

1996 (1)

E. Abramochkin and V. Volostnikov, “Spiral-type beams: optical and quantum aspects,” Opt. Commun. 125, 302–323 (1996).
[Crossref]

1993 (2)

E. Abramochkin and V. Volostnikov, “Spiral-type beams,” Opt. Commun. 102, 336–350 (1993).
[Crossref]

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[Crossref]

1992 (1)

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

1982 (1)

Abel, M.

K. Ahnert and M. Abel, “Numerical differentiation of experimental data: local versus global methods,” Comput. Phys. Commun. 177, 764–774 (2007).
[Crossref]

Abramochkin, E.

E. Abramochkin and V. Volostnikov, “Spiral-type beams: optical and quantum aspects,” Opt. Commun. 125, 302–323 (1996).
[Crossref]

E. Abramochkin and V. Volostnikov, “Spiral-type beams,” Opt. Commun. 102, 336–350 (1993).
[Crossref]

Abramochkin, E. G.

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Physics-Uspekhi 47, 1177–1203 (2004).
[Crossref]

Ahmed, N.

J. Wang, J. 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,” Nature Photon. 6, 488–496 (2012).
[Crossref]

Ahnert, K.

K. Ahnert and M. Abel, “Numerical differentiation of experimental data: local versus global methods,” Comput. Phys. Commun. 177, 764–774 (2007).
[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, 8185–8189 (1992).
[Crossref] [PubMed]

Allison, I.

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum and Semiclass. Opt. 4, S52–S57 (2002).
[Crossref]

Amaral, A. M.

Ando, T.

Aoki, N.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12, 3645–3649 (2012).
[Crossref] [PubMed]

Arita, Y.

Beijersbergen, M.

G. Berkhout and M. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[Crossref] [PubMed]

Beijersbergen, M. W.

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

Bekshaev, A. Y.

A. Y. Bekshaev, M. V. Vasnetsov, and M. S. Soskin, “Description of the morphology of optical vortices using the orbital angular momentum and its components,” Opt. Spectrosc. 100, 910–915 (2006).
[Crossref]

Berkhout, G.

G. Berkhout and M. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[Crossref] [PubMed]

Bernet, S.

A. Jesacher, C. Maurer, S. Fuerhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Optical tweezers of programmable shape with transverse scattering forces,” Opt. Commun. 281, 2207–2212 (2008).
[Crossref]

Berry, M. V.

M. V. Berry, “Optical currents,” J. Opt. A: Pure Appl. Opt. 11, 094001 (2009).
[Crossref]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6, 259–268 (2004).
[Crossref]

M. V. Berry, “Paraxial beams of spinning light,” Proc. SPIE 3487, 6 (1998).
[Crossref]

Brasselet, E.

E. Brasselet, G. Gervinskas, G. Seniutinas, and S. Juodkazis, “Topological shaping of light by closed-path nanoslits,” Phys. Rev. Lett. 111, 193901 (2013).
[Crossref] [PubMed]

Chávez-Cerda, S.

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

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum and Semiclass. Opt. 4, S52–S57 (2002).
[Crossref]

Chen, M.

Cho, S.-W.

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10, 529–536 (2010).
[Crossref] [PubMed]

Courtial, J.

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum and Semiclass. Opt. 4, S52–S57 (2002).
[Crossref]

Curtis, J. E.

Davidson, N.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[Crossref] [PubMed]

de Araújo, C. B.

Dennis, M.

Dholakia, K.

Dolinar, S.

J. Wang, J. 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,” Nature Photon. 6, 488–496 (2012).
[Crossref]

Drezet, A.

Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, “Generating far-field orbital angular momenta from near-field optical chirality,” Phys. Rev. Lett. 110, 203906 (2013).
[Crossref] [PubMed]

Dudley, A.

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

Duparré, M.

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

Ebbesen, T. W.

Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, “Generating far-field orbital angular momenta from near-field optical chirality,” Phys. Rev. Lett. 110, 203906 (2013).
[Crossref] [PubMed]

Falcão-Filho, E. L.

Fazal, I. M.

J. Wang, J. 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,” Nature Photon. 6, 488–496 (2012).
[Crossref]

Fickler, R.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, “Quantum orbital angular momentum of elliptically symmetric light,” Phys. Rev. A 87, 033806 (2013).
[Crossref]

Firstenberg, O.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[Crossref] [PubMed]

Flamm, D.

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

Fonseca, E. J. S.

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

Forbes, A.

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

Fuerhapter, S.

A. Jesacher, C. Maurer, S. Fuerhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Optical tweezers of programmable shape with transverse scattering forces,” Opt. Commun. 281, 2207–2212 (2008).
[Crossref]

Genet, C.

Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, “Generating far-field orbital angular momenta from near-field optical chirality,” Phys. Rev. Lett. 110, 203906 (2013).
[Crossref] [PubMed]

Gervinskas, G.

E. Brasselet, G. Gervinskas, G. Seniutinas, and S. Juodkazis, “Topological shaping of light by closed-path nanoslits,” Phys. Rev. Lett. 111, 193901 (2013).
[Crossref] [PubMed]

Gorodetski, Y.

Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, “Generating far-field orbital angular momenta from near-field optical chirality,” Phys. Rev. Lett. 110, 203906 (2013).
[Crossref] [PubMed]

Gorshkov, V.

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

Grier, D. G.

Gutiérrez-Vega, J.

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum and Semiclass. Opt. 4, S52–S57 (2002).
[Crossref]

Heckenberg, N.

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

Hickmann, J. M.

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

Huang, H.

J. Wang, J. 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,” Nature Photon. 6, 488–496 (2012).
[Crossref]

Ina, H.

Indebetouw, G.

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[Crossref]

Inoue, T.

Jesacher, A.

A. Jesacher, C. Maurer, S. Fuerhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Optical tweezers of programmable shape with transverse scattering forces,” Opt. Commun. 281, 2207–2212 (2008).
[Crossref]

Juodkazis, S.

E. Brasselet, G. Gervinskas, G. Seniutinas, and S. Juodkazis, “Topological shaping of light by closed-path nanoslits,” Phys. Rev. Lett. 111, 193901 (2013).
[Crossref] [PubMed]

Kang, M.

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10, 529–536 (2010).
[Crossref] [PubMed]

Kim, H.

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10, 529–536 (2010).
[Crossref] [PubMed]

Kobayashi, S.

Krenn, M.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, “Quantum orbital angular momentum of elliptically symmetric light,” Phys. Rev. A 87, 033806 (2013).
[Crossref]

Leach, J.

J. Leach, E. Yao, and M. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[Crossref]

Lee, B.

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10, 529–536 (2010).
[Crossref] [PubMed]

Lee, S.-Y.

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10, 529–536 (2010).
[Crossref] [PubMed]

MacVicar, I.

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum and Semiclass. Opt. 4, S52–S57 (2002).
[Crossref]

Mair, A.

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

Malos, J.

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

Matsumoto, N.

Maurer, C.

A. Jesacher, C. Maurer, S. Fuerhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Optical tweezers of programmable shape with transverse scattering forces,” Opt. Commun. 281, 2207–2212 (2008).
[Crossref]

Mazilu, M.

Miyamoto, K.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12, 3645–3649 (2012).
[Crossref] [PubMed]

Morita, R.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12, 3645–3649 (2012).
[Crossref] [PubMed]

Nakahara, M.

M. Nakahara, Geometry, Topology and Physics (Taylor & Francis, 2003).

New, G.

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum and Semiclass. Opt. 4, S52–S57 (2002).
[Crossref]

O’Neil, A.

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum and Semiclass. Opt. 4, S52–S57 (2002).
[Crossref]

Ohtake, Y.

Omatsu, T.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12, 3645–3649 (2012).
[Crossref] [PubMed]

Padgett, M.

J. Leach, E. Yao, and M. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[Crossref]

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum and Semiclass. Opt. 4, S52–S57 (2002).
[Crossref]

Padgett, M. J.

Park, J.

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10, 529–536 (2010).
[Crossref] [PubMed]

Plick, W. N.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, “Quantum orbital angular momentum of elliptically symmetric light,” Phys. Rev. A 87, 033806 (2013).
[Crossref]

Pugatch, R.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[Crossref] [PubMed]

Ramelow, S.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, “Quantum orbital angular momentum of elliptically symmetric light,” Phys. Rev. A 87, 033806 (2013).
[Crossref]

Ren, Y.

J. Wang, J. 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,” Nature Photon. 6, 488–496 (2012).
[Crossref]

Ritsch-Marte, M.

A. Jesacher, C. Maurer, S. Fuerhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Optical tweezers of programmable shape with transverse scattering forces,” Opt. Commun. 281, 2207–2212 (2008).
[Crossref]

Ron, A.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[Crossref] [PubMed]

Roux, F. S.

F. S. Roux, “Distribution of angular momentum and vortex morphology in optical beams,” Opt. Commun. 242, 45–55 (2004).
[Crossref]

Rury, A.

A. Rury, “Coherent control of plasmonic spectra using the orbital angular momentum of light,” Phys. Rev. B 88, 205132 (2013).
[Crossref]

Schulze, C.

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

Schwaighofer, A.

A. Jesacher, C. Maurer, S. Fuerhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Optical tweezers of programmable shape with transverse scattering forces,” Opt. Commun. 281, 2207–2212 (2008).
[Crossref]

Seniutinas, G.

E. Brasselet, G. Gervinskas, G. Seniutinas, and S. Juodkazis, “Topological shaping of light by closed-path nanoslits,” Phys. Rev. Lett. 111, 193901 (2013).
[Crossref] [PubMed]

Shuker, M.

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[Crossref] [PubMed]

Soares, W. C.

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

Soskin, M.

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

Soskin, M. S.

A. Y. Bekshaev, M. V. Vasnetsov, and M. S. Soskin, “Description of the morphology of optical vortices using the orbital angular momentum and its components,” Opt. Spectrosc. 100, 910–915 (2006).
[Crossref]

Spreeuw, R. J. C.

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

Takeda, M.

Takiguchi, Y.

Toyoda, K.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12, 3645–3649 (2012).
[Crossref] [PubMed]

Tur, M.

J. Wang, J. 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,” Nature Photon. 6, 488–496 (2012).
[Crossref]

Vasnetsov, M.

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

Vasnetsov, M. V.

A. Y. Bekshaev, M. V. Vasnetsov, and M. S. Soskin, “Description of the morphology of optical vortices using the orbital angular momentum and its components,” Opt. Spectrosc. 100, 910–915 (2006).
[Crossref]

Vaziri, A.

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

Volostnikov, V.

E. Abramochkin and V. Volostnikov, “Spiral-type beams: optical and quantum aspects,” Opt. Commun. 125, 302–323 (1996).
[Crossref]

E. Abramochkin and V. Volostnikov, “Spiral-type beams,” Opt. Commun. 102, 336–350 (1993).
[Crossref]

Volostnikov, V. G.

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Physics-Uspekhi 47, 1177–1203 (2004).
[Crossref]

Wang, J.

J. Wang, J. 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,” Nature Photon. 6, 488–496 (2012).
[Crossref]

Weihs, G.

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

Willner, A. E.

J. Wang, J. 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,” Nature Photon. 6, 488–496 (2012).
[Crossref]

Woerdman, J. P.

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

Wright, E.

Yan, Y.

J. Wang, J. 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,” Nature Photon. 6, 488–496 (2012).
[Crossref]

Yang, J.

J. Wang, J. 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,” Nature Photon. 6, 488–496 (2012).
[Crossref]

Yao, A. M.

Yao, E.

J. Leach, E. Yao, and M. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[Crossref]

Yue, Y.

J. Wang, J. 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,” Nature Photon. 6, 488–496 (2012).
[Crossref]

Zeilinger, A.

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, “Quantum orbital angular momentum of elliptically symmetric light,” Phys. Rev. A 87, 033806 (2013).
[Crossref]

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

Zhan, Q.

Adv. Opt. Photon. (1)

Comput. Phys. Commun. (1)

K. Ahnert and M. Abel, “Numerical differentiation of experimental data: local versus global methods,” Comput. Phys. Commun. 177, 764–774 (2007).
[Crossref]

J. Mod. Opt. (1)

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[Crossref]

J. Opt. A: Pure Appl. Opt. (2)

M. V. Berry, “Optical currents,” J. Opt. A: Pure Appl. Opt. 11, 094001 (2009).
[Crossref]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6, 259–268 (2004).
[Crossref]

J. Opt. B: Quantum and Semiclass. Opt. (1)

S. Chávez-Cerda, M. Padgett, I. Allison, G. New, J. Gutiérrez-Vega, A. O’Neil, I. MacVicar, and J. Courtial, “Holographic generation and orbital angular momentum of high-order Mathieu beams,” J. Opt. B: Quantum and Semiclass. Opt. 4, S52–S57 (2002).
[Crossref]

J. Opt. Soc. Am. (1)

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

Nano Lett. (2)

H. Kim, J. Park, S.-W. Cho, S.-Y. Lee, M. Kang, and B. Lee, “Synthesis and dynamic switching of surface plasmon vortices with plasmonic vortex lens,” Nano Lett. 10, 529–536 (2010).
[Crossref] [PubMed]

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12, 3645–3649 (2012).
[Crossref] [PubMed]

Nature (1)

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

Nature Photon. (1)

J. Wang, J. 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,” Nature Photon. 6, 488–496 (2012).
[Crossref]

New J. Phys. (2)

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

J. Leach, E. Yao, and M. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[Crossref]

Opt. Commun. (4)

F. S. Roux, “Distribution of angular momentum and vortex morphology in optical beams,” Opt. Commun. 242, 45–55 (2004).
[Crossref]

A. Jesacher, C. Maurer, S. Fuerhapter, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Optical tweezers of programmable shape with transverse scattering forces,” Opt. Commun. 281, 2207–2212 (2008).
[Crossref]

E. Abramochkin and V. Volostnikov, “Spiral-type beams,” Opt. Commun. 102, 336–350 (1993).
[Crossref]

E. Abramochkin and V. Volostnikov, “Spiral-type beams: optical and quantum aspects,” Opt. Commun. 125, 302–323 (1996).
[Crossref]

Opt. Lett. (5)

Opt. Spectrosc. (1)

A. Y. Bekshaev, M. V. Vasnetsov, and M. S. Soskin, “Description of the morphology of optical vortices using the orbital angular momentum and its components,” Opt. Spectrosc. 100, 910–915 (2006).
[Crossref]

Phys. Rev. A (3)

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

W. N. Plick, M. Krenn, R. Fickler, S. Ramelow, and A. Zeilinger, “Quantum orbital angular momentum of elliptically symmetric light,” Phys. Rev. A 87, 033806 (2013).
[Crossref]

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

Phys. Rev. B (1)

A. Rury, “Coherent control of plasmonic spectra using the orbital angular momentum of light,” Phys. Rev. B 88, 205132 (2013).
[Crossref]

Phys. Rev. Lett. (5)

Y. Gorodetski, A. Drezet, C. Genet, and T. W. Ebbesen, “Generating far-field orbital angular momenta from near-field optical chirality,” Phys. Rev. Lett. 110, 203906 (2013).
[Crossref] [PubMed]

E. Brasselet, G. Gervinskas, G. Seniutinas, and S. Juodkazis, “Topological shaping of light by closed-path nanoslits,” Phys. Rev. Lett. 111, 193901 (2013).
[Crossref] [PubMed]

G. Berkhout and M. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[Crossref] [PubMed]

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

R. Pugatch, M. Shuker, O. Firstenberg, A. Ron, and N. Davidson, “Topological stability of stored optical vortices,” Phys. Rev. Lett. 98, 203601 (2007).
[Crossref] [PubMed]

Physics-Uspekhi (1)

E. G. Abramochkin and V. G. Volostnikov, “Spiral light beams,” Physics-Uspekhi 47, 1177–1203 (2004).
[Crossref]

Proc. SPIE (1)

M. V. Berry, “Paraxial beams of spinning light,” Proc. SPIE 3487, 6 (1998).
[Crossref]

Other (1)

M. Nakahara, Geometry, Topology and Physics (Taylor & Francis, 2003).

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Figures (7)

Fig. 1
Fig. 1 (a) Experimental setup (not to scale). The output of a fiber coupled laser diode emitting at 805 nm is collimated with a lens with long focal distance (f = 25 cm), producing a nearly plane wave. The collimated light goes to a Michelson interferometer (MI) in which the arm 1 contains a SLM (Hamamatsu - LCOS X10468-02). The MI arm 2 provides the plane wave reference when the mirror is on the beam line, or allows intensity measurements when the mirror is off the beam line. The reference (red line) and modulated (blue line) beams have a small relative angle and are spatially filtered and then imaged on a CCD camera (Thorlabs - DCC1240M) positioned at the SLM image plane (z = 0 cm). (b) Fluxogram of the experimental procedure to determine the beam amplitude and phase profiles, as described in the text.
Fig. 2
Fig. 2 Application of the concepts developed in sec. 3 to a c-OV for χOV = 5ϕ. Experimentally measured amplitude (a) and phase (b) beam profiles. OAM density profile (c), from which it was determined that 〈l〉 = 4.9. Experimental (d) and theoretically expected (e) -OAM profiles for this beam. For this beam it was measured QT = 5.0.
Fig. 3
Fig. 3 Typical experimental s-OV profiles of amplitude and phase, and the corresponding -OAM and OAM density. The data represent TC distributed over a line (a), a corner (b) and a triangle (c). The values of 〈l〉 and QT were calculated, respectively, by applying Eqs. (7) and (11) to the experimental data.
Fig. 4
Fig. 4 Experimental data for TC lines with different line lengths and a fixed total applied TC= 10 at z = 0 cm. The line length increases from (a) to (c), and the respective OV are in the regimes of high TC density, elongated OV core and small TC density.
Fig. 5
Fig. 5 Measurements corresponding to a TC line at distinct z planes. z = 0 cm, 5 cm, 10 cm respectively in (a–c). Notice that both QT and 〈l〉 are conserved under propagation.
Fig. 6
Fig. 6 (a) Profiles of amplitude, phase, OAM density and LOAM for a corner-shaped TC distribution with a fixed geometry and varying total applied TC. (b) Relation between the measured QT and 〈l〉 in terms of the applied TC at the SLM. All measurements were taken at z = 0 cm.
Fig. 7
Fig. 7 (a) Profiles of amplitude, phase, OAM density and -OAM for a triangle-shaped TC distribution with a fixed geometry and varying total applied TC. (b) Relation between the measured QT and 〈l〉 in terms of the applied TC at the SLM. All measurements were taken at z = 0 cm.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

A ( r , t ) = ε ^ ( 2 μ 0 ω k P 0 ) 1 2 𝒜 ( r ) exp i [ χ ( r ) + k z ω t ] ,
( 2 2 i k z ) 𝒜 ( r ) e i χ ( r ) = 0 ,
Q T = 1 2 π C d x χ ( r ) ,
Q T = 1 2 π 0 2 π w ( ρ = c , ϕ , z 0 ) d ϕ ,
w ( r ) = χ ϕ ( r ) .
L z = P 0 ω c [ 𝒜 * ( r ) χ ϕ 𝒜 ( r ) ] .
l = ρ d ρ d ϕ 𝒜 * ( r ) χ ϕ 𝒜 ( r ) .
I CCD ( ϕ Offset ) = I OV + I Ref 2 I OV I Ref cos ( χ Rel + ϕ Offset ) ,
1 2 π 0 2 π d ϕ Offset I CCD ( ϕ Offset ) e i ϕ Offset = I OV I Ref e i χ Rel ,
w ( r ) = χ ϕ = 𝔢 { e i χ [ i ( x y y x ) ] e i χ } ,
Q T = 1 2 π ρ d ρ d ϕ p ( ρ ) w ( ρ , ϕ , z 0 ) .

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