Abstract

Colloidal media with well-defined optical properties have been widely used as model systems in many fundamental and applied studies of light-matter interactions in complex media. Recent progress in the field of engineered nanoscale optical materials with fundamentally new physical properties opens new opportunities for tailoring the properties of colloids. In this work, we experimentally demonstrate the evolution of the optical vortex beams of different topological charges propagating in engineered nano-colloidal suspension of negative polarizability with saturable nonlinearities. Due to the high power of the incident beam, the modulation instability leads to an exponential growth of weak perturbations and thus splits the original vortex beam into a necklace beam consisting of several bright spots. At a fixed power, the number of observed bright spots is intrinsically determined by the topological charge of the incident beam and agrees well with the predictions of our linear stability analysis and numerical simulations. Besides contributing to the fundamental science of light-matter interactions in engineered soft-matter media, this work opens new opportunities for dynamic optical manipulation and transmission of light through scattering media as well as formation of complex optical patterns and light filamentation in naturally existing colloids such as fog and clouds.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (3)

S. J. Boehm, L. Kang, D. H. Werner, and C. D. Keating, “Field-switchable broadband polarizer based on reconfigurable nanowire assemblies,” Adv. Funct. Mater. 27, 1604703 (2017).
[Crossref]

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

W. Walasik, S. Z. Silahli, and N. M. Litchinitser, “Dynamics of necklace beams in nonlinear colloidal suspensions,” Sci. Rep. 7, 11709 (2017).
[Crossref] [PubMed]

2016 (3)

Y. Montelongo, A. K. Yetisen, H. Butt, and S.-H. Yun, “Reconfigurable optical assembly of nanostructures,” Nat. Commun. 7, 12002 (2016).
[Crossref] [PubMed]

M. Liu, K. Fan, W. Padilla, D. A. Powell, X. Zhang, and I. V. Shadrivov, “Meta-liquid crystals: Tunable meta-liquid crystals,” Adv. Mater. 28, 1525 (2016).
[Crossref]

T. S. Kelly, Y.-X. Ren, A. Samadi, A. Bezryadina, D. Christodoulides, and Z. Chen, “Guiding and nonlinear coupling of light in plasmonic nanosuspensions,” Opt. Lett. 41, 3817–3820 (2016).
[Crossref] [PubMed]

2015 (1)

2013 (3)

H. Xie, Y. Liu, D. Jin, P. J. Santangelo, and P. Xi, “Analytical description of high-aperture sted resolution with 0–2π vortex phase modulation,” J. Opt. Soc. Am. A 30, 1640–1645 (2013).
[Crossref]

Z. A. Kudyshev, M. C. Richardson, and N. M. Litchinitser, “Virtual hyperbolic metamaterials for manipulating radar signals in air,” Nat. Commun. 4, 2557 (2013).
[Crossref] [PubMed]

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” Phys. Rev. Lett. 111, 218302 (2013).
[Crossref] [PubMed]

2012 (1)

S. Hernández-Navarro, J. Ignés-Mullol, F. Sagués, and P. Tierno, “Role of anisotropy in electrodynamically induced colloidal aggregates,” Langmuir 28, 5981–5986 (2012).
[Crossref] [PubMed]

2011 (1)

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[Crossref]

2010 (1)

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photon. 4, 451–456 (2010).
[Crossref]

2008 (1)

2007 (2)

2006 (2)

A. Vinçotte and L. Bergé, “Atmospheric propagation of gradient-shaped and spinning femtosecond light pulses,” Physica D: Nonlinear Phenomena 223, 163–173 (2006).
[Crossref]

W. M. Lee, V. Garcés-Chävez, and K. Dholakia, “Interference from multiple trapped colloids in an optical vortex beam,” Opt. Express 14, 7436–7446 (2006).
[Crossref] [PubMed]

2005 (1)

A. Vinçotte and L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett. 95, 193901 (2005).
[Crossref] [PubMed]

2004 (1)

2002 (1)

B. J. Battersby, G. A. Lawrie, A. P. R. Johnston, and M. Trau, “Optical barcoding of colloidal suspensions: applications in genomics, proteomics and drug discovery,” Chem. Commun. 14, 1435–1441 (2002).
[Crossref]

1981 (1)

M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109–125 (1981).
[Crossref]

1978 (1)

Agrawal, G. P.

M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109–125 (1981).
[Crossref]

Alpmann, C.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

Andrews, D.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

Baker, M.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

Banzer, P.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

Batteh, J. H.

M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109–125 (1981).
[Crossref]

Battersby, B. J.

B. J. Battersby, G. A. Lawrie, A. P. R. Johnston, and M. Trau, “Optical barcoding of colloidal suspensions: applications in genomics, proteomics and drug discovery,” Chem. Commun. 14, 1435–1441 (2002).
[Crossref]

Bauer, T.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

Belmonte, A.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

Bergé, L.

A. Vinçotte and L. Bergé, “Atmospheric propagation of gradient-shaped and spinning femtosecond light pulses,” Physica D: Nonlinear Phenomena 223, 163–173 (2006).
[Crossref]

A. Vinçotte and L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett. 95, 193901 (2005).
[Crossref] [PubMed]

Berry, M.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

Bezryadina, A.

Bigelow, N.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

Boehm, S. J.

S. J. Boehm, L. Kang, D. H. Werner, and C. D. Keating, “Field-switchable broadband polarizer based on reconfigurable nanowire assemblies,” Adv. Funct. Mater. 27, 1604703 (2017).
[Crossref]

Butt, H.

Y. Montelongo, A. K. Yetisen, H. Butt, and S.-H. Yun, “Reconfigurable optical assembly of nanostructures,” Nat. Commun. 7, 12002 (2016).
[Crossref] [PubMed]

Chen, Z.

T. S. Kelly, Y.-X. Ren, A. Samadi, A. Bezryadina, D. Christodoulides, and Z. Chen, “Guiding and nonlinear coupling of light in plasmonic nanosuspensions,” Opt. Lett. 41, 3817–3820 (2016).
[Crossref] [PubMed]

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” Phys. Rev. Lett. 111, 218302 (2013).
[Crossref] [PubMed]

Christodoulides, D.

Christodoulides, D. N.

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[Crossref]

Dennis, M.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

Denz, C.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

Dholakia, K.

Einstein, A.

A. Einstein, Investigations on the Theory of the Brownian Movement (Dover, 1926).

El-Ganainy, R.

Fan, K.

M. Liu, K. Fan, W. Padilla, D. A. Powell, X. Zhang, and I. V. Shadrivov, “Meta-liquid crystals: Tunable meta-liquid crystals,” Adv. Mater. 28, 1525 (2016).
[Crossref]

Fardad, S.

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” Phys. Rev. Lett. 111, 218302 (2013).
[Crossref] [PubMed]

Feit, M. D.

Fickler, R.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

Fleck, J. A.

Forbes, A.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

Garcés-Chävez, V.

Gordon, R.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

Grier, D. G.

Hajjarian, Z.

Hao, Z.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photon. 4, 451–456 (2010).
[Crossref]

Heinrich, M.

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” Phys. Rev. Lett. 111, 218302 (2013).
[Crossref] [PubMed]

Henin, S.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photon. 4, 451–456 (2010).
[Crossref]

Hernández-Navarro, S.

S. Hernández-Navarro, J. Ignés-Mullol, F. Sagués, and P. Tierno, “Role of anisotropy in electrodynamically induced colloidal aggregates,” Langmuir 28, 5981–5986 (2012).
[Crossref] [PubMed]

Hunter, R. J.

R. J. Hunter, Foundations of Colloid Science (Oxford University Press, 2001).

Ignés-Mullol, J.

S. Hernández-Navarro, J. Ignés-Mullol, F. Sagués, and P. Tierno, “Role of anisotropy in electrodynamically induced colloidal aggregates,” Langmuir 28, 5981–5986 (2012).
[Crossref] [PubMed]

Jin, D.

Johnston, A. P. R.

B. J. Battersby, G. A. Lawrie, A. P. R. Johnston, and M. Trau, “Optical barcoding of colloidal suspensions: applications in genomics, proteomics and drug discovery,” Chem. Commun. 14, 1435–1441 (2002).
[Crossref]

Kang, L.

S. J. Boehm, L. Kang, D. H. Werner, and C. D. Keating, “Field-switchable broadband polarizer based on reconfigurable nanowire assemblies,” Adv. Funct. Mater. 27, 1604703 (2017).
[Crossref]

Karimi, E.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photon. 4, 451–456 (2010).
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Keating, C. D.

S. J. Boehm, L. Kang, D. H. Werner, and C. D. Keating, “Field-switchable broadband polarizer based on reconfigurable nanowire assemblies,” Adv. Funct. Mater. 27, 1604703 (2017).
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Kelly, T. S.

Kudyshev, Z. A.

Z. A. Kudyshev, M. C. Richardson, and N. M. Litchinitser, “Virtual hyperbolic metamaterials for manipulating radar signals in air,” Nat. Commun. 4, 2557 (2013).
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Ladavac, K.

Lascoux, N.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photon. 4, 451–456 (2010).
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Lau, M.

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” Phys. Rev. Lett. 111, 218302 (2013).
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B. J. Battersby, G. A. Lawrie, A. P. R. Johnston, and M. Trau, “Optical barcoding of colloidal suspensions: applications in genomics, proteomics and drug discovery,” Chem. Commun. 14, 1435–1441 (2002).
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M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109–125 (1981).
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Lee, W. M.

Litchinitser, N.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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Litchinitser, N. M.

W. Walasik, S. Z. Silahli, and N. M. Litchinitser, “Dynamics of necklace beams in nonlinear colloidal suspensions,” Sci. Rep. 7, 11709 (2017).
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S. Z. Silahli, W. Walasik, and N. M. Litchinitser, “Necklace beam generation in nonlinear colloidal engineered media,” Opt. Lett. 40, 5714–5717 (2015).
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Z. A. Kudyshev, M. C. Richardson, and N. M. Litchinitser, “Virtual hyperbolic metamaterials for manipulating radar signals in air,” Nat. Commun. 4, 2557 (2013).
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M. Liu, K. Fan, W. Padilla, D. A. Powell, X. Zhang, and I. V. Shadrivov, “Meta-liquid crystals: Tunable meta-liquid crystals,” Adv. Mater. 28, 1525 (2016).
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Man, W.

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” Phys. Rev. Lett. 111, 218302 (2013).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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Nakaema, W. M.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photon. 4, 451–456 (2010).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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Powell, D. A.

M. Liu, K. Fan, W. Padilla, D. A. Powell, X. Zhang, and I. V. Shadrivov, “Meta-liquid crystals: Tunable meta-liquid crystals,” Adv. Mater. 28, 1525 (2016).
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W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” Phys. Rev. Lett. 111, 218302 (2013).
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P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photon. 4, 451–456 (2010).
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Z. A. Kudyshev, M. C. Richardson, and N. M. Litchinitser, “Virtual hyperbolic metamaterials for manipulating radar signals in air,” Nat. Commun. 4, 2557 (2013).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photon. 4, 451–456 (2010).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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Rubinsztein-Dunlop, H.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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Salame, R.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photon. 4, 451–456 (2010).
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Salmon, E.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photon. 4, 451–456 (2010).
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Shadrivov, I. V.

M. Liu, K. Fan, W. Padilla, D. A. Powell, X. Zhang, and I. V. Shadrivov, “Meta-liquid crystals: Tunable meta-liquid crystals,” Adv. Mater. 28, 1525 (2016).
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W. Walasik, S. Z. Silahli, and N. M. Litchinitser, “Dynamics of necklace beams in nonlinear colloidal suspensions,” Sci. Rep. 7, 11709 (2017).
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S. Z. Silahli, W. Walasik, and N. M. Litchinitser, “Necklace beam generation in nonlinear colloidal engineered media,” Opt. Lett. 40, 5714–5717 (2015).
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Stelmaszczyk, K.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photon. 4, 451–456 (2010).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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S. Hernández-Navarro, J. Ignés-Mullol, F. Sagués, and P. Tierno, “Role of anisotropy in electrodynamically induced colloidal aggregates,” Langmuir 28, 5981–5986 (2012).
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Torres, J.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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B. J. Battersby, G. A. Lawrie, A. P. R. Johnston, and M. Trau, “Optical barcoding of colloidal suspensions: applications in genomics, proteomics and drug discovery,” Chem. Commun. 14, 1435–1441 (2002).
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W. Walasik, S. Z. Silahli, and N. M. Litchinitser, “Dynamics of necklace beams in nonlinear colloidal suspensions,” Sci. Rep. 7, 11709 (2017).
[Crossref] [PubMed]

S. Z. Silahli, W. Walasik, and N. M. Litchinitser, “Necklace beam generation in nonlinear colloidal engineered media,” Opt. Lett. 40, 5714–5717 (2015).
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Weiner, A.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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S. J. Boehm, L. Kang, D. H. Werner, and C. D. Keating, “Field-switchable broadband polarizer based on reconfigurable nanowire assemblies,” Adv. Funct. Mater. 27, 1604703 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photon. 4, 451–456 (2010).
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P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salame, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photon. 4, 451–456 (2010).
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Xi, P.

Xie, G.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
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Xie, H.

Yetisen, A. K.

Y. Montelongo, A. K. Yetisen, H. Butt, and S.-H. Yun, “Reconfigurable optical assembly of nanostructures,” Nat. Commun. 7, 12002 (2016).
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Yun, S.-H.

Y. Montelongo, A. K. Yetisen, H. Butt, and S.-H. Yun, “Reconfigurable optical assembly of nanostructures,” Nat. Commun. 7, 12002 (2016).
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Zhang, P.

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” Phys. Rev. Lett. 111, 218302 (2013).
[Crossref] [PubMed]

Zhang, X.

M. Liu, K. Fan, W. Padilla, D. A. Powell, X. Zhang, and I. V. Shadrivov, “Meta-liquid crystals: Tunable meta-liquid crystals,” Adv. Mater. 28, 1525 (2016).
[Crossref]

Zhang, Z.

W. Man, S. Fardad, Z. Zhang, J. Prakash, M. Lau, P. Zhang, M. Heinrich, D. N. Christodoulides, and Z. Chen, “Optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities,” Phys. Rev. Lett. 111, 218302 (2013).
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Adv. Funct. Mater. (1)

S. J. Boehm, L. Kang, D. H. Werner, and C. D. Keating, “Field-switchable broadband polarizer based on reconfigurable nanowire assemblies,” Adv. Funct. Mater. 27, 1604703 (2017).
[Crossref]

Adv. Mater. (1)

M. Liu, K. Fan, W. Padilla, D. A. Powell, X. Zhang, and I. V. Shadrivov, “Meta-liquid crystals: Tunable meta-liquid crystals,” Adv. Mater. 28, 1525 (2016).
[Crossref]

Appl. Opt. (2)

Chem. Commun. (1)

B. J. Battersby, G. A. Lawrie, A. P. R. Johnston, and M. Trau, “Optical barcoding of colloidal suspensions: applications in genomics, proteomics and drug discovery,” Chem. Commun. 14, 1435–1441 (2002).
[Crossref]

J. Appl. Phys. (1)

M. Lax, J. H. Batteh, and G. P. Agrawal, “Channeling of intense electromagnetic beams,” J. Appl. Phys. 52, 109–125 (1981).
[Crossref]

J. Opt. (1)

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. Litchinitser, N. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. Torres, T. Neely, M. Baker, R. Gordon, A. Stilgoe, J. Romero, A. White, R. Fickler, A. Willner, G. Xie, B. McMorran, and A. Weiner, “Roadmap on structured light,” J. Opt. 19, 013011 (2017).
[Crossref]

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

Langmuir (1)

S. Hernández-Navarro, J. Ignés-Mullol, F. Sagués, and P. Tierno, “Role of anisotropy in electrodynamically induced colloidal aggregates,” Langmuir 28, 5981–5986 (2012).
[Crossref] [PubMed]

Nat. Commun. (2)

Y. Montelongo, A. K. Yetisen, H. Butt, and S.-H. Yun, “Reconfigurable optical assembly of nanostructures,” Nat. Commun. 7, 12002 (2016).
[Crossref] [PubMed]

Z. A. Kudyshev, M. C. Richardson, and N. M. Litchinitser, “Virtual hyperbolic metamaterials for manipulating radar signals in air,” Nat. Commun. 4, 2557 (2013).
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Figures (4)

Fig. 1
Fig. 1 Propagation of a charge one optical vortex beam in a colloidal solution with negative polarizability. In free space, the helical wave front (right) and the doughnut intensity profile of the beam (left) are schematically shown. Inside the colloidal medium, the input vortex beam transforms into a rotating necklace beam. The repulsion of the particles in the path of the high intensity beam leads to a local nonlinear index change.
Fig. 2
Fig. 2 Azimuthal modulation instability gain. (a) Analytically computed instability gain gm(M) as a function of the perturbation azimuthal index deviation M, for negative polarizability particle-based systems for different topological charges m of the initial steady-state vortex solution. (b)–(c) Inverse of the beam breakup distance recorded in numerical simulations of seeded MI. Dashed lines show analytical curves with rescaled magnitude that help guide the eye.
Fig. 3
Fig. 3 Experimental setup. (a) Interference setup used to test the vortex beams with different charges generated by the corresponding spiral phase plate. (b) Setup used to study (seeded) modulation instability of vortex beams in colloidal media. Collimated beam from Verdi V6 laser (λ0 = 532 nm) is initially split into two beams using beam splitters with reflectivity varying in the range from 0.6% to 8% of the total power. The high intensity beam is transmitted through a spiral phase plate (SPP) to generate the main vortex beam with lower charge. In the seeded configuration, the low intensity beam is transmitted through a SPP with a higher charge to generate the perturbation beam. The beams are then recombined at the second beam splitter and focused onto the cuvette by a lens (f = 10 cm). The longitudinal beam profile inside the cuvette and the transverse beam profile behind the cuvette are recorded by a camera and shown in the insets.
Fig. 4
Fig. 4 Experimental results showing the formation of the necklace beam from an initial vortex beam propagating in a nonlinear colloidal suspension with negative polarizability particles. (a)–(c) Intensity profiles of the incident vortex beams of charges 1, 2, and 4. (d)–(f) Interference patterns corresponding to vortex beams with topological charges in (a)–(c), respectively. (g)–(i) Intensity distributions of the resulting necklace beams after the propagation in the colloidal medium corresponding to the incident beams (a)–(c), respectively. Necklace beam generated by: a single vortex beam with charge 1 (g); vortex beam with charge 2 with perturbation of charges 4 and 8 with power levels corresponding to 3% of the main beam (h); vortex beam with charge 4 with perturbation of charge 8 with power corresponding to 3% of the main beam (i).

Equations (3)

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i E z + 1 2 k 0 n b 2 E + k 0 ( n b n p ) V p ρ 0 e α 4 k B T | E | 2 E + i 2 σ ρ 0 e α 4 k B T | E | 2 E = 0
E ( θ , z ) = [ | E 0 | + a 1 e i ( M θ + μ z ) + a 2 * e i ( M θ + μ * z ) ] e i ( m θ + λ z )
Im ( μ ) = g m ( M ) = | M | 2 k 0 n b r m × Im M 2 r m 2 | α | 2 k B T L 2 | E 0 | 2 exp ( α 2 k B T | E 0 | 2 )

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