Abstract

We study nonlinear propagation of light in colloidal suspension of metallic nanoparticles, in the regime of particles surface plasmon resonance. We show that the propagation exhibits features typical for purely defocusing media and the observed spatial confinement is not a real self-trapping, as for solitons, but rather than is caused by the phase modulation of the beam via nonlocal defocusing nonlinearity. We also show that the light-induced refractive index change in the suspension leads to stabilization of structured light beams. In particular, we demonstrate a stable nonlinear propagation of bright ring beams with complex states of polarization, including practically important radial and azimuthal states.

© 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 (2)

V. Amendola, R. Pilot, M. Frasconi, O. M. Maragò, and M. A. Iatì, “Surface plasmon resonance in gold nanoparticles: a review,” J. Phys.: Condens. Matter 29, 203002 (2017).

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 (2)

2015 (2)

J. Olson, S. Dominguez-Medina, A. Hoggard, L.-Y. Wang, W.-S. Chang, and S. Link, “Optical characterization of single plasmonic nanoparticles,” Chem. Soc. Rev. 44, 40–57 (2015).
[Crossref]

M. Shen, B. Li, L. Ge, W. Chen, and D. Wu, “Stability of vortex solitons under competing local and nonlocal cubic nonlinearities,” Opt. Commun. 338, 27–33 (2015).
[Crossref]

2014 (3)

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8, 846–850 (2014).
[Crossref]

A. S. Reyna, K. C. Jorge, and C. B. de Araújo, “Two-dimensional solitons in a quintic-septimal medium,” Phys. Rev. A 90, 063835 (2014).
[Crossref]

S. Fardad, A. Salandrino, M. Heinrich, P. Zhang, Z. Chen, and D. N. Christodoulides, “Plasmonic resonant solitons in metallic nanosuspensions,” Nano Lett. 14, 2498–2504 (2014).
[Crossref] [PubMed]

2013 (2)

S. IIto, H. Yamauchi, M. Tamura, S. Hidaka, H. Hattori, T. Hamada, K. Nishida, S. Tokonami, T. Itoh, H. Miyasaka, and T. Iida, “Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams,” Sci. Rep. 3, 3047 (2013).
[Crossref]

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]

2011 (1)

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106, 123901 (2011).
[Crossref] [PubMed]

2009 (4)

2008 (5)

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape-and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24, 5233–5237 (2008).
[Crossref] [PubMed]

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442 (2008).
[Crossref] [PubMed]

M. Matuszewski, W. Krolikowski, and Y. S. Kivshar, “Spatial solitons and light-induced instabilities in colloidal media,” Opt. Express 16, 1371–1376 (2008).
[Crossref] [PubMed]

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008).
[Crossref] [PubMed]

R. F. Souza, M. A. R. C. Alencar, E. C. da Silva, M. R. Meneghetti, and J. M. Hickmann, “Nonlinear optical properties of au nanoparticles colloidal system: Local and nonlocal responses,” Appl. Phys. Lett. 92, 201902 (2008).
[Crossref]

2007 (5)

K. Watanabe, N. Horiguchi, and H. Kano, “Optimized measurement probe of the localized surface plasmon microscope by using radially polarized illumination,” Appl. Opt. 46, 4985–4990 (2007).
[Crossref] [PubMed]

E. Yew and C. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275, 453–457 (2007).
[Crossref]

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641 (2007).
[Crossref]

P. Reece, E. Wright, and K. Dholakia, “Experimental observation of modulation instability and optical spatial soliton arrays in soft condensed matter,” Phys. Rev. Lett. 98, 203902 (2007).
[Crossref] [PubMed]

R. El-Ganainy, D. Christodoulides, C. Rotschild, and M. Segev, “Soliton dynamics and self-induced transparency in nonlinear nanosuspensions,” Opt. Express 15, 10207–10218 (2007).
[Crossref] [PubMed]

2006 (1)

2005 (2)

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937–1942 (2005).
[Crossref] [PubMed]

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[Crossref]

2004 (2)

Q. Zhan, “Trapping metallic rayleigh particles with radial polarization,” Opt. Express 12, 3377–3382 (2004).
[Crossref] [PubMed]

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

2003 (1)

2002 (1)

2001 (1)

L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251 (2001).
[Crossref] [PubMed]

1994 (1)

1990 (1)

P. Schiebener, J. Straub, J. Levelt Sengers, and J. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[Crossref]

Agrawal, G.

Y. S. Kivshar and G. Agrawal, Optical solitons: from fibers to photonic crystals (Academic Press, 2003).

Alencar, M. A. R. C.

R. F. Souza, M. A. R. C. Alencar, E. C. da Silva, M. R. Meneghetti, and J. M. Hickmann, “Nonlinear optical properties of au nanoparticles colloidal system: Local and nonlocal responses,” Appl. Phys. Lett. 92, 201902 (2008).
[Crossref]

Amendola, V.

V. Amendola, R. Pilot, M. Frasconi, O. M. Maragò, and M. A. Iatì, “Surface plasmon resonance in gold nanoparticles: a review,” J. Phys.: Condens. Matter 29, 203002 (2017).

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442 (2008).
[Crossref] [PubMed]

Beversluis, M.

L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251 (2001).
[Crossref] [PubMed]

Bezryadina, A.

Bhatia, V. K.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937–1942 (2005).
[Crossref] [PubMed]

Biss, D.

Block, S. M.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (John Wiley & Sons, 2008).

Brasselet, E.

Brown, T.

D. Biss and T. Brown, “Polarization-vortex-driven second-harmonic generation,” Opt. Lett. 28, 923–925 (2003).
[Crossref] [PubMed]

L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251 (2001).
[Crossref] [PubMed]

Carpenter, A. E.

Chang, W.-S.

J. Olson, S. Dominguez-Medina, A. Hoggard, L.-Y. Wang, W.-S. Chang, and S. Link, “Optical characterization of single plasmonic nanoparticles,” Chem. Soc. Rev. 44, 40–57 (2015).
[Crossref]

Chen, H.

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape-and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24, 5233–5237 (2008).
[Crossref] [PubMed]

Chen, W.

M. Shen, B. Li, L. Ge, W. Chen, and D. Wu, “Stability of vortex solitons under competing local and nonlocal cubic nonlinearities,” Opt. Commun. 338, 27–33 (2015).
[Crossref]

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]

S. Fardad, A. Salandrino, M. Heinrich, P. Zhang, Z. Chen, and D. N. Christodoulides, “Plasmonic resonant solitons in metallic nanosuspensions,” Nano Lett. 14, 2498–2504 (2014).
[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.

S. Fardad, A. Salandrino, M. Heinrich, P. Zhang, Z. Chen, and D. N. Christodoulides, “Plasmonic resonant solitons in metallic nanosuspensions,” Nano Lett. 14, 2498–2504 (2014).
[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]

da Silva, E. C.

R. F. Souza, M. A. R. C. Alencar, E. C. da Silva, M. R. Meneghetti, and J. M. Hickmann, “Nonlinear optical properties of au nanoparticles colloidal system: Local and nonlocal responses,” Appl. Phys. Lett. 92, 201902 (2008).
[Crossref]

Davoyan, A. R.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8, 846–850 (2014).
[Crossref]

De Araujo, C. B.

de Araújo, C. B.

A. S. Reyna, K. C. Jorge, and C. B. de Araújo, “Two-dimensional solitons in a quintic-septimal medium,” Phys. Rev. A 90, 063835 (2014).
[Crossref]

Desyatnikov, A. S.

Dholakia, K.

W. Lee, R. El-Ganainy, D. Christodoulides, K. Dholakia, and E. Wright, “Nonlinear optical response of colloidal suspensions,” Opt. Express 17, 10277–10289 (2009).
[Crossref] [PubMed]

P. Reece, E. Wright, and K. Dholakia, “Experimental observation of modulation instability and optical spatial soliton arrays in soft condensed matter,” Phys. Rev. Lett. 98, 203902 (2007).
[Crossref] [PubMed]

Dominguez-Medina, S.

J. Olson, S. Dominguez-Medina, A. Hoggard, L.-Y. Wang, W.-S. Chang, and S. Link, “Optical characterization of single plasmonic nanoparticles,” Chem. Soc. Rev. 44, 40–57 (2015).
[Crossref]

El-Ganainy, R.

Engheta, N.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8, 846–850 (2014).
[Crossref]

Fardad, S.

S. Fardad, A. Salandrino, M. Heinrich, P. Zhang, Z. Chen, and D. N. Christodoulides, “Plasmonic resonant solitons in metallic nanosuspensions,” Nano Lett. 14, 2498–2504 (2014).
[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]

Frasconi, M.

V. Amendola, R. Pilot, M. Frasconi, O. M. Maragò, and M. A. Iatì, “Surface plasmon resonance in gold nanoparticles: a review,” J. Phys.: Condens. Matter 29, 203002 (2017).

Gallagher, J.

P. Schiebener, J. Straub, J. Levelt Sengers, and J. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[Crossref]

Ge, L.

M. Shen, B. Li, L. Ge, W. Chen, and D. Wu, “Stability of vortex solitons under competing local and nonlocal cubic nonlinearities,” Opt. Commun. 338, 27–33 (2015).
[Crossref]

Halas, N. J.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641 (2007).
[Crossref]

Hall, W. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442 (2008).
[Crossref] [PubMed]

Hamada, T.

S. IIto, H. Yamauchi, M. Tamura, S. Hidaka, H. Hattori, T. Hamada, K. Nishida, S. Tokonami, T. Itoh, H. Miyasaka, and T. Iida, “Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams,” Sci. Rep. 3, 3047 (2013).
[Crossref]

Hansen, P. M.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937–1942 (2005).
[Crossref] [PubMed]

Harrit, N.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937–1942 (2005).
[Crossref] [PubMed]

Hattori, H.

S. IIto, H. Yamauchi, M. Tamura, S. Hidaka, H. Hattori, T. Hamada, K. Nishida, S. Tokonami, T. Itoh, H. Miyasaka, and T. Iida, “Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams,” Sci. Rep. 3, 3047 (2013).
[Crossref]

Hayazawa, N.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

Heinrich, M.

S. Fardad, A. Salandrino, M. Heinrich, P. Zhang, Z. Chen, and D. N. Christodoulides, “Plasmonic resonant solitons in metallic nanosuspensions,” Nano Lett. 14, 2498–2504 (2014).
[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]

Hickmann, J. M.

R. F. Souza, M. A. R. C. Alencar, E. C. da Silva, M. R. Meneghetti, and J. M. Hickmann, “Nonlinear optical properties of au nanoparticles colloidal system: Local and nonlocal responses,” Appl. Phys. Lett. 92, 201902 (2008).
[Crossref]

Hidaka, S.

S. IIto, H. Yamauchi, M. Tamura, S. Hidaka, H. Hattori, T. Hamada, K. Nishida, S. Tokonami, T. Itoh, H. Miyasaka, and T. Iida, “Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams,” Sci. Rep. 3, 3047 (2013).
[Crossref]

Hnatovsky, C.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8, 846–850 (2014).
[Crossref]

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106, 123901 (2011).
[Crossref] [PubMed]

Hoggard, A.

J. Olson, S. Dominguez-Medina, A. Hoggard, L.-Y. Wang, W.-S. Chang, and S. Link, “Optical characterization of single plasmonic nanoparticles,” Chem. Soc. Rev. 44, 40–57 (2015).
[Crossref]

Horiguchi, N.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (John Wiley & Sons, 2008).

Iatì, M. A.

V. Amendola, R. Pilot, M. Frasconi, O. M. Maragò, and M. A. Iatì, “Surface plasmon resonance in gold nanoparticles: a review,” J. Phys.: Condens. Matter 29, 203002 (2017).

Iida, T.

S. IIto, H. Yamauchi, M. Tamura, S. Hidaka, H. Hattori, T. Hamada, K. Nishida, S. Tokonami, T. Itoh, H. Miyasaka, and T. Iida, “Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams,” Sci. Rep. 3, 3047 (2013).
[Crossref]

IIto, S.

S. IIto, H. Yamauchi, M. Tamura, S. Hidaka, H. Hattori, T. Hamada, K. Nishida, S. Tokonami, T. Itoh, H. Miyasaka, and T. Iida, “Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams,” Sci. Rep. 3, 3047 (2013).
[Crossref]

Itoh, T.

S. IIto, H. Yamauchi, M. Tamura, S. Hidaka, H. Hattori, T. Hamada, K. Nishida, S. Tokonami, T. Itoh, H. Miyasaka, and T. Iida, “Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams,” Sci. Rep. 3, 3047 (2013).
[Crossref]

Izdebskaya, Y.

Jorge, K. C.

A. S. Reyna, K. C. Jorge, and C. B. de Araújo, “Two-dimensional solitons in a quintic-septimal medium,” Phys. Rev. A 90, 063835 (2014).
[Crossref]

Kano, H.

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stabilization of higher-order vortices and multihump solitons in media with synthetic nonlocal nonlinearities,” Phys. Rev. A 79, 013803 (2009).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Engineering soliton nonlinearities: from local to strongly nonlocal,” Opt. Lett. 34, 1543–1545 (2009).
[Crossref] [PubMed]

Kawata, S.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

Kelly, T. S.

Kivshar, Y. S.

Kou, X.

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape-and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24, 5233–5237 (2008).
[Crossref] [PubMed]

Krolikowski, W.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8, 846–850 (2014).
[Crossref]

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106, 123901 (2011).
[Crossref] [PubMed]

E. Brasselet, Y. Izdebskaya, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Dynamics of optical spin-orbit coupling in uniaxial crystals,” Opt. Lett. 34, 1021–1023 (2009).
[Crossref] [PubMed]

M. Matuszewski, W. Krolikowski, and Y. S. Kivshar, “Spatial solitons and light-induced instabilities in colloidal media,” Opt. Express 16, 1371–1376 (2008).
[Crossref] [PubMed]

Lal, S.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641 (2007).
[Crossref]

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).
[Crossref] [PubMed]

Lee, W.

Leger, J. R.

Levelt Sengers, J.

P. Schiebener, J. Straub, J. Levelt Sengers, and J. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[Crossref]

Li, B.

M. Shen, B. Li, L. Ge, W. Chen, and D. Wu, “Stability of vortex solitons under competing local and nonlocal cubic nonlinearities,” Opt. Commun. 338, 27–33 (2015).
[Crossref]

Link, S.

J. Olson, S. Dominguez-Medina, A. Hoggard, L.-Y. Wang, W.-S. Chang, and S. Link, “Optical characterization of single plasmonic nanoparticles,” Chem. Soc. Rev. 44, 40–57 (2015).
[Crossref]

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641 (2007).
[Crossref]

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).
[Crossref] [PubMed]

Lyandres, O.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442 (2008).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Maragò, O. M.

V. Amendola, R. Pilot, M. Frasconi, O. M. Maragò, and M. A. Iatì, “Surface plasmon resonance in gold nanoparticles: a review,” J. Phys.: Condens. Matter 29, 203002 (2017).

Matuszewski, M.

Meneghetti, M. R.

R. F. Souza, M. A. R. C. Alencar, E. C. da Silva, M. R. Meneghetti, and J. M. Hickmann, “Nonlinear optical properties of au nanoparticles colloidal system: Local and nonlocal responses,” Appl. Phys. Lett. 92, 201902 (2008).
[Crossref]

Miyasaka, H.

S. IIto, H. Yamauchi, M. Tamura, S. Hidaka, H. Hattori, T. Hamada, K. Nishida, S. Tokonami, T. Itoh, H. Miyasaka, and T. Iida, “Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams,” Sci. Rep. 3, 3047 (2013).
[Crossref]

Ni, W.

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape-and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24, 5233–5237 (2008).
[Crossref] [PubMed]

Nishida, K.

S. IIto, H. Yamauchi, M. Tamura, S. Hidaka, H. Hattori, T. Hamada, K. Nishida, S. Tokonami, T. Itoh, H. Miyasaka, and T. Iida, “Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams,” Sci. Rep. 3, 3047 (2013).
[Crossref]

Novotny, L.

L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251 (2001).
[Crossref] [PubMed]

Oddershede, L.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937–1942 (2005).
[Crossref] [PubMed]

Oddershede, L. B.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008).
[Crossref] [PubMed]

Olson, J.

J. Olson, S. Dominguez-Medina, A. Hoggard, L.-Y. Wang, W.-S. Chang, and S. Link, “Optical characterization of single plasmonic nanoparticles,” Chem. Soc. Rev. 44, 40–57 (2015).
[Crossref]

Perkins, T. T.

Pilot, R.

V. Amendola, R. Pilot, M. Frasconi, O. M. Maragò, and M. A. Iatì, “Surface plasmon resonance in gold nanoparticles: a review,” J. Phys.: Condens. Matter 29, 203002 (2017).

Prakash, J.

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]

Reece, P.

P. Reece, E. Wright, and K. Dholakia, “Experimental observation of modulation instability and optical spatial soliton arrays in soft condensed matter,” Phys. Rev. Lett. 98, 203902 (2007).
[Crossref] [PubMed]

Ren, Y.-X.

Reyna, A. S.

A. S. Reyna and C. B. De Araujo, “Guiding and confinement of light induced by optical vortex solitons in a cubic–quintic medium,” Opt. Lett. 41, 191–194 (2016).
[Crossref]

A. S. Reyna, K. C. Jorge, and C. B. de Araújo, “Two-dimensional solitons in a quintic-septimal medium,” Phys. Rev. A 90, 063835 (2014).
[Crossref]

Rode, A.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106, 123901 (2011).
[Crossref] [PubMed]

Rotschild, C.

Saito, Y.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

Salandrino, A.

S. Fardad, A. Salandrino, M. Heinrich, P. Zhang, Z. Chen, and D. N. Christodoulides, “Plasmonic resonant solitons in metallic nanosuspensions,” Nano Lett. 14, 2498–2504 (2014).
[Crossref] [PubMed]

Samadi, A.

Schiebener, P.

P. Schiebener, J. Straub, J. Levelt Sengers, and J. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[Crossref]

Schubert, O.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008).
[Crossref] [PubMed]

Segev, M.

Selhuber-Unkel, C.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008).
[Crossref] [PubMed]

Seol, Y.

Shah, N. C.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442 (2008).
[Crossref] [PubMed]

Shen, M.

M. Shen, B. Li, L. Ge, W. Chen, and D. Wu, “Stability of vortex solitons under competing local and nonlocal cubic nonlinearities,” Opt. Commun. 338, 27–33 (2015).
[Crossref]

Sheppard, C.

E. Yew and C. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275, 453–457 (2007).
[Crossref]

Shvedov, V.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8, 846–850 (2014).
[Crossref]

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106, 123901 (2011).
[Crossref] [PubMed]

E. Brasselet, Y. Izdebskaya, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Dynamics of optical spin-orbit coupling in uniaxial crystals,” Opt. Lett. 34, 1021–1023 (2009).
[Crossref] [PubMed]

Silahli, S. Z.

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

Sonnichsen, C.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008).
[Crossref] [PubMed]

Souza, R. F.

R. F. Souza, M. A. R. C. Alencar, E. C. da Silva, M. R. Meneghetti, and J. M. Hickmann, “Nonlinear optical properties of au nanoparticles colloidal system: Local and nonlocal responses,” Appl. Phys. Lett. 92, 201902 (2008).
[Crossref]

Straub, J.

P. Schiebener, J. Straub, J. Levelt Sengers, and J. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[Crossref]

Svoboda, K.

Tamura, M.

S. IIto, H. Yamauchi, M. Tamura, S. Hidaka, H. Hattori, T. Hamada, K. Nishida, S. Tokonami, T. Itoh, H. Miyasaka, and T. Iida, “Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams,” Sci. Rep. 3, 3047 (2013).
[Crossref]

Tokonami, S.

S. IIto, H. Yamauchi, M. Tamura, S. Hidaka, H. Hattori, T. Hamada, K. Nishida, S. Tokonami, T. Itoh, H. Miyasaka, and T. Iida, “Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams,” Sci. Rep. 3, 3047 (2013).
[Crossref]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stabilization of higher-order vortices and multihump solitons in media with synthetic nonlocal nonlinearities,” Phys. Rev. A 79, 013803 (2009).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Engineering soliton nonlinearities: from local to strongly nonlocal,” Opt. Lett. 34, 1543–1545 (2009).
[Crossref] [PubMed]

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[Crossref]

Van Duyne, R. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442 (2008).
[Crossref] [PubMed]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stabilization of higher-order vortices and multihump solitons in media with synthetic nonlocal nonlinearities,” Phys. Rev. A 79, 013803 (2009).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Engineering soliton nonlinearities: from local to strongly nonlocal,” Opt. Lett. 34, 1543–1545 (2009).
[Crossref] [PubMed]

Walasik, W.

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

Wang, J.

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape-and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24, 5233–5237 (2008).
[Crossref] [PubMed]

Wang, L.-Y.

J. Olson, S. Dominguez-Medina, A. Hoggard, L.-Y. Wang, W.-S. Chang, and S. Link, “Optical characterization of single plasmonic nanoparticles,” Chem. Soc. Rev. 44, 40–57 (2015).
[Crossref]

Watanabe, K.

Wright, E.

W. Lee, R. El-Ganainy, D. Christodoulides, K. Dholakia, and E. Wright, “Nonlinear optical response of colloidal suspensions,” Opt. Express 17, 10277–10289 (2009).
[Crossref] [PubMed]

P. Reece, E. Wright, and K. Dholakia, “Experimental observation of modulation instability and optical spatial soliton arrays in soft condensed matter,” Phys. Rev. Lett. 98, 203902 (2007).
[Crossref] [PubMed]

Wu, D.

M. Shen, B. Li, L. Ge, W. Chen, and D. Wu, “Stability of vortex solitons under competing local and nonlocal cubic nonlinearities,” Opt. Commun. 338, 27–33 (2015).
[Crossref]

Yamauchi, H.

S. IIto, H. Yamauchi, M. Tamura, S. Hidaka, H. Hattori, T. Hamada, K. Nishida, S. Tokonami, T. Itoh, H. Miyasaka, and T. Iida, “Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams,” Sci. Rep. 3, 3047 (2013).
[Crossref]

Yang, Z.

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape-and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24, 5233–5237 (2008).
[Crossref] [PubMed]

Yew, E.

E. Yew and C. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275, 453–457 (2007).
[Crossref]

Youngworth, K.

L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251 (2001).
[Crossref] [PubMed]

Zhan, Q.

Zhang, P.

S. Fardad, A. Salandrino, M. Heinrich, P. Zhang, Z. Chen, and D. N. Christodoulides, “Plasmonic resonant solitons in metallic nanosuspensions,” Nano Lett. 14, 2498–2504 (2014).
[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]

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).
[Crossref] [PubMed]

Zhao, J.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442 (2008).
[Crossref] [PubMed]

Zins, I.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85, 6239–6241 (2004).
[Crossref]

R. F. Souza, M. A. R. C. Alencar, E. C. da Silva, M. R. Meneghetti, and J. M. Hickmann, “Nonlinear optical properties of au nanoparticles colloidal system: Local and nonlocal responses,” Appl. Phys. Lett. 92, 201902 (2008).
[Crossref]

Chem. Soc. Rev. (1)

J. Olson, S. Dominguez-Medina, A. Hoggard, L.-Y. Wang, W.-S. Chang, and S. Link, “Optical characterization of single plasmonic nanoparticles,” Chem. Soc. Rev. 44, 40–57 (2015).
[Crossref]

J. Phys. Chem. Ref. Data (1)

P. Schiebener, J. Straub, J. Levelt Sengers, and J. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data 19, 677–717 (1990).
[Crossref]

J. Phys.: Condens. Matter (1)

V. Amendola, R. Pilot, M. Frasconi, O. M. Maragò, and M. A. Iatì, “Surface plasmon resonance in gold nanoparticles: a review,” J. Phys.: Condens. Matter 29, 203002 (2017).

Langmuir (1)

H. Chen, X. Kou, Z. Yang, W. Ni, and J. Wang, “Shape-and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24, 5233–5237 (2008).
[Crossref] [PubMed]

Nano Lett. (3)

S. Fardad, A. Salandrino, M. Heinrich, P. Zhang, Z. Chen, and D. N. Christodoulides, “Plasmonic resonant solitons in metallic nanosuspensions,” Nano Lett. 14, 2498–2504 (2014).
[Crossref] [PubMed]

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937–1942 (2005).
[Crossref] [PubMed]

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998–3003 (2008).
[Crossref] [PubMed]

Nat. Mater. (1)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442 (2008).
[Crossref] [PubMed]

Nat. Photonics (2)

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641 (2007).
[Crossref]

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, “A long-range polarization-controlled optical tractor beam,” Nat. Photonics 8, 846–850 (2014).
[Crossref]

Opt. Commun. (2)

M. Shen, B. Li, L. Ge, W. Chen, and D. Wu, “Stability of vortex solitons under competing local and nonlocal cubic nonlinearities,” Opt. Commun. 338, 27–33 (2015).
[Crossref]

E. Yew and C. Sheppard, “Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams,” Opt. Commun. 275, 453–457 (2007).
[Crossref]

Opt. Express (5)

Opt. Lett. (7)

Phys. Rev. A (2)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stabilization of higher-order vortices and multihump solitons in media with synthetic nonlocal nonlinearities,” Phys. Rev. A 79, 013803 (2009).
[Crossref]

A. S. Reyna, K. C. Jorge, and C. B. de Araújo, “Two-dimensional solitons in a quintic-septimal medium,” Phys. Rev. A 90, 063835 (2014).
[Crossref]

Phys. Rev. Lett. (4)

P. Reece, E. Wright, and K. Dholakia, “Experimental observation of modulation instability and optical spatial soliton arrays in soft condensed matter,” Phys. Rev. Lett. 98, 203902 (2007).
[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]

L. Novotny, M. Beversluis, K. Youngworth, and T. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251 (2001).
[Crossref] [PubMed]

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106, 123901 (2011).
[Crossref] [PubMed]

Prog. Opt. (1)

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[Crossref]

Sci. Rep. (2)

S. IIto, H. Yamauchi, M. Tamura, S. Hidaka, H. Hattori, T. Hamada, K. Nishida, S. Tokonami, T. Itoh, H. Miyasaka, and T. Iida, “Selective optical assembly of highly uniform nanoparticles by doughnut-shaped beams,” Sci. Rep. 3, 3047 (2013).
[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]

Other (2)

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (John Wiley & Sons, 2008).

Y. S. Kivshar and G. Agrawal, Optical solitons: from fibers to photonic crystals (Academic Press, 2003).

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Figures (5)

Fig. 1
Fig. 1 Illustration of the beam propagation concept in the aqueous suspension of gold nanospheres. (a),(b) the beam propagation in a linear (a) and nonlinear (b) regimes when its waist is at the input facet of the cell with the suspension. The low light power has no effects on the random particle distribution in the suspension (a). Increasing the beam power leads to the decreasing of the refractive index of the suspension caused by the negative thermo-optical response of water (orange zone) (b). The probable optical force increases the defocusing effect. (c), (d) The beam propagation in a linear (c) and nonlinear (d, e) regimes when its waist is inside the suspension. In the nonlinear regime (d) the optical forces play no role and the heated water lowers the refractive index of the suspension defocusing the beam and, as result, the actual beam waist increases lowering the beam divergence. In the nonlinear regime (e) the optical forces may locally increase the concentration of particles near the focus creating both positive nonlinearity with high local refractive index in the beam maximum and negative nonlocal thermal optical response with a low refractive index of the surrounding liquid (orange region). The competition between these nonlinear processes may potentially lead to the self-guiding of the beam. (f) Calculated maximal radiation force acting on gold nanospheres as a function of beam waist w0 and a position of the focus (f) measured from the front facet of the cell. The absorption coefficient of the suspension is assumed to be η = 0.27 × 103 m−1.
Fig. 2
Fig. 2 Side-view observation of Gaussian beam propagation in suspension of 20-nm-radius gold nanospheres with absorption coefficient η=0.133 m−1. (a–c) Evolution of the beam radius with power. Insets show magnified sections around beam waist. (d) Measured width of the beam at the output versus input power. (e) Distortion of interference fringes and corresponding inhomogeneous phase shift (f) induced by the beam.
Fig. 3
Fig. 3 Schematic diagram of the experimental setup for the beam convertor and ring beam formation. In the upper row, the uniaxial crystal (UC), microobjectives MO1 and MO2, pinhole PH and lens L3 are used to separate the radially polarized beam from a circularly polarized vortex. Blue arrows show the direction of a vortex rotation; red arrows show the states of polarization. The polarizer, half-wave plates and quarter-wave plates used to change the polarization state of the beam are denoted by P, λ/2 and λ/4, respectively. In the lower row, the crystal is replaced with a glass prism GP with the same optical length to give a free pass to the initial optical vortex. The lenses L3 and L4 are used to collimate and focus a beam to the sample. Examples of the radially polarized beam at the input and output facets in linear (1 mW) and nonlinear (80 mW) regimes are shown in black pictures.
Fig. 4
Fig. 4 Results of the nonlinear propagation of ring-shaped beams in suspension of gold nanospheres (a–c) and gold nanorods (d–f). (a), (d) Measured power absorption of the suspensions. (b,c) and (e,f) Radius of the ring-shaped beams at the output facet of cuvettes as a function of the initial beam power and position of the beam waist for the nanospheres and nanorods, respectively. Dots represent experimental data while lines are averaged fits.
Fig. 5
Fig. 5 Observation of stable nonlinear propagation of ring-shaped beams in the suspension of gold nanospheres. Each beam of identical intensity distributions was initially focused inside the cell, 6 mm from its front facet. (a)–(d) Input and (e)–(t) output profiles for a linearly polarized vortex (first row), circularly polarized vortex (second row), radially (third row) and azimuthally polarized vector (fourth row) beams. Yellow arrows indicate the state of polarization. (e)–(p) Output beam profiles after 2.5 cm of propagation at different input power levels, showing the transition from diffractive broadening at 1 mW to nonlinear narrowing at 80 mW. (q), (r) The interferograms confirming the vortex nature. (s), (t) Intensity distributions of radially and azimuthally polarized beams after an analyzer. The scale bar in (a) corresponds to 500 μm.

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