Abstract

We report a study of the nonlinear birefringence induced in a metal-dielectric nanocomposite due to the contributions of third- and fifth-order optical nonlinearities. A theoretical model describing the evolution of the light polarization state of a confined laser beam propagating through the nonlinear medium is developed with basis on a pair of coupled dissipative cubic-quintic nonlinear differential equations related to the two orthogonal polarizations of the optical field. As a proof-of-principle experiment we demonstrate the control of the light beam polarization in a silver-nanocolloid by changing the silver nanoparticles volume fraction, f, and the light intensity. A large nonlinear phase-shift (~20π) was observed using a 9 cm long capillary filled with silver nanoparticles suspended in carbon disulfide. Experiments using colloids with 1.0×105f4.5×105 and maximum light intensities of tens of MW/cm2 are performed. In addition, we demonstrate that the modulation instability is highly sensitive to the quintic nonlinearity contribution performed showing good agreement with the experimental results.

© 2017 Optical Society of America

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    [Crossref] [PubMed]
  44. A. S. Reyna and C. B. de Araújo, “An optimization procedure for the design of all-optical switches based on metal-dielectric nanocomposites,” Opt. Express 23(6), 7659–7666 (2015).
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2016 (2)

A. Choudhuri, H. Triki, and K. Porsezian, “Self-similar localized pulses for the nonlinear Schrödinger equation with distributed cubic-quintic nonlinearity,” Phys. Rev. A 94(6), 063814 (2016).
[Crossref]

A. S. Reyna and C. B. de Araújo, “Guiding and confinement of light induced by optical vortex solitons in a cubic-quintic medium,” Opt. Lett. 41(1), 191–194 (2016).
[Crossref] [PubMed]

2015 (6)

A. S. Reyna and C. B. de Araújo, “An optimization procedure for the design of all-optical switches based on metal-dielectric nanocomposites,” Opt. Express 23(6), 7659–7666 (2015).
[Crossref] [PubMed]

S. Loomba, R. Pal, and C. N. Kumar, “Bright solitons of the nonautonomous cubic-quintic nonlinear Schrödinger equation with sign-reversal nonlinearity,” Phys. Rev. A 92(3), 033811 (2015).
[Crossref]

S. Wang, Y. Zhang, R. Zhang, H. Yu, H. Zhang, and Q. Xiong, “High-order nonlinearity of surface plasmon resonance in Au nanoparticles: paradoxical combination of saturable and reverse-saturable absorption,” Adv. Opt. Mat. 3(10), 1342–1348 (2015).
[Crossref]

D. L. Weerawarne, X. Gao, A. L. Gaeta, and B. Shim, “Higher-order nonlinearities revisited and their effect on harmonic generation,” Phys. Rev. Lett. 114(9), 093901 (2015).
[Crossref] [PubMed]

I. Danshita, D. Yamamoto, and Y. Kato, “Cubic-quintic nonlinearity in superfluid Bose-Bose mixtures in optical lattices: Heavy solitary waves, barrier-induced criticality, and current-phase relations,” Phys. Rev. A 91(1), 013630 (2015).
[Crossref]

Y. Liu, Y. L. Xue, and C. Yu, “Modulation instability induced by cross-phase modulation in negative index materials with higher-order nonlinearity,” Opt. Commun. 339, 66–73 (2015).
[Crossref]

2014 (8)

A. S. Reyna and C. B. de Araújo, “Nonlinearity management of photonic composites and observation of spatial-modulation instability due to quintic nonlinearity,” Phys. Rev. A 89(6), 063803 (2014).
[Crossref]

V. Besse, G. Boudebs, and H. Leblond, “Determination of the third- and fifth-order optical nonlinearities: the general case,” Appl. Phys. B 116(4), 911–917 (2014).
[Crossref]

R. Sato, M. Ohnuma, K. Oyoshi, and Y. Takeda, “Experimental investigation of nonlinear optical properties of Ag nanoparticles: Effects of size quantization,” Phys. Rev. B 90(12), 125417 (2014).
[Crossref]

B. G. O. Essama, J. Atangana, B. M. Frederick, B. Mokhtari, N. C. Eddeqaqi, and T. C. Kofane, “Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 90(3), 032911 (2014).
[Crossref] [PubMed]

M. Shen, H. Zhao, B. Li, J. Shi, Q. Wang, and R. K. Lee, “Stabilization of vortex solitons by combining competing cubic-quintic nonlinearities with a finite degree of nonlocality,” Phys. Rev. A 89(2), 025804 (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(6), 063835 (2014).
[Crossref]

C. Schnebelin, C. Cassagne, C. B. de Araújo, and G. Boudebs, “Measurements of the third- and fifth-order optical nonlinearities of water at 532 and 1064 nm using the D4σ method,” Opt. Lett. 39(17), 5046–5049 (2014).
[Crossref] [PubMed]

A. S. Reyna and C. B. de Araújo, “Spatial phase modulation due to quintic and septic nonlinearities in metal colloids,” Opt. Express 22(19), 22456–22469 (2014).
[Crossref] [PubMed]

2013 (3)

M. Saha and A. K. Sarma, “Modulation instability in nonlinear metamaterials induced by cubic–quintic nonlinearities and higher order dispersive effects,” Opt. Commun. 291, 321–325 (2013).
[Crossref]

S. Wang and L. Zhang, “An efficient split-step compact finite difference method for cubic–quintic complex Ginzburg–Landau equations,” Comput. Phys. Commun. 184(6), 1511–1521 (2013).
[Crossref]

E. L. Falcão-Filho, C. B. de Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110(1), 013901 (2013).
[Crossref] [PubMed]

2012 (3)

E. Almeida, A. C. L. Moreira, A. M. Brito-Silva, A. Galembeck, C. P. de Melo, L. S. de Menezes, and C. B. de Araújo, “Ultrafast dephasing of localized surface plasmons in colloidal silver nanoparticles: the influence of stabilizing agents,” Appl. Phys. B 108(1), 9–16 (2012).

C. G. L. Tiofack, A. Mohamadou, K. Alim, K. Porsezian, and T. C. Kofane, “Modulational instability in metamaterials with saturable nonlinearity and higher-order dispersion,” J. Mod. Opt. 591(11), 972–979 (2012).

N. J. Dawson and J. H. Andrews, “The local-field factor and microscopic cascading: a self-consistent method applied to confined systems of molecules,” J. Phys. At. Mol. Opt. Phys. 45(3), 035401 (2012).
[Crossref]

2011 (5)

2010 (4)

2009 (3)

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
[Crossref] [PubMed]

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94(18), 181902 (2009).
[Crossref]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components,” Opt. Express 17(16), 13429–13434 (2009).
[Crossref] [PubMed]

2008 (3)

Y. Xu, X. Chen, and Y. Zhu, “Modeling of micro-diameter-scale liquid core optical fiber filled with various liquids,” Opt. Express 16(12), 9205–9212 (2008).
[Crossref] [PubMed]

L. A. Gómez, C. B. de Araújo, A. M. Brito-Silva, and A. Galembeck, “Solvent effects on the linear and nonlinear optical response of silver nanoparticles,” Appl. Phys. B 92(1), 61–66 (2008).
[Crossref]

R. A. Ganeev, M. Suzuki, M. Baba, M. Ichihara, and H. Kuroda, “High-order harmonic generation in Ag nanoparticle-containing plasma,” J. Phys. At. Mol. Opt. Phys. 41(4), 045603 (2008).
[Crossref]

2007 (3)

2006 (1)

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96(2), 023903 (2006).
[Crossref] [PubMed]

2005 (1)

F. Kh. Abdullaev and M. Salerno, “Gap-Townes solitons and localized excitations in low-dimensional Bose-Einstein condensates in optical lattices,” Phys. Rev. A 72(3), 033617 (2005).
[Crossref]

2003 (1)

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219(1-6), 427–433 (2003).
[Crossref]

2001 (1)

A. Minguzzi, P. Vignolo, M. L. Chiofalo, and M. P. Tosi, “Hydrodynamic excitations in a spin-polarized Fermi gas under harmonic confinement in one dimension,” Phys. Rev. A 64(3), 033605 (2001).
[Crossref]

2000 (2)

A. M. Glass, D. J. Di Giovanni, T. A. Strasser, A. J. Stentz, R. E. Slusher, A. E. White, A. R. Kortan, and B. J. Eggleton, “Advances in fiber optics,” Bell Labs Tech. J. 5(1), 168–187 (2000).
[Crossref]

Y. M. Wu, L. Gao, and Z. Y. Li, “The influence of particle shape on nonlinear optical properties of metal–dielectric composites,” Phys. Status Solidi, B Basic Res. 220(2), 997–1008 (2000).
[Crossref]

1995 (1)

L. Lefortand and A. Barthelemy, “All-optical transistor action by polarisation rotation during type-II phase-matched second harmonic generation,” Electron. Lett. 31(11), 910–911 (1995).
[Crossref]

1992 (2)

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46(3), 1614–1629 (1992).
[Crossref] [PubMed]

R. Kashyap and N. Finlayson, “Nonlinear polarization coupling and instabilities in single-mode liquid-cored optical fibers,” Opt. Lett. 17(6), 405–407 (1992).
[Crossref] [PubMed]

1990 (1)

G.-D. Peng and A. Ankiewicz, “All-optical fibre devices using polarization ellipse rotation,” Opt. Quantum Electron. 22(4), 343–350 (1990).
[Crossref]

1986 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Abdullaev, F. Kh.

F. Kh. Abdullaev and M. Salerno, “Gap-Townes solitons and localized excitations in low-dimensional Bose-Einstein condensates in optical lattices,” Phys. Rev. A 72(3), 033617 (2005).
[Crossref]

Abou’ou, M. N. Z.

Agrawal, G. P.

Akhmediev, N.

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
[Crossref] [PubMed]

Alim, K.

C. G. L. Tiofack, A. Mohamadou, K. Alim, K. Porsezian, and T. C. Kofane, “Modulational instability in metamaterials with saturable nonlinearity and higher-order dispersion,” J. Mod. Opt. 591(11), 972–979 (2012).

Almeida, E.

E. Almeida, A. C. L. Moreira, A. M. Brito-Silva, A. Galembeck, C. P. de Melo, L. S. de Menezes, and C. B. de Araújo, “Ultrafast dephasing of localized surface plasmons in colloidal silver nanoparticles: the influence of stabilizing agents,” Appl. Phys. B 108(1), 9–16 (2012).

Andrews, J. H.

N. J. Dawson and J. H. Andrews, “The local-field factor and microscopic cascading: a self-consistent method applied to confined systems of molecules,” J. Phys. At. Mol. Opt. Phys. 45(3), 035401 (2012).
[Crossref]

Ankiewicz, A.

G.-D. Peng and A. Ankiewicz, “All-optical fibre devices using polarization ellipse rotation,” Opt. Quantum Electron. 22(4), 343–350 (1990).
[Crossref]

Atangana, J.

B. G. O. Essama, J. Atangana, B. M. Frederick, B. Mokhtari, N. C. Eddeqaqi, and T. C. Kofane, “Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 90(3), 032911 (2014).
[Crossref] [PubMed]

Baba, M.

R. A. Ganeev, M. Suzuki, M. Baba, M. Ichihara, and H. Kuroda, “High-order harmonic generation in Ag nanoparticle-containing plasma,” J. Phys. At. Mol. Opt. Phys. 41(4), 045603 (2008).
[Crossref]

Barbosa-Silva, R.

Barthelemy, A.

L. Lefortand and A. Barthelemy, “All-optical transistor action by polarisation rotation during type-II phase-matched second harmonic generation,” Electron. Lett. 31(11), 910–911 (1995).
[Crossref]

Besse, V.

V. Besse, G. Boudebs, and H. Leblond, “Determination of the third- and fifth-order optical nonlinearities: the general case,” Appl. Phys. B 116(4), 911–917 (2014).
[Crossref]

Boudebs, G.

V. Besse, G. Boudebs, and H. Leblond, “Determination of the third- and fifth-order optical nonlinearities: the general case,” Appl. Phys. B 116(4), 911–917 (2014).
[Crossref]

C. Schnebelin, C. Cassagne, C. B. de Araújo, and G. Boudebs, “Measurements of the third- and fifth-order optical nonlinearities of water at 532 and 1064 nm using the D4σ method,” Opt. Lett. 39(17), 5046–5049 (2014).
[Crossref] [PubMed]

E. L. Falcão-Filho, C. B. de Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110(1), 013901 (2013).
[Crossref] [PubMed]

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219(1-6), 427–433 (2003).
[Crossref]

Boyd, R.

Boyd, R. W.

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
[Crossref] [PubMed]

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46(3), 1614–1629 (1992).
[Crossref] [PubMed]

Brito-Silva, A. M.

E. Almeida, A. C. L. Moreira, A. M. Brito-Silva, A. Galembeck, C. P. de Melo, L. S. de Menezes, and C. B. de Araújo, “Ultrafast dephasing of localized surface plasmons in colloidal silver nanoparticles: the influence of stabilizing agents,” Appl. Phys. B 108(1), 9–16 (2012).

A. M. Brito-Silva, L. A. Gómez, C. B. de Araújo, and A. Galembeck, “Laser ablated silver nanoparticles with nearly the same size in different carrier media,” J. Nanomater. 2010, 142897 (2010).
[Crossref]

E. L. Falcão-Filho, R. Barbosa-Silva, R. G. Sobral-Filho, A. M. Brito-Silva, A. Galembeck, and C. B. de Araújo, “High-order nonlinearity of silica-gold nanoshells in chloroform at 1560 nm,” Opt. Express 18(21), 21636–21644 (2010).
[Crossref] [PubMed]

L. A. Gómez, C. B. de Araújo, A. M. Brito-Silva, and A. Galembeck, “Solvent effects on the linear and nonlinear optical response of silver nanoparticles,” Appl. Phys. B 92(1), 61–66 (2008).
[Crossref]

L. A. Gómez, C. B. de Araújo, A. M. Brito-Silva, and A. Galembeck, “Influence of stabilizing agents on the nonlinear susceptibility of silver nanoparticles,” J. Opt. Soc. Am. B 24(9), 2136–2140 (2007).
[Crossref]

Cassagne, C.

Chari, R.

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94(18), 181902 (2009).
[Crossref]

Chen, X.

Cherukulappurath, S.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219(1-6), 427–433 (2003).
[Crossref]

Chiofalo, M. L.

A. Minguzzi, P. Vignolo, M. L. Chiofalo, and M. P. Tosi, “Hydrodynamic excitations in a spin-polarized Fermi gas under harmonic confinement in one dimension,” Phys. Rev. A 64(3), 033605 (2001).
[Crossref]

Choudhuri, A.

A. Choudhuri, H. Triki, and K. Porsezian, “Self-similar localized pulses for the nonlinear Schrödinger equation with distributed cubic-quintic nonlinearity,” Phys. Rev. A 94(6), 063814 (2016).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Daino, B.

Danshita, I.

I. Danshita, D. Yamamoto, and Y. Kato, “Cubic-quintic nonlinearity in superfluid Bose-Bose mixtures in optical lattices: Heavy solitary waves, barrier-induced criticality, and current-phase relations,” Phys. Rev. A 91(1), 013630 (2015).
[Crossref]

Dawson, N. J.

N. J. Dawson and J. H. Andrews, “The local-field factor and microscopic cascading: a self-consistent method applied to confined systems of molecules,” J. Phys. At. Mol. Opt. Phys. 45(3), 035401 (2012).
[Crossref]

de Araújo, C. B.

A. S. Reyna and C. B. de Araújo, “Guiding and confinement of light induced by optical vortex solitons in a cubic-quintic medium,” Opt. Lett. 41(1), 191–194 (2016).
[Crossref] [PubMed]

A. S. Reyna and C. B. de Araújo, “An optimization procedure for the design of all-optical switches based on metal-dielectric nanocomposites,” Opt. Express 23(6), 7659–7666 (2015).
[Crossref] [PubMed]

C. Schnebelin, C. Cassagne, C. B. de Araújo, and G. Boudebs, “Measurements of the third- and fifth-order optical nonlinearities of water at 532 and 1064 nm using the D4σ method,” Opt. Lett. 39(17), 5046–5049 (2014).
[Crossref] [PubMed]

A. S. Reyna and C. B. de Araújo, “Nonlinearity management of photonic composites and observation of spatial-modulation instability due to quintic nonlinearity,” Phys. Rev. A 89(6), 063803 (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(6), 063835 (2014).
[Crossref]

A. S. Reyna and C. B. de Araújo, “Spatial phase modulation due to quintic and septic nonlinearities in metal colloids,” Opt. Express 22(19), 22456–22469 (2014).
[Crossref] [PubMed]

E. L. Falcão-Filho, C. B. de Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110(1), 013901 (2013).
[Crossref] [PubMed]

E. Almeida, A. C. L. Moreira, A. M. Brito-Silva, A. Galembeck, C. P. de Melo, L. S. de Menezes, and C. B. de Araújo, “Ultrafast dephasing of localized surface plasmons in colloidal silver nanoparticles: the influence of stabilizing agents,” Appl. Phys. B 108(1), 9–16 (2012).

A. M. Brito-Silva, L. A. Gómez, C. B. de Araújo, and A. Galembeck, “Laser ablated silver nanoparticles with nearly the same size in different carrier media,” J. Nanomater. 2010, 142897 (2010).
[Crossref]

E. L. Falcão-Filho, R. Barbosa-Silva, R. G. Sobral-Filho, A. M. Brito-Silva, A. Galembeck, and C. B. de Araújo, “High-order nonlinearity of silica-gold nanoshells in chloroform at 1560 nm,” Opt. Express 18(21), 21636–21644 (2010).
[Crossref] [PubMed]

L. A. Gómez, C. B. de Araújo, A. M. Brito-Silva, and A. Galembeck, “Solvent effects on the linear and nonlinear optical response of silver nanoparticles,” Appl. Phys. B 92(1), 61–66 (2008).
[Crossref]

E. L. Falcão-Filho, C. B. de Araújo, and J. J. Rodrigues., “High-order nonlinearities of aqueous colloids containing silver nanoparticles,” J. Opt. Soc. Am. B 24(12), 2948–2956 (2007).
[Crossref]

L. A. Gómez, C. B. de Araújo, A. M. Brito-Silva, and A. Galembeck, “Influence of stabilizing agents on the nonlinear susceptibility of silver nanoparticles,” J. Opt. Soc. Am. B 24(9), 2136–2140 (2007).
[Crossref]

de Melo, C. P.

E. Almeida, A. C. L. Moreira, A. M. Brito-Silva, A. Galembeck, C. P. de Melo, L. S. de Menezes, and C. B. de Araújo, “Ultrafast dephasing of localized surface plasmons in colloidal silver nanoparticles: the influence of stabilizing agents,” Appl. Phys. B 108(1), 9–16 (2012).

de Menezes, L. S.

E. Almeida, A. C. L. Moreira, A. M. Brito-Silva, A. Galembeck, C. P. de Melo, L. S. de Menezes, and C. B. de Araújo, “Ultrafast dephasing of localized surface plasmons in colloidal silver nanoparticles: the influence of stabilizing agents,” Appl. Phys. B 108(1), 9–16 (2012).

Di Giovanni, D. J.

A. M. Glass, D. J. Di Giovanni, T. A. Strasser, A. J. Stentz, R. E. Slusher, A. E. White, A. R. Kortan, and B. J. Eggleton, “Advances in fiber optics,” Bell Labs Tech. J. 5(1), 168–187 (2000).
[Crossref]

Dinda, P. T.

Dolgaleva, K.

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
[Crossref] [PubMed]

Dudley, J. M.

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
[Crossref] [PubMed]

Eddeqaqi, N. C.

B. G. O. Essama, J. Atangana, B. M. Frederick, B. Mokhtari, N. C. Eddeqaqi, and T. C. Kofane, “Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 90(3), 032911 (2014).
[Crossref] [PubMed]

Eggleton, B. J.

A. M. Glass, D. J. Di Giovanni, T. A. Strasser, A. J. Stentz, R. E. Slusher, A. E. White, A. R. Kortan, and B. J. Eggleton, “Advances in fiber optics,” Bell Labs Tech. J. 5(1), 168–187 (2000).
[Crossref]

Erkintalo, M.

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
[Crossref] [PubMed]

Essama, B. G. O.

B. G. O. Essama, J. Atangana, B. M. Frederick, B. Mokhtari, N. C. Eddeqaqi, and T. C. Kofane, “Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 90(3), 032911 (2014).
[Crossref] [PubMed]

Falcão-Filho, E. L.

Faucher, O.

Fauchet, P. M.

Finlayson, N.

Finot, C.

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
[Crossref] [PubMed]

Frederick, B. M.

B. G. O. Essama, J. Atangana, B. M. Frederick, B. Mokhtari, N. C. Eddeqaqi, and T. C. Kofane, “Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 90(3), 032911 (2014).
[Crossref] [PubMed]

Gaeta, A. L.

D. L. Weerawarne, X. Gao, A. L. Gaeta, and B. Shim, “Higher-order nonlinearities revisited and their effect on harmonic generation,” Phys. Rev. Lett. 114(9), 093901 (2015).
[Crossref] [PubMed]

Galembeck, A.

E. Almeida, A. C. L. Moreira, A. M. Brito-Silva, A. Galembeck, C. P. de Melo, L. S. de Menezes, and C. B. de Araújo, “Ultrafast dephasing of localized surface plasmons in colloidal silver nanoparticles: the influence of stabilizing agents,” Appl. Phys. B 108(1), 9–16 (2012).

A. M. Brito-Silva, L. A. Gómez, C. B. de Araújo, and A. Galembeck, “Laser ablated silver nanoparticles with nearly the same size in different carrier media,” J. Nanomater. 2010, 142897 (2010).
[Crossref]

E. L. Falcão-Filho, R. Barbosa-Silva, R. G. Sobral-Filho, A. M. Brito-Silva, A. Galembeck, and C. B. de Araújo, “High-order nonlinearity of silica-gold nanoshells in chloroform at 1560 nm,” Opt. Express 18(21), 21636–21644 (2010).
[Crossref] [PubMed]

L. A. Gómez, C. B. de Araújo, A. M. Brito-Silva, and A. Galembeck, “Solvent effects on the linear and nonlinear optical response of silver nanoparticles,” Appl. Phys. B 92(1), 61–66 (2008).
[Crossref]

L. A. Gómez, C. B. de Araújo, A. M. Brito-Silva, and A. Galembeck, “Influence of stabilizing agents on the nonlinear susceptibility of silver nanoparticles,” J. Opt. Soc. Am. B 24(9), 2136–2140 (2007).
[Crossref]

Ganeev, R. A.

R. A. Ganeev, M. Suzuki, M. Baba, M. Ichihara, and H. Kuroda, “High-order harmonic generation in Ag nanoparticle-containing plasma,” J. Phys. At. Mol. Opt. Phys. 41(4), 045603 (2008).
[Crossref]

Gao, L.

Y. M. Wu, L. Gao, and Z. Y. Li, “The influence of particle shape on nonlinear optical properties of metal–dielectric composites,” Phys. Status Solidi, B Basic Res. 220(2), 997–1008 (2000).
[Crossref]

Gao, X.

D. L. Weerawarne, X. Gao, A. L. Gaeta, and B. Shim, “Higher-order nonlinearities revisited and their effect on harmonic generation,” Phys. Rev. Lett. 114(9), 093901 (2015).
[Crossref] [PubMed]

Genty, G.

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
[Crossref] [PubMed]

Glass, A. M.

A. M. Glass, D. J. Di Giovanni, T. A. Strasser, A. J. Stentz, R. E. Slusher, A. E. White, A. R. Kortan, and B. J. Eggleton, “Advances in fiber optics,” Bell Labs Tech. J. 5(1), 168–187 (2000).
[Crossref]

Gómez, L. A.

A. M. Brito-Silva, L. A. Gómez, C. B. de Araújo, and A. Galembeck, “Laser ablated silver nanoparticles with nearly the same size in different carrier media,” J. Nanomater. 2010, 142897 (2010).
[Crossref]

L. A. Gómez, C. B. de Araújo, A. M. Brito-Silva, and A. Galembeck, “Solvent effects on the linear and nonlinear optical response of silver nanoparticles,” Appl. Phys. B 92(1), 61–66 (2008).
[Crossref]

L. A. Gómez, C. B. de Araújo, A. M. Brito-Silva, and A. Galembeck, “Influence of stabilizing agents on the nonlinear susceptibility of silver nanoparticles,” J. Opt. Soc. Am. B 24(9), 2136–2140 (2007).
[Crossref]

Gregori, G.

Hammani, K.

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
[Crossref] [PubMed]

Hertz, E.

Ichihara, M.

R. A. Ganeev, M. Suzuki, M. Baba, M. Ichihara, and H. Kuroda, “High-order harmonic generation in Ag nanoparticle-containing plasma,” J. Phys. At. Mol. Opt. Phys. 41(4), 045603 (2008).
[Crossref]

Jayabalan, J.

J. Jayabalan, “Origin and time dependence of higher-order nonlinearities in metal nanocomposites,” J. Opt. Soc. Am. B 28(10), 2448–2455 (2011).
[Crossref]

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94(18), 181902 (2009).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

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(6), 063835 (2014).
[Crossref]

Kashyap, R.

Kato, Y.

I. Danshita, D. Yamamoto, and Y. Kato, “Cubic-quintic nonlinearity in superfluid Bose-Bose mixtures in optical lattices: Heavy solitary waves, barrier-induced criticality, and current-phase relations,” Phys. Rev. A 91(1), 013630 (2015).
[Crossref]

Khan, S.

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94(18), 181902 (2009).
[Crossref]

Kibler, B.

M. N. Z. Abou’ou, P. T. Dinda, C. M. Ngabireng, B. Kibler, and F. Smektala, “Impact of the material absorption on the modulational instability spectra of wave propagation in high-index glass fibers,” J. Opt. Soc. Am. B 28(6), 1518–1528 (2011).
[Crossref]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-Order Modulation Instability in Nonlinear Fiber Optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
[Crossref] [PubMed]

Kofane, T. C.

B. G. O. Essama, J. Atangana, B. M. Frederick, B. Mokhtari, N. C. Eddeqaqi, and T. C. Kofane, “Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 90(3), 032911 (2014).
[Crossref] [PubMed]

C. G. L. Tiofack, A. Mohamadou, K. Alim, K. Porsezian, and T. C. Kofane, “Modulational instability in metamaterials with saturable nonlinearity and higher-order dispersion,” J. Mod. Opt. 591(11), 972–979 (2012).

Kolesik, M.

Kortan, A. R.

A. M. Glass, D. J. Di Giovanni, T. A. Strasser, A. J. Stentz, R. E. Slusher, A. E. White, A. R. Kortan, and B. J. Eggleton, “Advances in fiber optics,” Bell Labs Tech. J. 5(1), 168–187 (2000).
[Crossref]

Kumar, C. N.

S. Loomba, R. Pal, and C. N. Kumar, “Bright solitons of the nonautonomous cubic-quintic nonlinear Schrödinger equation with sign-reversal nonlinearity,” Phys. Rev. A 92(3), 033811 (2015).
[Crossref]

Kuroda, H.

R. A. Ganeev, M. Suzuki, M. Baba, M. Ichihara, and H. Kuroda, “High-order harmonic generation in Ag nanoparticle-containing plasma,” J. Phys. At. Mol. Opt. Phys. 41(4), 045603 (2008).
[Crossref]

Lavorel, B.

Leblond, H.

V. Besse, G. Boudebs, and H. Leblond, “Determination of the third- and fifth-order optical nonlinearities: the general case,” Appl. Phys. B 116(4), 911–917 (2014).
[Crossref]

E. L. Falcão-Filho, C. B. de Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110(1), 013901 (2013).
[Crossref] [PubMed]

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219(1-6), 427–433 (2003).
[Crossref]

Lee, J. Y.

Lee, R. K.

M. Shen, H. Zhao, B. Li, J. Shi, Q. Wang, and R. K. Lee, “Stabilization of vortex solitons by combining competing cubic-quintic nonlinearities with a finite degree of nonlocality,” Phys. Rev. A 89(2), 025804 (2014).
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Lefortand, L.

L. Lefortand and A. Barthelemy, “All-optical transistor action by polarisation rotation during type-II phase-matched second harmonic generation,” Electron. Lett. 31(11), 910–911 (1995).
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Li, B.

M. Shen, H. Zhao, B. Li, J. Shi, Q. Wang, and R. K. Lee, “Stabilization of vortex solitons by combining competing cubic-quintic nonlinearities with a finite degree of nonlocality,” Phys. Rev. A 89(2), 025804 (2014).
[Crossref]

Li, R.

Li, Z. Y.

Y. M. Wu, L. Gao, and Z. Y. Li, “The influence of particle shape on nonlinear optical properties of metal–dielectric composites,” Phys. Status Solidi, B Basic Res. 220(2), 997–1008 (2000).
[Crossref]

Liu, J.

Liu, Y.

Y. Liu, Y. L. Xue, and C. Yu, “Modulation instability induced by cross-phase modulation in negative index materials with higher-order nonlinearity,” Opt. Commun. 339, 66–73 (2015).
[Crossref]

Loomba, S.

S. Loomba, R. Pal, and C. N. Kumar, “Bright solitons of the nonautonomous cubic-quintic nonlinear Schrödinger equation with sign-reversal nonlinearity,” Phys. Rev. A 92(3), 033811 (2015).
[Crossref]

Loriot, V.

Michinel, H.

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96(2), 023903 (2006).
[Crossref] [PubMed]

Minguzzi, A.

A. Minguzzi, P. Vignolo, M. L. Chiofalo, and M. P. Tosi, “Hydrodynamic excitations in a spin-polarized Fermi gas under harmonic confinement in one dimension,” Phys. Rev. A 64(3), 033605 (2001).
[Crossref]

Mohamadou, A.

C. G. L. Tiofack, A. Mohamadou, K. Alim, K. Porsezian, and T. C. Kofane, “Modulational instability in metamaterials with saturable nonlinearity and higher-order dispersion,” J. Mod. Opt. 591(11), 972–979 (2012).

Mokhtari, B.

B. G. O. Essama, J. Atangana, B. M. Frederick, B. Mokhtari, N. C. Eddeqaqi, and T. C. Kofane, “Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 90(3), 032911 (2014).
[Crossref] [PubMed]

Moloney, J. V.

Moreira, A. C. L.

E. Almeida, A. C. L. Moreira, A. M. Brito-Silva, A. Galembeck, C. P. de Melo, L. S. de Menezes, and C. B. de Araújo, “Ultrafast dephasing of localized surface plasmons in colloidal silver nanoparticles: the influence of stabilizing agents,” Appl. Phys. B 108(1), 9–16 (2012).

Ngabireng, C. M.

Oak, S. M.

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94(18), 181902 (2009).
[Crossref]

Ohnuma, M.

R. Sato, M. Ohnuma, K. Oyoshi, and Y. Takeda, “Experimental investigation of nonlinear optical properties of Ag nanoparticles: Effects of size quantization,” Phys. Rev. B 90(12), 125417 (2014).
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Oyoshi, K.

R. Sato, M. Ohnuma, K. Oyoshi, and Y. Takeda, “Experimental investigation of nonlinear optical properties of Ag nanoparticles: Effects of size quantization,” Phys. Rev. B 90(12), 125417 (2014).
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Pal, R.

S. Loomba, R. Pal, and C. N. Kumar, “Bright solitons of the nonautonomous cubic-quintic nonlinear Schrödinger equation with sign-reversal nonlinearity,” Phys. Rev. A 92(3), 033811 (2015).
[Crossref]

Papazoglou, D. G.

Paz-Alonso, M. J.

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96(2), 023903 (2006).
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H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96(2), 023903 (2006).
[Crossref] [PubMed]

Porsezian, K.

A. Choudhuri, H. Triki, and K. Porsezian, “Self-similar localized pulses for the nonlinear Schrödinger equation with distributed cubic-quintic nonlinearity,” Phys. Rev. A 94(6), 063814 (2016).
[Crossref]

C. G. L. Tiofack, A. Mohamadou, K. Alim, K. Porsezian, and T. C. Kofane, “Modulational instability in metamaterials with saturable nonlinearity and higher-order dispersion,” J. Mod. Opt. 591(11), 972–979 (2012).

Reyna, A. S.

Rodrigues, J. J.

Saha, M.

M. Saha and A. K. Sarma, “Modulation instability in nonlinear metamaterials induced by cubic–quintic nonlinearities and higher order dispersive effects,” Opt. Commun. 291, 321–325 (2013).
[Crossref]

Salerno, M.

F. Kh. Abdullaev and M. Salerno, “Gap-Townes solitons and localized excitations in low-dimensional Bose-Einstein condensates in optical lattices,” Phys. Rev. A 72(3), 033617 (2005).
[Crossref]

Sanchez, F.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219(1-6), 427–433 (2003).
[Crossref]

Sarma, A. K.

M. Saha and A. K. Sarma, “Modulation instability in nonlinear metamaterials induced by cubic–quintic nonlinearities and higher order dispersive effects,” Opt. Commun. 291, 321–325 (2013).
[Crossref]

Sato, R.

R. Sato, M. Ohnuma, K. Oyoshi, and Y. Takeda, “Experimental investigation of nonlinear optical properties of Ag nanoparticles: Effects of size quantization,” Phys. Rev. B 90(12), 125417 (2014).
[Crossref]

Schnebelin, C.

Shen, M.

M. Shen, H. Zhao, B. Li, J. Shi, Q. Wang, and R. K. Lee, “Stabilization of vortex solitons by combining competing cubic-quintic nonlinearities with a finite degree of nonlocality,” Phys. Rev. A 89(2), 025804 (2014).
[Crossref]

Shi, J.

M. Shen, H. Zhao, B. Li, J. Shi, Q. Wang, and R. K. Lee, “Stabilization of vortex solitons by combining competing cubic-quintic nonlinearities with a finite degree of nonlocality,” Phys. Rev. A 89(2), 025804 (2014).
[Crossref]

Shim, B.

D. L. Weerawarne, X. Gao, A. L. Gaeta, and B. Shim, “Higher-order nonlinearities revisited and their effect on harmonic generation,” Phys. Rev. Lett. 114(9), 093901 (2015).
[Crossref] [PubMed]

Shin, H.

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
[Crossref] [PubMed]

Shum,

Singh, A.

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94(18), 181902 (2009).
[Crossref]

Sipe, J. E.

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46(3), 1614–1629 (1992).
[Crossref] [PubMed]

Skarka, V.

E. L. Falcão-Filho, C. B. de Araújo, G. Boudebs, H. Leblond, and V. Skarka, “Robust two-dimensional spatial solitons in liquid carbon disulfide,” Phys. Rev. Lett. 110(1), 013901 (2013).
[Crossref] [PubMed]

Slusher, R. E.

A. M. Glass, D. J. Di Giovanni, T. A. Strasser, A. J. Stentz, R. E. Slusher, A. E. White, A. R. Kortan, and B. J. Eggleton, “Advances in fiber optics,” Bell Labs Tech. J. 5(1), 168–187 (2000).
[Crossref]

Smektala, F.

M. N. Z. Abou’ou, P. T. Dinda, C. M. Ngabireng, B. Kibler, and F. Smektala, “Impact of the material absorption on the modulational instability spectra of wave propagation in high-index glass fibers,” J. Opt. Soc. Am. B 28(6), 1518–1528 (2011).
[Crossref]

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219(1-6), 427–433 (2003).
[Crossref]

Sobral-Filho, R. G.

Srivastava, H.

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94(18), 181902 (2009).
[Crossref]

Stegeman, G.

Stentz, A. J.

A. M. Glass, D. J. Di Giovanni, T. A. Strasser, A. J. Stentz, R. E. Slusher, A. E. White, A. R. Kortan, and B. J. Eggleton, “Advances in fiber optics,” Bell Labs Tech. J. 5(1), 168–187 (2000).
[Crossref]

Strasser, T. A.

A. M. Glass, D. J. Di Giovanni, T. A. Strasser, A. J. Stentz, R. E. Slusher, A. E. White, A. R. Kortan, and B. J. Eggleton, “Advances in fiber optics,” Bell Labs Tech. J. 5(1), 168–187 (2000).
[Crossref]

Suzuki, M.

R. A. Ganeev, M. Suzuki, M. Baba, M. Ichihara, and H. Kuroda, “High-order harmonic generation in Ag nanoparticle-containing plasma,” J. Phys. At. Mol. Opt. Phys. 41(4), 045603 (2008).
[Crossref]

Takeda, Y.

R. Sato, M. Ohnuma, K. Oyoshi, and Y. Takeda, “Experimental investigation of nonlinear optical properties of Ag nanoparticles: Effects of size quantization,” Phys. Rev. B 90(12), 125417 (2014).
[Crossref]

Tiofack, C. G. L.

C. G. L. Tiofack, A. Mohamadou, K. Alim, K. Porsezian, and T. C. Kofane, “Modulational instability in metamaterials with saturable nonlinearity and higher-order dispersion,” J. Mod. Opt. 591(11), 972–979 (2012).

Tosi, M. P.

A. Minguzzi, P. Vignolo, M. L. Chiofalo, and M. P. Tosi, “Hydrodynamic excitations in a spin-polarized Fermi gas under harmonic confinement in one dimension,” Phys. Rev. A 64(3), 033605 (2001).
[Crossref]

Triki, H.

A. Choudhuri, H. Triki, and K. Porsezian, “Self-similar localized pulses for the nonlinear Schrödinger equation with distributed cubic-quintic nonlinearity,” Phys. Rev. A 94(6), 063814 (2016).
[Crossref]

Troles, J.

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219(1-6), 427–433 (2003).
[Crossref]

Tzortzakis, S.

Vignolo, P.

A. Minguzzi, P. Vignolo, M. L. Chiofalo, and M. P. Tosi, “Hydrodynamic excitations in a spin-polarized Fermi gas under harmonic confinement in one dimension,” Phys. Rev. A 64(3), 033605 (2001).
[Crossref]

Wabnitz, S.

Wang, Q.

M. Shen, H. Zhao, B. Li, J. Shi, Q. Wang, and R. K. Lee, “Stabilization of vortex solitons by combining competing cubic-quintic nonlinearities with a finite degree of nonlocality,” Phys. Rev. A 89(2), 025804 (2014).
[Crossref]

Wang, S.

S. Wang, Y. Zhang, R. Zhang, H. Yu, H. Zhang, and Q. Xiong, “High-order nonlinearity of surface plasmon resonance in Au nanoparticles: paradoxical combination of saturable and reverse-saturable absorption,” Adv. Opt. Mat. 3(10), 1342–1348 (2015).
[Crossref]

S. Wang and L. Zhang, “An efficient split-step compact finite difference method for cubic–quintic complex Ginzburg–Landau equations,” Comput. Phys. Commun. 184(6), 1511–1521 (2013).
[Crossref]

Wang, Z.

Weerawarne, D. L.

D. L. Weerawarne, X. Gao, A. L. Gaeta, and B. Shim, “Higher-order nonlinearities revisited and their effect on harmonic generation,” Phys. Rev. Lett. 114(9), 093901 (2015).
[Crossref] [PubMed]

White, A. E.

A. M. Glass, D. J. Di Giovanni, T. A. Strasser, A. J. Stentz, R. E. Slusher, A. E. White, A. R. Kortan, and B. J. Eggleton, “Advances in fiber optics,” Bell Labs Tech. J. 5(1), 168–187 (2000).
[Crossref]

Wright, E. M.

Wu, Y. M.

Y. M. Wu, L. Gao, and Z. Y. Li, “The influence of particle shape on nonlinear optical properties of metal–dielectric composites,” Phys. Status Solidi, B Basic Res. 220(2), 997–1008 (2000).
[Crossref]

Xiong, Q.

S. Wang, Y. Zhang, R. Zhang, H. Yu, H. Zhang, and Q. Xiong, “High-order nonlinearity of surface plasmon resonance in Au nanoparticles: paradoxical combination of saturable and reverse-saturable absorption,” Adv. Opt. Mat. 3(10), 1342–1348 (2015).
[Crossref]

Xu, Y.

Xu, Z.

Xue, Y. L.

Y. Liu, Y. L. Xue, and C. Yu, “Modulation instability induced by cross-phase modulation in negative index materials with higher-order nonlinearity,” Opt. Commun. 339, 66–73 (2015).
[Crossref]

Yamamoto, D.

I. Danshita, D. Yamamoto, and Y. Kato, “Cubic-quintic nonlinearity in superfluid Bose-Bose mixtures in optical lattices: Heavy solitary waves, barrier-induced criticality, and current-phase relations,” Phys. Rev. A 91(1), 013630 (2015).
[Crossref]

Yin, L.

Yosia, P.

Yu, C.

Y. Liu, Y. L. Xue, and C. Yu, “Modulation instability induced by cross-phase modulation in negative index materials with higher-order nonlinearity,” Opt. Commun. 339, 66–73 (2015).
[Crossref]

Yu, H.

S. Wang, Y. Zhang, R. Zhang, H. Yu, H. Zhang, and Q. Xiong, “High-order nonlinearity of surface plasmon resonance in Au nanoparticles: paradoxical combination of saturable and reverse-saturable absorption,” Adv. Opt. Mat. 3(10), 1342–1348 (2015).
[Crossref]

Zhang, C.

Zhang, H.

S. Wang, Y. Zhang, R. Zhang, H. Yu, H. Zhang, and Q. Xiong, “High-order nonlinearity of surface plasmon resonance in Au nanoparticles: paradoxical combination of saturable and reverse-saturable absorption,” Adv. Opt. Mat. 3(10), 1342–1348 (2015).
[Crossref]

Zhang, L.

S. Wang and L. Zhang, “An efficient split-step compact finite difference method for cubic–quintic complex Ginzburg–Landau equations,” Comput. Phys. Commun. 184(6), 1511–1521 (2013).
[Crossref]

Zhang, R.

S. Wang, Y. Zhang, R. Zhang, H. Yu, H. Zhang, and Q. Xiong, “High-order nonlinearity of surface plasmon resonance in Au nanoparticles: paradoxical combination of saturable and reverse-saturable absorption,” Adv. Opt. Mat. 3(10), 1342–1348 (2015).
[Crossref]

Zhang, Y.

S. Wang, Y. Zhang, R. Zhang, H. Yu, H. Zhang, and Q. Xiong, “High-order nonlinearity of surface plasmon resonance in Au nanoparticles: paradoxical combination of saturable and reverse-saturable absorption,” Adv. Opt. Mat. 3(10), 1342–1348 (2015).
[Crossref]

Zhao, H.

M. Shen, H. Zhao, B. Li, J. Shi, Q. Wang, and R. K. Lee, “Stabilization of vortex solitons by combining competing cubic-quintic nonlinearities with a finite degree of nonlocality,” Phys. Rev. A 89(2), 025804 (2014).
[Crossref]

Zhu, Y.

Adv. Opt. Mat. (1)

S. Wang, Y. Zhang, R. Zhang, H. Yu, H. Zhang, and Q. Xiong, “High-order nonlinearity of surface plasmon resonance in Au nanoparticles: paradoxical combination of saturable and reverse-saturable absorption,” Adv. Opt. Mat. 3(10), 1342–1348 (2015).
[Crossref]

Appl. Phys. B (3)

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[Crossref]

Appl. Phys. Lett. (1)

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94(18), 181902 (2009).
[Crossref]

Bell Labs Tech. J. (1)

A. M. Glass, D. J. Di Giovanni, T. A. Strasser, A. J. Stentz, R. E. Slusher, A. E. White, A. R. Kortan, and B. J. Eggleton, “Advances in fiber optics,” Bell Labs Tech. J. 5(1), 168–187 (2000).
[Crossref]

Comput. Phys. Commun. (1)

S. Wang and L. Zhang, “An efficient split-step compact finite difference method for cubic–quintic complex Ginzburg–Landau equations,” Comput. Phys. Commun. 184(6), 1511–1521 (2013).
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C. G. L. Tiofack, A. Mohamadou, K. Alim, K. Porsezian, and T. C. Kofane, “Modulational instability in metamaterials with saturable nonlinearity and higher-order dispersion,” J. Mod. Opt. 591(11), 972–979 (2012).

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A. M. Brito-Silva, L. A. Gómez, C. B. de Araújo, and A. Galembeck, “Laser ablated silver nanoparticles with nearly the same size in different carrier media,” J. Nanomater. 2010, 142897 (2010).
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J. Opt. Soc. Am. B (4)

J. Phys. At. Mol. Opt. Phys. (2)

R. A. Ganeev, M. Suzuki, M. Baba, M. Ichihara, and H. Kuroda, “High-order harmonic generation in Ag nanoparticle-containing plasma,” J. Phys. At. Mol. Opt. Phys. 41(4), 045603 (2008).
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Opt. Commun. (3)

G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219(1-6), 427–433 (2003).
[Crossref]

M. Saha and A. K. Sarma, “Modulation instability in nonlinear metamaterials induced by cubic–quintic nonlinearities and higher order dispersive effects,” Opt. Commun. 291, 321–325 (2013).
[Crossref]

Y. Liu, Y. L. Xue, and C. Yu, “Modulation instability induced by cross-phase modulation in negative index materials with higher-order nonlinearity,” Opt. Commun. 339, 66–73 (2015).
[Crossref]

Opt. Express (7)

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Phys. Rev. A (9)

A. S. Reyna, K. C. Jorge, and C. B. de Araújo, “Two-dimensional solitons in a quintic-septimal medium,” Phys. Rev. A 90(6), 063835 (2014).
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A. S. Reyna and C. B. de Araújo, “Nonlinearity management of photonic composites and observation of spatial-modulation instability due to quintic nonlinearity,” Phys. Rev. A 89(6), 063803 (2014).
[Crossref]

F. Kh. Abdullaev and M. Salerno, “Gap-Townes solitons and localized excitations in low-dimensional Bose-Einstein condensates in optical lattices,” Phys. Rev. A 72(3), 033617 (2005).
[Crossref]

I. Danshita, D. Yamamoto, and Y. Kato, “Cubic-quintic nonlinearity in superfluid Bose-Bose mixtures in optical lattices: Heavy solitary waves, barrier-induced criticality, and current-phase relations,” Phys. Rev. A 91(1), 013630 (2015).
[Crossref]

A. Minguzzi, P. Vignolo, M. L. Chiofalo, and M. P. Tosi, “Hydrodynamic excitations in a spin-polarized Fermi gas under harmonic confinement in one dimension,” Phys. Rev. A 64(3), 033605 (2001).
[Crossref]

M. Shen, H. Zhao, B. Li, J. Shi, Q. Wang, and R. K. Lee, “Stabilization of vortex solitons by combining competing cubic-quintic nonlinearities with a finite degree of nonlocality,” Phys. Rev. A 89(2), 025804 (2014).
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A. Choudhuri, H. Triki, and K. Porsezian, “Self-similar localized pulses for the nonlinear Schrödinger equation with distributed cubic-quintic nonlinearity,” Phys. Rev. A 94(6), 063814 (2016).
[Crossref]

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46(3), 1614–1629 (1992).
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Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

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D. L. Weerawarne, X. Gao, A. L. Gaeta, and B. Shim, “Higher-order nonlinearities revisited and their effect on harmonic generation,” Phys. Rev. Lett. 114(9), 093901 (2015).
[Crossref] [PubMed]

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
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Figures (5)

Fig. 1
Fig. 1 (a) The experimental setup: polarizer (P), beam splitter (BS), spherical lenses with f = 5 cm (L), 40x microscope objective (L1), 20x microscope objective (L2), polarizing beam splitter cube (PBS) and reference detector (RD). The transmitted light with vertical and horizontal polarization was captured in the fast detectors D1 and D2, respectively. (b) Inner diameter of capillary, in a portion of 5 mm, showing small asymmetries. The inset is an optical microscope image of a small section of the hollow capillary core (length: 1 mm).
Fig. 2
Fig. 2 Local gain spectra of modulation instability versus the frequency shift along the fast axis, for the five samples.
Fig. 3
Fig. 3 Numerical pulse shape evolution for sample A (S-A), sample B (S-B), sample C (S-C), sample D (S-D) and sample E (S-E), with input intensity of 60 MW/cm2. Pulse duration: 80 ps. Propagation length: 9 cm.
Fig. 4
Fig. 4 Normalized transmittance as a function of the incident polarization azimuth angle, θ, for (a) sample A, (b) sample B, (c) sample C, (d) sample D and (e) sample E. From top to bottom, the incident peak intensities are 6, 24, 42 and 60 MW/cm2, in each row. Black circles and red squares correspond to vertical and horizontal polarization transmittance, respectively. Solid lines were obtained from numerical solutions of Eq. (24) and the parameters of Table 1.
Fig. 5
Fig. 5 Vertical (black circles) and horizontal (red squares) polarization transmittance as a function of the incident peak intensities variation, for (a) sample A, (b) sample B, (c) sample C, (d) sample D and (e) sample E. Black and red solid lines were obtained from numerical solutions of Eq. (24) and the parameters of Table 1. Blue dashed lines represent the numerical solutions of Eq. (24) neglecting the contribution of Re( χ ( 5 ) ).

Tables (1)

Tables Icon

Table 1 Linear absorption coefficienta, second-order dispersion coefficienta, third and fifth-order susceptibilitiesb for pure CS2 (S-A) and silver-colloids with different nanoparticles volume fraction.

Equations (37)

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

E( r,t )= 1 2 ( x ^ E x + y ^ E y )exp( i ω 0 t )+c.c,
2 E( r,ω )+ k 0 2 ε( ω )E( r,ω )=0,
2 E μ ( r,ω )+ k 0 2 ε μσ ( ω ) E σ ( r,ω )=0,
P μ NL ( ω )= ε 0 ε μ NL ( ω ) E μ ( ω ),
P μ (3) ( ω )=3 ε 0 { 2 χ xxyy (3) ( ω ) E μ ( ω )[ E( ω ) E * ( ω ) ]+ χ xyyx (3) ( ω ) E μ * ( ω )[ E( ω )E( ω ) ] },
P μ (5) ( ω )=10 ε 0 { 10 3 χ xxyyxx (5) ( ω ) | E μ ( ω ) | 2 [ E( ω )E( ω ) ] E μ * ( ω ) + 5 3 χ xxyyyy (5) ( ω ) σ=x,y | E σ ( ω ) | 4 E μ ( ω ) },
ε μ NL ( ω )=3[ ( 2 χ xxyy (3) ( ω )+ χ xyyx (3) ( ω ) ) | E μ ( ω ) | 2 +2 χ xxyy (3) ( ω ) σ=x,y | E σ ( ω ) | 2 ( 1 δ μ,σ ) ] +10[ 10 3 χ xxyyxx (5) ( ω ) | E μ ( ω ) | 4 + 5 3 χ xxyyyy (5) ( ω )( | E μ ( ω ) | 4 + σ=x,y | E σ ( ω ) | 4 ( 1 δ μ,σ ) ) ] +[ 3 χ xyyx (3) ( ω )+10 10 3 χ xxyyxx (5) ( ω ) | E μ ( ω ) | 2 ] σ=x,y [ E σ ( ω ) ] 2 ( 1 δ μ,σ ) E μ * ( ω ) E μ ( ω ) .
E μ ( r,ω )=F( x,y ) A μ ( z,ω ω 0 )exp( i β 0,μ z ),
2i β 0,μ A μ z +( β μ 2 β 0,μ 2 ) A μ =0,
2 F x 2 + 2 F y 2 +[ ε μ ( ω ) k 0 2 β μ 2 ]F=0,
ε μ = ( n 0,μ +Δ N μ ) 2 ( n 0,μ ) 2 +2( n 0,μ )( Δ N μ ),
( Δ n μ +i Δ α μ 2 k 0 )= 3 2 n 0,μ | F | 2 [ ( 2 χ xxyy (3) + χ xyyx (3) ) | A μ | 2 +2 χ xxyy (3) σ=x,y | A σ | 2 ( 1 δ μ,σ ) ] + 10 2 n 0,μ | F | 4 [ 10 3 χ xxyyxx (5) | A μ | 4 + 5 3 χ xxyyyy (5) ( | A μ | 4 + σ=x,y | A σ | 4 ( 1 δ μ,σ ) ) ] + 1 2 n 0,μ | F | 2 [ 3 χ xyyx (3) +10 10 3 χ xxyyxx (5) | F | 2 | A μ | 2 ] σ=x,y [ A σ ( ω ) ] 2 ( 1 δ μ,σ ) A μ * A μ exp[ 2i( β 0,σ β 0,μ )z ].
F= F (0) +ξ F (1) +,
β μ 2 = ( β μ ) 2 +ξ2 β μ ( Δ β μ )+,
ξ 0 : [ ( 2 x 2 + 2 y 2 + n 0,μ 2 k 0 2 ) β μ 2 ] F (0) =0,
ξ 1 : [ ( 2 x 2 + 2 y 2 + n 0,μ 2 k 0 2 ) β μ 2 ] F (1) +[ 2( n 0,μ )( Δ N μ ) k 0 2 2 β μ Δ β μ ] F (0) =0.
F core ( 0 ) ( ρ )= C 1 J m ( ρ n 0,μ 2 k 0 2 β μ 2 ),
F cladding ( 0 ) ( ρ )= C 2 K m ( ρ β μ 2 n cladding 2 k 0 2 ).
Δ β μ = k 0 ( Δ N μ ) | F ( 0 ) | 2 dxdy | F ( 0 ) | 2 dxdy ,
A μ z =i( β μ +Δ β μ β 0,μ ) A μ ,
β μ ( ω )= β 0,μ + β μ (1) ( ω ω 0 )+ 1 2 β μ (2) ( ω ω 0 ) 2 +O[ ( ω ω 0 ) 3 ],
A μ z + β μ (1) A μ t +i β (2) 2 2 A μ t 2 + α 0 2 A μ =i k 0 2 n 0,μ 3 F (1) { [ ( 2 χ xxyy (3) + χ xyyx (3) ) | A μ | 2 +2 χ xxyy (3) σ=x,y ( 1 δ μ,σ ) | A σ | 2 ] A μ + χ xyyx (3) [ σ=x,y ( 1 δ μ,σ ) ( A σ ) 2 ] A μ * exp[ 2i( β 0,σ β 0,μ )z ] } +i k 0 2 n 0,μ 10 F (2) { [ 10 3 χ xxyyxx (5) | A μ | 4 + 5 3 χ xxyyyy (5) [ | A μ | 4 + σ=x,y ( 1 δ μ,σ ) | A σ | 4 ] ] A μ + 10 3 χ xxyyxx (5) [ σ=x,y ( 1 δ μ,σ ) | A μ | 2 ( A σ ) 2 ] A μ * exp[ 2i( β 0,σ β 0,μ )z ] },
A ± z + 1 2 [ β + (1) A ± t + β (1) A t ]+ i 2 β (2) 2 A ± t 2 + α 0 2 A ± = i 2 ( Δ β 0 ) A +i 3 ω 0 n 0 c F ( 1 ) [ χ xxyy (3) ( | A + | 2 + | A | 2 )+ χ xyyx (3) | A | 2 ] A ± +i 5 ω 0 2 n 0 c F ( 2 ) { 10 3 χ xxyyxx (5) [ | A + + A | 2 ( A + + A ) * | A + A | 2 ( A + A ) * ] A + 5 6 χ xxyyyy (5) [ | A + + A | 4 + | A + A | 4 ] } A ± ,
A ± z + i 2 β (2) 2 A ± τ 2 + α 0 2 A ± = i 2 ( Δ β 0 ) A +i ω 0 n 0 c F ( 1 ) χ xxxx (3) [ ( | A + | 2 + | A | 2 )+ | A | 2 ] A ± +i 5 ω 0 12 n 0 c F ( 2 ) χ xxxxxx (5) { 4[ | A + + A | 2 ( A + + A ) * | A + A | 2 ( A + A ) * ] A +[ | A + + A | 4 + | A + A | 4 ] } A ± ,
ε eff ( λ,f )= ε h ( λ )[ 1+ 3Θ( λ )f 1Θ( λ )f ],
ε h ( λ )= [ n C S 2 ( λ ) ] 2 = [ 1.580826+ 1.52389× 10 2 λ 2 + 4.8578× 10 4 λ 4 + 8.2863× 10 5 λ 6 + 1.4619× 10 5 λ 8 ] 2 .
ε NP ( λ )=( 1 λ 2 λ p 2 )+i( 1 2πc τ r λ 3 λ p 2 ),
β (1) ( λ,f )= 1 c [ n eff ( λ,f )λ d[ n eff ( λ,f ) ] dλ ],
β (2) ( λ,f )= λ 3 2π c 2 d 2 [ n eff ( λ,f ) ] d λ 2 .
A ± ( z,τ )=±iB( z,τ )exp( α 0 z 2 i Δ β 0 2 z )exp( τ 2 τ 0 2 ),
Λ( τ )= B 0 2 ω 0 c [ 3 F ( 1 ) Im( χ ( 3 ) )+20 B 0 2 F ( 2 ) Im( χ ( 5 ) )exp( 2 τ 2 τ 0 2 ) ]exp( 2 τ 2 τ 0 2 ),
Φ( τ )= 1 2 β ( 2 ) [ 2 τ 0 2 ( 1 2 τ 2 τ 0 2 ) ] + B 0 2 ω 0 c [ 3 F ( 1 ) Re( χ ( 3 ) )+20 B 0 2 F ( 2 ) Re( χ ( 5 ) )exp( 2 τ 2 τ 0 2 ) ]exp( 2 τ 2 τ 0 2 ).
a ± ( z,τ )=±i{ B 0 exp[ Λ( τ )z ]+ B 1,± ( z,τ ) }exp( α 0 z 2 i Δ β 0 2 z )exp[ iΦ( τ )z ]exp( τ 2 τ 0 2 ),
i{ B 1,± z +iΦ B 1,± i 2 ( Δ β 0 )( B 1,+ B 1, ) } 1 2 β (2) { 2 B 1,± τ 2 +2[ iz Φ τ 2τ τ 0 2 ] B 1,± τ +iz B 1,± [ 2 Φ τ 2 4τ τ 0 2 Φ τ +iz ( Φ τ ) 2 ]+ 2 τ 0 2 [ 2 τ 2 τ 0 2 1 ] B 1,± } = ω 0 c | B 0 | 2 F ( 1 ) χ xxxx (3) { 5 B 1,± +2[ B 1,+ + B 1, ] }exp( 2Λz α 0 z2 τ 2 τ 0 2 ) 5 ω 0 12c F ( 2 ) χ xxxxxx (5) { 16 | B 0 | 4 [ 3 B 1,± +2( B 1,+ + B 1, + B 1, ) ] +48 | B 0 | 2 B 0 2 [ B 1,+ + B 1, ] * }exp( 4Λz2 α 0 z4 τ 2 τ 0 2 ).
K 2 +[ 2 β (2) Ω( z Φ τ ) ]KM=0,
M=Re( N 2 )2 β (2) Ω[ z Φ τ Re( N ) 2τ τ 0 2 Im( N ) ] + [ 40 ω 0 c B 0 2 | B 0 | 2 F ( 2 ) exp( 4Λz2 α 0 z4 τ 2 τ 0 2 ) ] 2 Re[ ( χ xxxxxx 5 ) 2 ],
N=Φ+ 1 2 β (2) { Ω[ Ω+2i( iz Φ τ 2τ τ 0 2 ) ]+iz[ 2 Φ τ 2 4τ τ 0 2 Φ τ +iz ( Φ τ ) 2 ]+ 2 τ 0 2 [ 2 τ 2 τ 0 2 1 ] } 3 ω 0 c | B 0 | 2 exp( 2Λz α 0 z2 τ 2 τ 0 2 )[ 3 F ( 1 ) χ xxxx (3) +20 | B 0 | 2 F ( 2 ) χ xxxxxx (5) exp( 2Λz α 0 z2 τ 2 τ 0 2 ) ].

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