Abstract

We investigate the nonlinear propagation of surface plasmon polaritons guided on gold nanowires surrounded by silica glass. Based on the Lorentz reciprocity theorem, we derive a formula for the complex nonlinear susceptibility, and study its dependence on waveguide parameters and wavelength for the fundamental mode. Depending on these parameters both positive and negative signs of the real and imaginary parts of the nonlinear coefficient are predicted. This implies that nanowires exhibit the property of saturable absorption or optical limiting as well as positive and negative nonlinear phase shifts. The physical origin of this phenomenon is discussed.

© 2016 Optical Society of America

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    [Crossref]
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2015 (3)

A. Baron, T. B. Hoang, C. Fang, M. H. Mikkelsen, and D. R. Smith, “Ultrafast self-action of surface-plasmon polaritons at an air/metal interface,” Phys. Rev. B 91, 195412 (2015).
[Crossref]

S.-J. Im and G.-S. Ho, “Plasmonic amplification and suppression in nanowaveguide coupled to gain-assisted high- quality plasmon resonances,” Laser Phys. Lett. 12, 045902 (2015).
[Crossref]

D. Wu, Jian Peng, Z. Cai, J. Weng, Z. Luo, N. Chen, and H. Xu, “Gold nanoparticles as a saturable absorber for visible 635 nm Q-switched pulse generation,” Opt. Express 23, 24071–24076 (2015).
[Crossref] [PubMed]

2014 (5)

2013 (1)

A. Marini, M. Conforti, G. D. Valle, H. W. Lee, W. C. Tr, X. Tran, M. A. Schmidt, S. Longhi, P. S. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” New J. of Phys. 15, 013033 (2013).
[Crossref]

2012 (2)

2011 (2)

D. V. Skryabin, A. Gorbach, and A. Marini, “Surface-induced nonlinearity enhancement of TM modes in planar subwavelength waveguides,” J. Opt. Soc. Am. B 28, 109–114 (2011).
[Crossref]

A. Marini, R. Hartley, A. V. Gorbach, and D. V. Skryabin, “Surface-induced nonlinearity enhancement in sub-wavelength rod waveguides,” Phys. Rev. A 84, 063839 (2011).
[Crossref]

2010 (3)

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

C. Zheng, X. Y. Ye, S. G. Cai, M. J. Wang, and X. Q. Xiao, “Observation of nonlinear saturable and reverse-saturable absorption in silver nanowires and their silica gel glass composite,” Appl. Phys. B 101, 835–840 (2010).
[Crossref]

K.-H. Kim, A. Husakou, and J. Herrmann, “Saturable absorption in composites doped with metal nanoparticles,” Opt. Express 18, 21918–21925 (2010).
[Crossref] [PubMed]

2009 (2)

S. V. Afshar and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express 17, 2298–2318 (2009).
[Crossref]

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–239 (2009).
[Crossref]

2008 (2)

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear plasmonic slot waveguides,” Opt. Express 26, 21209–21214 (2008).
[Crossref]

U. Gurudas, E. Brooks, D. M. Bubb, S. Heiroth, T. Lippert, and A. Wokaun, “Saturable and reverse saturable absorption in silver nanodots at 532 nm using picosecond laser pulses,” J. Appl. Phys. 104, 073107 (2008).
[Crossref]

2006 (2)

E. Ozbay, “Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection, and fan-Out in silver nanowires,” Nano Letters 6, 1822–1826 (2006).
[Crossref] [PubMed]

2005 (1)

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[Crossref] [PubMed]

2004 (1)

R. A. Ganeev, I. A. Ryasnyanskiy, A. L. Stepanov, and T. Usmanov, “Saturated absorption and nonlinear refraction of silicate glasses doped with silver nanoparticles at 532 nm,” Opt. and Quantum Electr. 36, 949–960 (2004).
[Crossref]

2003 (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

D. Michaelis, U. Peschel, C. Walter, and A. Bräuer, “Reciprocity theorem and perturbation theory for photonic crystal waveguides,” Phys. Rev. E 68, 065601 (2003).
[Crossref]

2002 (1)

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–665 (2002).
[Crossref]

2000 (1)

R. M. Dickson and L. Andrew Lyon, “Unidirectional plasmon propagation in metallic nanowires,” J. Phys. Chem. B 104, 6095–6098 (2000).
[Crossref]

1997 (1)

1988 (1)

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. 47, 347–357 (1988).

1972 (1)

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

Afshar, S. V.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

Aussenegg, F. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[Crossref] [PubMed]

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–665 (2002).
[Crossref]

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Baron, A.

A. Baron, T. B. Hoang, C. Fang, M. H. Mikkelsen, and D. R. Smith, “Ultrafast self-action of surface-plasmon polaritons at an air/metal interface,” Phys. Rev. B 91, 195412 (2015).
[Crossref]

A. Baron, S. Larouche, D. J. Gauthier, and D. R. Smith, “Scaling of the nonlinear response of the surface plasmon polariton at a metal/dielectric interface,” J. Opt. Soc. Am. B 32, 9–14 (2014).
[Crossref]

Biancalana, F.

A. Marini, M. Conforti, G. D. Valle, H. W. Lee, W. C. Tr, X. Tran, M. A. Schmidt, S. Longhi, P. S. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” New J. of Phys. 15, 013033 (2013).
[Crossref]

Boyd, R. W.

Bräuer, A.

D. Michaelis, U. Peschel, C. Walter, and A. Bräuer, “Reciprocity theorem and perturbation theory for photonic crystal waveguides,” Phys. Rev. E 68, 065601 (2003).
[Crossref]

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

Brooks, E.

U. Gurudas, E. Brooks, D. M. Bubb, S. Heiroth, T. Lippert, and A. Wokaun, “Saturable and reverse saturable absorption in silver nanodots at 532 nm using picosecond laser pulses,” J. Appl. Phys. 104, 073107 (2008).
[Crossref]

Bubb, D. M.

U. Gurudas, E. Brooks, D. M. Bubb, S. Heiroth, T. Lippert, and A. Wokaun, “Saturable and reverse saturable absorption in silver nanodots at 532 nm using picosecond laser pulses,” J. Appl. Phys. 104, 073107 (2008).
[Crossref]

Cai, S. G.

C. Zheng, X. Y. Ye, S. G. Cai, M. J. Wang, and X. Q. Xiao, “Observation of nonlinear saturable and reverse-saturable absorption in silver nanowires and their silica gel glass composite,” Appl. Phys. B 101, 835–840 (2010).
[Crossref]

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

Cai, Z.

Chen, N.

Christy, R. W.

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

Conforti, M.

A. Marini, M. Conforti, G. D. Valle, H. W. Lee, W. C. Tr, X. Tran, M. A. Schmidt, S. Longhi, P. S. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” New J. of Phys. 15, 013033 (2013).
[Crossref]

Davoyan, A. R.

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear plasmonic slot waveguides,” Opt. Express 26, 21209–21214 (2008).
[Crossref]

De Leon, I.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Dickson, R. M.

R. M. Dickson and L. Andrew Lyon, “Unidirectional plasmon propagation in metallic nanowires,” J. Phys. Chem. B 104, 6095–6098 (2000).
[Crossref]

Ditlbacher, H.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[Crossref] [PubMed]

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–665 (2002).
[Crossref]

Dufresne, E. R.

A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection, and fan-Out in silver nanowires,” Nano Letters 6, 1822–1826 (2006).
[Crossref] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Fang, C.

A. Baron, T. B. Hoang, C. Fang, M. H. Mikkelsen, and D. R. Smith, “Ultrafast self-action of surface-plasmon polaritons at an air/metal interface,” Phys. Rev. B 91, 195412 (2015).
[Crossref]

Fischer, G.

Flytzanis, C.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. 47, 347–357 (1988).

Ganeev, R. A.

R. A. Ganeev, I. A. Ryasnyanskiy, A. L. Stepanov, and T. Usmanov, “Saturated absorption and nonlinear refraction of silicate glasses doped with silver nanoparticles at 532 nm,” Opt. and Quantum Electr. 36, 949–960 (2004).
[Crossref]

Gauthier, D. J.

Gorbach, A.

Gorbach, A. V.

A. Marini, R. Hartley, A. V. Gorbach, and D. V. Skryabin, “Surface-induced nonlinearity enhancement in sub-wavelength rod waveguides,” Phys. Rev. A 84, 063839 (2011).
[Crossref]

Gregory, D. A.

Griebner, U.

Gurudas, U.

U. Gurudas, E. Brooks, D. M. Bubb, S. Heiroth, T. Lippert, and A. Wokaun, “Saturable and reverse saturable absorption in silver nanodots at 532 nm using picosecond laser pulses,” J. Appl. Phys. 104, 073107 (2008).
[Crossref]

Hache, F.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. 47, 347–357 (1988).

Han, Y. P.

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–239 (2009).
[Crossref]

Hartley, R.

A. Marini, R. Hartley, A. V. Gorbach, and D. V. Skryabin, “Surface-induced nonlinearity enhancement in sub-wavelength rod waveguides,” Phys. Rev. A 84, 063839 (2011).
[Crossref]

Heiroth, S.

U. Gurudas, E. Brooks, D. M. Bubb, S. Heiroth, T. Lippert, and A. Wokaun, “Saturable and reverse saturable absorption in silver nanodots at 532 nm using picosecond laser pulses,” J. Appl. Phys. 104, 073107 (2008).
[Crossref]

Herrmann, J.

Ho, G.-S.

S.-J. Im and G.-S. Ho, “Plasmonic amplification and suppression in nanowaveguide coupled to gain-assisted high- quality plasmon resonances,” Laser Phys. Lett. 12, 045902 (2015).
[Crossref]

Hoang, T. B.

A. Baron, T. B. Hoang, C. Fang, M. H. Mikkelsen, and D. R. Smith, “Ultrafast self-action of surface-plasmon polaritons at an air/metal interface,” Phys. Rev. B 91, 195412 (2015).
[Crossref]

Hofer, F.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[Crossref] [PubMed]

Hohenau, A.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[Crossref] [PubMed]

Husakou, A.

Im, S.-J.

S.-J. Im and G.-S. Ho, “Plasmonic amplification and suppression in nanowaveguide coupled to gain-assisted high- quality plasmon resonances,” Laser Phys. Lett. 12, 045902 (2015).
[Crossref]

Johnson, P. B.

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

Jun, Y. C.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

Karthikeyan, B.

R. Udabyabhaskar, M. S. Ollakkan, and B. Karthikeyan, “Preparation, optical and non-linear optical power limiting properties of Cu, CuNi nanowires,” Appl. Phys. Lett. 104, 013107 (2014).
[Crossref]

Kauranen, M.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nature Photon. 6, 737–748 (2012)
[Crossref]

Kim, K.-H.

Kivshar, Y. S.

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear plasmonic slot waveguides,” Opt. Express 26, 21209–21214 (2008).
[Crossref]

Kivshar, Yuri S.

Kreibig, U.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[Crossref] [PubMed]

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. 47, 347–357 (1988).

Krenn, J. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[Crossref] [PubMed]

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–665 (2002).
[Crossref]

Kruk, S. S.

Lamprecht, B.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–665 (2002).
[Crossref]

Larouche, S.

Lee, H. W.

A. Marini, M. Conforti, G. D. Valle, H. W. Lee, W. C. Tr, X. Tran, M. A. Schmidt, S. Longhi, P. S. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” New J. of Phys. 15, 013033 (2013).
[Crossref]

Leitner, A.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–665 (2002).
[Crossref]

Liapis, A. C.

Lippert, T.

U. Gurudas, E. Brooks, D. M. Bubb, S. Heiroth, T. Lippert, and A. Wokaun, “Saturable and reverse saturable absorption in silver nanodots at 532 nm using picosecond laser pulses,” J. Appl. Phys. 104, 073107 (2008).
[Crossref]

Longhi, S.

A. Marini, M. Conforti, G. D. Valle, H. W. Lee, W. C. Tr, X. Tran, M. A. Schmidt, S. Longhi, P. S. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” New J. of Phys. 15, 013033 (2013).
[Crossref]

Love, J. D.

A.W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Luo, Z.

Lyon, L. Andrew

R. M. Dickson and L. Andrew Lyon, “Unidirectional plasmon propagation in metallic nanowires,” J. Phys. Chem. B 104, 6095–6098 (2000).
[Crossref]

Marini, A.

A. Marini, M. Conforti, G. D. Valle, H. W. Lee, W. C. Tr, X. Tran, M. A. Schmidt, S. Longhi, P. S. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” New J. of Phys. 15, 013033 (2013).
[Crossref]

D. V. Skryabin, A. Gorbach, and A. Marini, “Surface-induced nonlinearity enhancement of TM modes in planar subwavelength waveguides,” J. Opt. Soc. Am. B 28, 109–114 (2011).
[Crossref]

A. Marini, R. Hartley, A. V. Gorbach, and D. V. Skryabin, “Surface-induced nonlinearity enhancement in sub-wavelength rod waveguides,” Phys. Rev. A 84, 063839 (2011).
[Crossref]

Michaelis, D.

D. Michaelis, U. Peschel, C. Walter, and A. Bräuer, “Reciprocity theorem and perturbation theory for photonic crystal waveguides,” Phys. Rev. E 68, 065601 (2003).
[Crossref]

Mikkelsen, M. H.

A. Baron, T. B. Hoang, C. Fang, M. H. Mikkelsen, and D. R. Smith, “Ultrafast self-action of surface-plasmon polaritons at an air/metal interface,” Phys. Rev. B 91, 195412 (2015).
[Crossref]

Monro, T. M.

Neshev, D. N.

Ollakkan, M. S.

R. Udabyabhaskar, M. S. Ollakkan, and B. Karthikeyan, “Preparation, optical and non-linear optical power limiting properties of Cu, CuNi nanowires,” Appl. Phys. Lett. 104, 013107 (2014).
[Crossref]

Ozbay, E.

E. Ozbay, “Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

Peng, Jian

Peschel, U.

D. Michaelis, U. Peschel, C. Walter, and A. Bräuer, “Reciprocity theorem and perturbation theory for photonic crystal waveguides,” Phys. Rev. E 68, 065601 (2003).
[Crossref]

Reed, M. A.

A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection, and fan-Out in silver nanowires,” Nano Letters 6, 1822–1826 (2006).
[Crossref] [PubMed]

Ricard, D.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. 47, 347–357 (1988).

Rogers, M.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[Crossref] [PubMed]

Routenberg, D. A.

A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection, and fan-Out in silver nanowires,” Nano Letters 6, 1822–1826 (2006).
[Crossref] [PubMed]

Russell, P. S. J.

A. Marini, M. Conforti, G. D. Valle, H. W. Lee, W. C. Tr, X. Tran, M. A. Schmidt, S. Longhi, P. S. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” New J. of Phys. 15, 013033 (2013).
[Crossref]

Ryasnyanskiy, I. A.

R. A. Ganeev, I. A. Ryasnyanskiy, A. L. Stepanov, and T. Usmanov, “Saturated absorption and nonlinear refraction of silicate glasses doped with silver nanoparticles at 532 nm,” Opt. and Quantum Electr. 36, 949–960 (2004).
[Crossref]

Salerno, M.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–665 (2002).
[Crossref]

Sanders, A. W.

A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection, and fan-Out in silver nanowires,” Nano Letters 6, 1822–1826 (2006).
[Crossref] [PubMed]

Schider, G.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–665 (2002).
[Crossref]

Schmidt, M. A.

A. Marini, M. Conforti, G. D. Valle, H. W. Lee, W. C. Tr, X. Tran, M. A. Schmidt, S. Longhi, P. S. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” New J. of Phys. 15, 013033 (2013).
[Crossref]

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

Shadrivov, I. V.

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear plasmonic slot waveguides,” Opt. Express 26, 21209–21214 (2008).
[Crossref]

Shi, G.

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–239 (2009).
[Crossref]

Shi, Z.

Sipe, J. E.

I. De Leon, J. E. Sipe, and R. W. Boyd, “Self-phase-modulation of surface plasmon polaritons,” Phys. Rev. A 89, 013855 (2014).
[Crossref]

Skryabin, D. V.

A. Marini, R. Hartley, A. V. Gorbach, and D. V. Skryabin, “Surface-induced nonlinearity enhancement in sub-wavelength rod waveguides,” Phys. Rev. A 84, 063839 (2011).
[Crossref]

D. V. Skryabin, A. Gorbach, and A. Marini, “Surface-induced nonlinearity enhancement of TM modes in planar subwavelength waveguides,” J. Opt. Soc. Am. B 28, 109–114 (2011).
[Crossref]

Smith, D. D.

Smith, D. R.

A. Baron, T. B. Hoang, C. Fang, M. H. Mikkelsen, and D. R. Smith, “Ultrafast self-action of surface-plasmon polaritons at an air/metal interface,” Phys. Rev. B 91, 195412 (2015).
[Crossref]

A. Baron, S. Larouche, D. J. Gauthier, and D. R. Smith, “Scaling of the nonlinear response of the surface plasmon polariton at a metal/dielectric interface,” J. Opt. Soc. Am. B 32, 9–14 (2014).
[Crossref]

Snyder, A.W.

A.W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Solntsev, A. S.

Stepanov, A. L.

R. A. Ganeev, I. A. Ryasnyanskiy, A. L. Stepanov, and T. Usmanov, “Saturated absorption and nonlinear refraction of silicate glasses doped with silver nanoparticles at 532 nm,” Opt. and Quantum Electr. 36, 949–960 (2004).
[Crossref]

Sukhorukov, A. A.

Sun, J. L.

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–239 (2009).
[Crossref]

Tr, W. C.

A. Marini, M. Conforti, G. D. Valle, H. W. Lee, W. C. Tr, X. Tran, M. A. Schmidt, S. Longhi, P. S. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” New J. of Phys. 15, 013033 (2013).
[Crossref]

Tran, X.

A. Marini, M. Conforti, G. D. Valle, H. W. Lee, W. C. Tr, X. Tran, M. A. Schmidt, S. Longhi, P. S. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” New J. of Phys. 15, 013033 (2013).
[Crossref]

Udabyabhaskar, R.

R. Udabyabhaskar, M. S. Ollakkan, and B. Karthikeyan, “Preparation, optical and non-linear optical power limiting properties of Cu, CuNi nanowires,” Appl. Phys. Lett. 104, 013107 (2014).
[Crossref]

Usmanov, T.

R. A. Ganeev, I. A. Ryasnyanskiy, A. L. Stepanov, and T. Usmanov, “Saturated absorption and nonlinear refraction of silicate glasses doped with silver nanoparticles at 532 nm,” Opt. and Quantum Electr. 36, 949–960 (2004).
[Crossref]

Valle, G. D.

A. Marini, M. Conforti, G. D. Valle, H. W. Lee, W. C. Tr, X. Tran, M. A. Schmidt, S. Longhi, P. S. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” New J. of Phys. 15, 013033 (2013).
[Crossref]

Wagner, D.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[Crossref] [PubMed]

Walter, C.

D. Michaelis, U. Peschel, C. Walter, and A. Bräuer, “Reciprocity theorem and perturbation theory for photonic crystal waveguides,” Phys. Rev. E 68, 065601 (2003).
[Crossref]

Wang, M. J.

C. Zheng, X. Y. Ye, S. G. Cai, M. J. Wang, and X. Q. Xiao, “Observation of nonlinear saturable and reverse-saturable absorption in silver nanowires and their silica gel glass composite,” Appl. Phys. B 101, 835–840 (2010).
[Crossref]

Weng, J.

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

Wiley, B. J.

A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection, and fan-Out in silver nanowires,” Nano Letters 6, 1822–1826 (2006).
[Crossref] [PubMed]

Wokaun, A.

U. Gurudas, E. Brooks, D. M. Bubb, S. Heiroth, T. Lippert, and A. Wokaun, “Saturable and reverse saturable absorption in silver nanodots at 532 nm using picosecond laser pulses,” J. Appl. Phys. 104, 073107 (2008).
[Crossref]

Wu, D.

Wu, W. Z.

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–239 (2009).
[Crossref]

Xia, Y.

A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection, and fan-Out in silver nanowires,” Nano Letters 6, 1822–1826 (2006).
[Crossref] [PubMed]

Xiao, X. Q.

C. Zheng, X. Y. Ye, S. G. Cai, M. J. Wang, and X. Q. Xiao, “Observation of nonlinear saturable and reverse-saturable absorption in silver nanowires and their silica gel glass composite,” Appl. Phys. B 101, 835–840 (2010).
[Crossref]

Xu, H.

Ye, H. A.

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–239 (2009).
[Crossref]

Ye, X. Y.

C. Zheng, X. Y. Ye, S. G. Cai, M. J. Wang, and X. Q. Xiao, “Observation of nonlinear saturable and reverse-saturable absorption in silver nanowires and their silica gel glass composite,” Appl. Phys. B 101, 835–840 (2010).
[Crossref]

Zayats, A. V.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nature Photon. 6, 737–748 (2012)
[Crossref]

Zheng, C.

C. Zheng, X. Y. Ye, S. G. Cai, M. J. Wang, and X. Q. Xiao, “Observation of nonlinear saturable and reverse-saturable absorption in silver nanowires and their silica gel glass composite,” Appl. Phys. B 101, 835–840 (2010).
[Crossref]

Appl. Phys. (1)

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. 47, 347–357 (1988).

Appl. Phys. B (2)

C. Zheng, X. Y. Ye, S. G. Cai, M. J. Wang, and X. Q. Xiao, “Observation of nonlinear saturable and reverse-saturable absorption in silver nanowires and their silica gel glass composite,” Appl. Phys. B 101, 835–840 (2010).
[Crossref]

Y. P. Han, J. L. Sun, H. A. Ye, W. Z. Wu, and G. Shi, “Nonlinear refraction of silver nanowires from nanosecond to femtosecond laser excitation,” Appl. Phys. B 94, 233–239 (2009).
[Crossref]

Appl. Phys. Lett. (1)

R. Udabyabhaskar, M. S. Ollakkan, and B. Karthikeyan, “Preparation, optical and non-linear optical power limiting properties of Cu, CuNi nanowires,” Appl. Phys. Lett. 104, 013107 (2014).
[Crossref]

Europhys. Lett. (1)

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–665 (2002).
[Crossref]

J. Appl. Phys. (1)

U. Gurudas, E. Brooks, D. M. Bubb, S. Heiroth, T. Lippert, and A. Wokaun, “Saturable and reverse saturable absorption in silver nanodots at 532 nm using picosecond laser pulses,” J. Appl. Phys. 104, 073107 (2008).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Phys. Chem. B (1)

R. M. Dickson and L. Andrew Lyon, “Unidirectional plasmon propagation in metallic nanowires,” J. Phys. Chem. B 104, 6095–6098 (2000).
[Crossref]

Laser Phys. Lett. (1)

S.-J. Im and G.-S. Ho, “Plasmonic amplification and suppression in nanowaveguide coupled to gain-assisted high- quality plasmon resonances,” Laser Phys. Lett. 12, 045902 (2015).
[Crossref]

Nano Letters (1)

A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection, and fan-Out in silver nanowires,” Nano Letters 6, 1822–1826 (2006).
[Crossref] [PubMed]

Nat. Mater. (1)

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010).
[Crossref] [PubMed]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Nature Photon. (1)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nature Photon. 6, 737–748 (2012)
[Crossref]

New J. of Phys. (1)

A. Marini, M. Conforti, G. D. Valle, H. W. Lee, W. C. Tr, X. Tran, M. A. Schmidt, S. Longhi, P. S. J. Russell, and F. Biancalana, “Ultrafast nonlinear dynamics of surface plasmon polaritons in gold nanowires due to the intrinsic nonlinearity of metals,” New J. of Phys. 15, 013033 (2013).
[Crossref]

Opt. and Quantum Electr. (1)

R. A. Ganeev, I. A. Ryasnyanskiy, A. L. Stepanov, and T. Usmanov, “Saturated absorption and nonlinear refraction of silicate glasses doped with silver nanoparticles at 532 nm,” Opt. and Quantum Electr. 36, 949–960 (2004).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. A (2)

I. De Leon, J. E. Sipe, and R. W. Boyd, “Self-phase-modulation of surface plasmon polaritons,” Phys. Rev. A 89, 013855 (2014).
[Crossref]

A. Marini, R. Hartley, A. V. Gorbach, and D. V. Skryabin, “Surface-induced nonlinearity enhancement in sub-wavelength rod waveguides,” Phys. Rev. A 84, 063839 (2011).
[Crossref]

Phys. Rev. B (2)

A. Baron, T. B. Hoang, C. Fang, M. H. Mikkelsen, and D. R. Smith, “Ultrafast self-action of surface-plasmon polaritons at an air/metal interface,” Phys. Rev. B 91, 195412 (2015).
[Crossref]

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

Phys. Rev. E (1)

D. Michaelis, U. Peschel, C. Walter, and A. Bräuer, “Reciprocity theorem and perturbation theory for photonic crystal waveguides,” Phys. Rev. E 68, 065601 (2003).
[Crossref]

Phys. Rev. Lett. (1)

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[Crossref] [PubMed]

Science (1)

E. Ozbay, “Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

Other (3)

A.W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

R. W. Boyd, Nonlinear Optics, 3rd ed (Academic, 2008).

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

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Figures (7)

Fig. 1
Fig. 1

Response of effective refractive index in a single gold-air interface to a perturbation of the permittivity in gold δε1 = 0.01, δε2 = 0. The solid curve, blue circles and red crosses represent the results by Eq. (5), the analytical formula Eq. (6), and of Eq. (7), respectively.

Fig. 2
Fig. 2

Power-dependence of the nonlinear phase shift for the wavelength of 535 nm and a propagation distance of 1000 nm (a) and nonlinear absorption for the wavelength of 502 nm and a propagation distance of 500 nm (b) for a single gold-air interface. The black line is the results obtained by Eq. (5), the red crosses by Eq. (7) and the blue circles correspond to a full-dimensional simulation.

Fig. 3
Fig. 3

Effective nonlinear coefficient of a gold nanowires with a wire radii 200 nm (a) and 50 nm (b) surrounded by silica glass for the fundamental TM mode (m=0). The red solid and blue dashed line shows the real and imaginary part of the effective nonlinear coefficient, respectively.

Fig. 4
Fig. 4

Real part of effective nonlinear coefficient of gold nanowires surrounded by silica glass for the fundamental TM mode (m=0) at the wavelength of 720 nm versus the wire radius. The third-order nonlinear susceptibility of gold χ gold ( 3 ) = ( 2 + i 15 ) × 10 17 m 2 / V 2 from [11] is used.

Fig. 5
Fig. 5

Imaginary part of effective nonlinear coefficient of gold nanowires surrounded by silica glass for the fundamental TM mode (m=0) at the wavelength of 630 nm versus the wire radius. The third-order nonlinear susceptibility of gold χ gold ( 3 ) = ( 20 i 5 ) × 10 17 m 2 / V 2 from [11] is used.

Fig. 6
Fig. 6

SPP propagation length Lspp (a) and figure of merit F = |γ| Lspp (b) of gold nanowires with wire radii 30nm (black solid), 50 nm (red dashed) and 200 nm (blue crosses) surrounded by silica glass for the fundamental TM mode (m=0).

Fig. 7
Fig. 7

Additional phase ϕ and field enhancement |E|4/|E04 due to metal loss versus r in the gold nanowire with different radii R = 30, 50, 80 nm. The wavelength is 630 nm and χ gold ( 3 ) = ( 20 i 5 ) × 10 17 m 2 / V 2 from [11] is used.

Equations (9)

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

E ( r ) = 1 / s 0 Ψ ( z ) exp ( i κ z ) e 0 ( r ) ,
H ( r ) = ( i ω μ 0 ) 1 × E = 1 / s 0 Ψ ( z ) exp ( i κ z ) h 0 ( r ) .
z [ E 1 ( r ) × H 2 ( r ) E 2 ( r ) × H 1 ( r ) ] z ^ d σ = i k 0 Z 0 [ ε 2 ( r ) ε 1 ( r ) ] E 1 ( r ) E 2 ( r ) d σ .
d Ψ d z = α 2 Ψ + i k 0 δ n eff Ψ ,
δ n eff = δ ε ( e 0 2 2 e 0 z 2 ) d σ 2 Z 0 ( e 0 × h 0 ) z ^ d σ .
δ n eff = ( ε 1 + δ ε 1 ) ( ε 2 + δ ε 2 ) ( ε 1 + δ ε 1 ) + ( ε 2 + δ ε 2 ) ε 1 ε 2 ε 1 + ε 2 .
δ n eff = δ ε | e 0 | 2 d σ 2 Z 0 Re ( e 0 × h 0 * ) z ^ d σ ,
d Ψ d z = α 2 Ψ + i γ | Ψ | 2 Ψ ,
γ = k 0 ( 3 / 4 ) χ ( 3 ) | e 0 | 2 ( e 0 2 2 e 0 z 2 ) d σ Z 0 ( e 0 × h 0 ) z ^ d σ Re ( e 0 × h 0 ) z ^ d σ ,

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