Abstract

We study the propagation of nonlinear waves in layered nonlinear dielectric/linear dielectric/metal planar structures. We develop vector models that describe the light propagation in such configurations and allow us to obtain both one- and two-dimensional solutions. We compute the nonlinear dispersion relation and the field profiles, and estimate losses. We use our models to design realistic structures, in terms of linear and nonlinear properties, which support soliton waves with a plasmon tail at low peak power around or below 1GW/cm2. These results open the way for potential observation of such states in chalcogenide waveguides associated with silica and metal films. In the proposed structures, the nonlinearity confines the field in both transverse directions. A recordable plasmonic part of the field extends in air.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  2. Y. S. Kivshar and G. P. Agrawal, Optical Solitons, From Fibers to Photonic Crystals (Academic, 2003).
  3. F. Drouart, G. Renversez, A. Nicolet, and C. Geuzaine, J. Opt. A: Pure Appl. Opt. 10, 125101 (2008).
    [CrossRef]
  4. E. Feigenbaum and M. Orenstein, Opt. Lett. 32, 674(2007).
    [CrossRef]
  5. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 17, 21732 (2009).
    [CrossRef]
  6. K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 41803 (2009).
    [CrossRef]
  7. V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, JETP Lett. 32, 512 (1980).
  8. W. J. Tomlinson, Opt. Lett. 5, 323 (1980).
    [CrossRef]
  9. J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, J. Appl. Phys. 58, 2460 (1985).
    [CrossRef]
  10. N. N. Akhmediev, Sov. Phys. JETP 56, 299 (1982).
  11. A. A. Maradudin, in Optical and Acoustics Waves in Solids—Modern Topics, M. Borissov, ed. (World Scientific, 1983), pp. 72–142.
  12. G. Boudebs, F. Sanchez, J. Troles, and F. Smektala, Opt. Commun. 199, 425 (2001).
    [CrossRef]
  13. V. Nazabal, F. Charpentier, J.-L. Adam, P. Nemec, H. Lhermite, M.-L. Brandily-Anne, J. Charrier, J.-P. Guin, and A. Moreac, Int. J. Appl. Ceram. Technol. 8, 990 (2011).
    [CrossRef]
  14. M. Chauvet, G. Fanjoux, K. P. Huy, V. Nazabal, F. Charpentier, T. Billeton, G. Boudebs, M. Cathelinaud, and S.-P. Gorza, Opt. Lett. 34, 1804 (2009).
    [CrossRef]
  15. R. A. Sammut, C. Pask, and Q. Y. Li, J. Opt. Soc. Am. B 10, 485 (1993).
    [CrossRef]

2011 (1)

V. Nazabal, F. Charpentier, J.-L. Adam, P. Nemec, H. Lhermite, M.-L. Brandily-Anne, J. Charrier, J.-P. Guin, and A. Moreac, Int. J. Appl. Ceram. Technol. 8, 990 (2011).
[CrossRef]

2009 (3)

2008 (1)

F. Drouart, G. Renversez, A. Nicolet, and C. Geuzaine, J. Opt. A: Pure Appl. Opt. 10, 125101 (2008).
[CrossRef]

2007 (1)

2001 (1)

G. Boudebs, F. Sanchez, J. Troles, and F. Smektala, Opt. Commun. 199, 425 (2001).
[CrossRef]

1993 (1)

1985 (1)

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, J. Appl. Phys. 58, 2460 (1985).
[CrossRef]

1982 (1)

N. N. Akhmediev, Sov. Phys. JETP 56, 299 (1982).

1980 (2)

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, JETP Lett. 32, 512 (1980).

W. J. Tomlinson, Opt. Lett. 5, 323 (1980).
[CrossRef]

Adam, J.-L.

V. Nazabal, F. Charpentier, J.-L. Adam, P. Nemec, H. Lhermite, M.-L. Brandily-Anne, J. Charrier, J.-P. Guin, and A. Moreac, Int. J. Appl. Ceram. Technol. 8, 990 (2011).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, JETP Lett. 32, 512 (1980).

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons, From Fibers to Photonic Crystals (Academic, 2003).

Akhmediev, N. N.

N. N. Akhmediev, Sov. Phys. JETP 56, 299 (1982).

Ariyasu, J.

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, J. Appl. Phys. 58, 2460 (1985).
[CrossRef]

Babichenko, V. S.

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, JETP Lett. 32, 512 (1980).

Billeton, T.

Bliokh, K. Y.

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 41803 (2009).
[CrossRef]

Bliokh, Y. P.

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 41803 (2009).
[CrossRef]

Boudebs, G.

Brandily-Anne, M.-L.

V. Nazabal, F. Charpentier, J.-L. Adam, P. Nemec, H. Lhermite, M.-L. Brandily-Anne, J. Charrier, J.-P. Guin, and A. Moreac, Int. J. Appl. Ceram. Technol. 8, 990 (2011).
[CrossRef]

Cathelinaud, M.

Charpentier, F.

V. Nazabal, F. Charpentier, J.-L. Adam, P. Nemec, H. Lhermite, M.-L. Brandily-Anne, J. Charrier, J.-P. Guin, and A. Moreac, Int. J. Appl. Ceram. Technol. 8, 990 (2011).
[CrossRef]

M. Chauvet, G. Fanjoux, K. P. Huy, V. Nazabal, F. Charpentier, T. Billeton, G. Boudebs, M. Cathelinaud, and S.-P. Gorza, Opt. Lett. 34, 1804 (2009).
[CrossRef]

Charrier, J.

V. Nazabal, F. Charpentier, J.-L. Adam, P. Nemec, H. Lhermite, M.-L. Brandily-Anne, J. Charrier, J.-P. Guin, and A. Moreac, Int. J. Appl. Ceram. Technol. 8, 990 (2011).
[CrossRef]

Chauvet, M.

Chernyak, V. Y.

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, JETP Lett. 32, 512 (1980).

Davoyan, A. R.

Drouart, F.

F. Drouart, G. Renversez, A. Nicolet, and C. Geuzaine, J. Opt. A: Pure Appl. Opt. 10, 125101 (2008).
[CrossRef]

Fanjoux, G.

Feigenbaum, E.

Ferrando, A.

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 41803 (2009).
[CrossRef]

Geuzaine, C.

F. Drouart, G. Renversez, A. Nicolet, and C. Geuzaine, J. Opt. A: Pure Appl. Opt. 10, 125101 (2008).
[CrossRef]

Gorza, S.-P.

Guin, J.-P.

V. Nazabal, F. Charpentier, J.-L. Adam, P. Nemec, H. Lhermite, M.-L. Brandily-Anne, J. Charrier, J.-P. Guin, and A. Moreac, Int. J. Appl. Ceram. Technol. 8, 990 (2011).
[CrossRef]

Huy, K. P.

Kivshar, Y. S.

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 17, 21732 (2009).
[CrossRef]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons, From Fibers to Photonic Crystals (Academic, 2003).

Lhermite, H.

V. Nazabal, F. Charpentier, J.-L. Adam, P. Nemec, H. Lhermite, M.-L. Brandily-Anne, J. Charrier, J.-P. Guin, and A. Moreac, Int. J. Appl. Ceram. Technol. 8, 990 (2011).
[CrossRef]

Li, Q. Y.

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Maradudin, A. A.

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, J. Appl. Phys. 58, 2460 (1985).
[CrossRef]

A. A. Maradudin, in Optical and Acoustics Waves in Solids—Modern Topics, M. Borissov, ed. (World Scientific, 1983), pp. 72–142.

Moreac, A.

V. Nazabal, F. Charpentier, J.-L. Adam, P. Nemec, H. Lhermite, M.-L. Brandily-Anne, J. Charrier, J.-P. Guin, and A. Moreac, Int. J. Appl. Ceram. Technol. 8, 990 (2011).
[CrossRef]

Nazabal, V.

V. Nazabal, F. Charpentier, J.-L. Adam, P. Nemec, H. Lhermite, M.-L. Brandily-Anne, J. Charrier, J.-P. Guin, and A. Moreac, Int. J. Appl. Ceram. Technol. 8, 990 (2011).
[CrossRef]

M. Chauvet, G. Fanjoux, K. P. Huy, V. Nazabal, F. Charpentier, T. Billeton, G. Boudebs, M. Cathelinaud, and S.-P. Gorza, Opt. Lett. 34, 1804 (2009).
[CrossRef]

Nemec, P.

V. Nazabal, F. Charpentier, J.-L. Adam, P. Nemec, H. Lhermite, M.-L. Brandily-Anne, J. Charrier, J.-P. Guin, and A. Moreac, Int. J. Appl. Ceram. Technol. 8, 990 (2011).
[CrossRef]

Nicolet, A.

F. Drouart, G. Renversez, A. Nicolet, and C. Geuzaine, J. Opt. A: Pure Appl. Opt. 10, 125101 (2008).
[CrossRef]

Orenstein, M.

Pask, C.

Renversez, G.

F. Drouart, G. Renversez, A. Nicolet, and C. Geuzaine, J. Opt. A: Pure Appl. Opt. 10, 125101 (2008).
[CrossRef]

Sammut, R. A.

Sanchez, F.

G. Boudebs, F. Sanchez, J. Troles, and F. Smektala, Opt. Commun. 199, 425 (2001).
[CrossRef]

Seaton, C. T.

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, J. Appl. Phys. 58, 2460 (1985).
[CrossRef]

Shadrivov, I. V.

Smektala, F.

G. Boudebs, F. Sanchez, J. Troles, and F. Smektala, Opt. Commun. 199, 425 (2001).
[CrossRef]

Stegeman, G. I.

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, J. Appl. Phys. 58, 2460 (1985).
[CrossRef]

Tomlinson, W. J.

Troles, J.

G. Boudebs, F. Sanchez, J. Troles, and F. Smektala, Opt. Commun. 199, 425 (2001).
[CrossRef]

Wallis, R. F.

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, J. Appl. Phys. 58, 2460 (1985).
[CrossRef]

Int. J. Appl. Ceram. Technol. (1)

V. Nazabal, F. Charpentier, J.-L. Adam, P. Nemec, H. Lhermite, M.-L. Brandily-Anne, J. Charrier, J.-P. Guin, and A. Moreac, Int. J. Appl. Ceram. Technol. 8, 990 (2011).
[CrossRef]

J. Appl. Phys. (1)

J. Ariyasu, C. T. Seaton, G. I. Stegeman, A. A. Maradudin, and R. F. Wallis, J. Appl. Phys. 58, 2460 (1985).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

F. Drouart, G. Renversez, A. Nicolet, and C. Geuzaine, J. Opt. A: Pure Appl. Opt. 10, 125101 (2008).
[CrossRef]

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

JETP Lett. (1)

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, JETP Lett. 32, 512 (1980).

Opt. Commun. (1)

G. Boudebs, F. Sanchez, J. Troles, and F. Smektala, Opt. Commun. 199, 425 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (1)

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 41803 (2009).
[CrossRef]

Sov. Phys. JETP (1)

N. N. Akhmediev, Sov. Phys. JETP 56, 299 (1982).

Other (3)

A. A. Maradudin, in Optical and Acoustics Waves in Solids—Modern Topics, M. Borissov, ed. (World Scientific, 1983), pp. 72–142.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons, From Fibers to Photonic Crystals (Academic, 2003).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Geometry of the four-layer nonlinear model used to study three-layer structures. ϵj denotes the linear permittivity of the jth layer (j{1,2,3,4}).

Fig. 2.
Fig. 2.

Dispersion curves obtained from the 1D model (dashed line) and from the 2D model (solid line). Parameters used are ϵ1=2.47072, n2=1013cm2/W (chalcogenide glass), ϵ2=1.4432 (silica), ϵ3=96 (gold), ϵ4=1 (air), L=15nm, d=40nm, λ=1.55μm.

Fig. 3.
Fig. 3.

Intensity profiles for low-power solutions of 1D problem. (a) Full solution and (b) zoom on the plasmon part at the metal interfaces. Material and geometric parameters are the same as in Fig. 2, x0=30μm.

Fig. 4.
Fig. 4.

2D intensity profile for the low-power plasmon–soliton in the four-layer planar nonlinear configuration. (a) Full solution and (b) zoom of the plasmon part at the metal/air interface. Parameters same as in Fig. 3.

Equations (8)

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

E(x,z,t)=ENL(x)exp[i(βNLk0zωt)],
d2ENL,xdx2k02q2(x)ENL,x+k02a(x)ENL,x3=0,
Φ+(q˜4+q˜3)exp(2k0q˜3ϵ3d)+Φ(q˜4q˜3)=0,
Φ±=(1±q˜1NLq˜3)+(q˜1NLq˜2±q˜2q˜4)tanh(k0q˜2ϵ2L),
E(x,y,z,t)=ENL(x)ψ(y,z)exp[i(βNLk0zωt)].
[F(βNL+Δβ)2G+1k02d2·dy2+A|ψ|2]ψ=0,
G=ϵ(x)ENL,x2,F=1k02d2ENL,xdx2ENL,x,A=3α(x)ϵ(x)k02ENL,x[ENL,xd2ENL,xdx2+2(dENL,xdx)2]+α(x)ENL,x4,and=+dx/+ENL,x2dx.
β=βNL+Δβ=[G+F+(k0ωy)2]1/2.

Metrics