Abstract

We demonstrate that soliplasmons (soliton–plasmon bound states) appear naturally as eigenmodes of nonlinear Maxwell’s equations for a metal/Kerr interface. Conservative stability analysis is performed by means of finite element numerical modeling of the time-independent nonlinear Maxwell equations. Dynamical features are in agreement with the presented nonlinear oscillator model.

© 2012 Optical Society of America

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  1. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 17, 21732 (2009).
    [CrossRef]
  2. E. Feigenbaum and M. Orenstein, Opt. Lett. 32, 674 (2007).
    [CrossRef]
  3. A. Marini, D. V. Skryabin, and B. Malomed, Opt. Express 19, 6616 (2011).
    [CrossRef]
  4. A. Marini and D. V. Skryabin, Phys. Rev. A 81, 033850 (2010).
    [CrossRef]
  5. F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
    [CrossRef]
  6. J. R. Salgueiro and Y. S. Kivshar, Appl. Phys. Lett. 97, 081106 (2010).
    [CrossRef]
  7. C. Milián and D. V. Skryabin, Appl. Phys. Lett. 98, 111104 (2011).
    [CrossRef]
  8. R. E. Noskov, P. A. Belov, and Y. S. Kivshar, Phys. Rev. Lett. 108, 093901 (2012).
    [CrossRef]
  9. D. V. Skryabin, A. V. Gorbach, and A. Marini, J. Opt. Soc. Am. B 28, 109 (2011).
    [CrossRef]
  10. K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 041803 (2009).
    [CrossRef]
  11. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
    [CrossRef]
  12. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  13. Y. S. Kivshar and G. P. Agrawal, Optical Solitons. From Fibers to Photonic Crystals (Academic, 2003).
  14. Y. Ekşioğlu, O. E. Müstecaplioğlu, and K. Güven, Phys. Rev. A 84, 033805 (2011).
    [CrossRef]
  15. V. M. Agranovich, V. S. Babichenko, and V. Ya. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1981).
  16. W. J. Tomlinson, Opt. Lett. 5, 323 (1980).
    [CrossRef]
  17. Details on this derivation will be reported elsewhere.

2012 (1)

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, Phys. Rev. Lett. 108, 093901 (2012).
[CrossRef]

2011 (4)

Y. Ekşioğlu, O. E. Müstecaplioğlu, and K. Güven, Phys. Rev. A 84, 033805 (2011).
[CrossRef]

C. Milián and D. V. Skryabin, Appl. Phys. Lett. 98, 111104 (2011).
[CrossRef]

D. V. Skryabin, A. V. Gorbach, and A. Marini, J. Opt. Soc. Am. B 28, 109 (2011).
[CrossRef]

A. Marini, D. V. Skryabin, and B. Malomed, Opt. Express 19, 6616 (2011).
[CrossRef]

2010 (3)

A. Marini and D. V. Skryabin, Phys. Rev. A 81, 033850 (2010).
[CrossRef]

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef]

J. R. Salgueiro and Y. S. Kivshar, Appl. Phys. Lett. 97, 081106 (2010).
[CrossRef]

2009 (2)

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 041803 (2009).
[CrossRef]

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

2007 (1)

2005 (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

1981 (1)

V. M. Agranovich, V. S. Babichenko, and V. Ya. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1981).

1980 (1)

Agranovich, V. M.

V. M. Agranovich, V. S. Babichenko, and V. Ya. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1981).

Agrawal, G. P.

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

Babichenko, V. S.

V. M. Agranovich, V. S. Babichenko, and V. Ya. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1981).

Belov, P. A.

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, Phys. Rev. Lett. 108, 093901 (2012).
[CrossRef]

Bliokh, K. Y.

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 041803 (2009).
[CrossRef]

Bliokh, Y. P.

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 041803 (2009).
[CrossRef]

Chernyak, V. Ya.

V. M. Agranovich, V. S. Babichenko, and V. Ya. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1981).

Davoyan, A. R.

Eksioglu, Y.

Y. Ekşioğlu, O. E. Müstecaplioğlu, and K. Güven, Phys. Rev. A 84, 033805 (2011).
[CrossRef]

Feigenbaum, E.

Ferrando, A.

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 041803 (2009).
[CrossRef]

Gorbach, A. V.

Güven, K.

Y. Ekşioğlu, O. E. Müstecaplioğlu, and K. Güven, Phys. Rev. A 84, 033805 (2011).
[CrossRef]

Hu, B.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef]

Kivshar, Y. S.

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, Phys. Rev. Lett. 108, 093901 (2012).
[CrossRef]

J. R. Salgueiro and Y. S. Kivshar, Appl. Phys. Lett. 97, 081106 (2010).
[CrossRef]

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).

Maier, S. A.

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

Malomed, B.

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

Marini, A.

Mihalache, D.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef]

Milián, C.

C. Milián and D. V. Skryabin, Appl. Phys. Lett. 98, 111104 (2011).
[CrossRef]

Müstecaplioglu, O. E.

Y. Ekşioğlu, O. E. Müstecaplioğlu, and K. Güven, Phys. Rev. A 84, 033805 (2011).
[CrossRef]

Noskov, R. E.

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, Phys. Rev. Lett. 108, 093901 (2012).
[CrossRef]

Orenstein, M.

Panoiu, N. C.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef]

Salgueiro, J. R.

J. R. Salgueiro and Y. S. Kivshar, Appl. Phys. Lett. 97, 081106 (2010).
[CrossRef]

Shadrivov, I. V.

Skryabin, D. V.

A. Marini, D. V. Skryabin, and B. Malomed, Opt. Express 19, 6616 (2011).
[CrossRef]

D. V. Skryabin, A. V. Gorbach, and A. Marini, J. Opt. Soc. Am. B 28, 109 (2011).
[CrossRef]

C. Milián and D. V. Skryabin, Appl. Phys. Lett. 98, 111104 (2011).
[CrossRef]

A. Marini and D. V. Skryabin, Phys. Rev. A 81, 033850 (2010).
[CrossRef]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

Tomlinson, W. J.

Ye, F.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

Appl. Phys. Lett. (2)

J. R. Salgueiro and Y. S. Kivshar, Appl. Phys. Lett. 97, 081106 (2010).
[CrossRef]

C. Milián and D. V. Skryabin, Appl. Phys. Lett. 98, 111104 (2011).
[CrossRef]

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

Opt. Express (2)

Opt. Lett. (2)

Phys. Rep. (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

Phys. Rev. A (3)

Y. Ekşioğlu, O. E. Müstecaplioğlu, and K. Güven, Phys. Rev. A 84, 033805 (2011).
[CrossRef]

A. Marini and D. V. Skryabin, Phys. Rev. A 81, 033850 (2010).
[CrossRef]

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, Phys. Rev. A 79, 041803 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, Phys. Rev. Lett. 108, 093901 (2012).
[CrossRef]

Sov. Phys. JETP Lett. (1)

V. M. Agranovich, V. S. Babichenko, and V. Ya. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1981).

Other (3)

Details on this derivation will be reported elsewhere.

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).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Metal/Kerr structure with linear dielectric constants εm=nm2, εK=nK2 and nonlinear Kerr index n2. (b) Dispersion of a SPP in a lossy metal (black) and a spatial soliton (gray) owning two different amplitudes (βs=knK[1+g|cs|2]). Circles enclose the matching points, and the dashed line marks the light cone ω=βc/εK.

Fig. 2.
Fig. 2.

P versus μ/k curves for δ=0 (right) and δ=π (left) soliplasmon families at ω1.26PHz (λ=1.5μm) for a=3μm (dotted), a=4μm (dashed), and a=5μm (solid). Insets: x (solid) and z (dashed) dimensionless components of the mode profiles Eχ(3)Eω.

Fig. 3.
Fig. 3.

(a) Ex of the π-soliplasmon with neff=1.464 along propagation. Left inset magnifies Ex over the area where it is placed. Contour lines of the Poynting vector norm show power flow, the magnitude of which is represented by the arrows, with the black ones being magnified. Right inset shows the diffraction observed in the linear regime over the first 12 μm. (b) Phase, ϕsp, and (c) amplitudes, |cs,p|, associated to (a). Initial jumps in (c) are due to input noise.

Fig. 4.
Fig. 4.

Propagation of the 0-soliplasmon with neff=1.472. (a) Ex, (b) soliton–plasmon relative phase, and (c) soliton and plasmon amplitudes.

Fig. 5.
Fig. 5.

Propagation under the initial conditions of Fig. 4, including ohmic losses, Im{ϵm}=8.3.

Equations (6)

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

[2z2+2x2+k2εL(x)]Eω=Lv(x)EωPNL,
Eω(x,z)=[cp(z)ep(x)+ucs(z)fs(xa;cs(z))]eiknKz,
i|c˙=M|c,M=[M^]=[μpq(|cs|)q¯(|cs|)μs],
β=knK+μ¯+eiδΔμ2+qq¯,δ=0,π,
Ex(x,z)cs0={q epx(x)μδμp+sech(κs[xa])}eiβz,
ϕ˙sp2Δμ+q|cs||cp|cosϕsp,|c˙p|=q|cs|sinϕsp.

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