Abstract

We analyze stability of the TM polarized optical solitons and nonlinear guided waves localized at a metal-dielectric interface. We demonstrate, both analytically and numerically, that the spatial solitons can experience vectorial transverse modulational instability that leads to the generation of arrays of two-dimensional TM polarized self-trapped localized beams. In a sharp contrast, we reveal that the transverse instability is completely eliminated for nonlinear surface plasmons.

© 2009 Optical Society of America

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  1. V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).
  2. Yu. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
    [CrossRef]
  3. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003).
  4. C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
    [CrossRef] [PubMed]
  5. A. W. Snyder, D. J. Mitchell, and Y. Chen, Opt. Lett. 19, 524 (1994).
    [CrossRef] [PubMed]
  6. B. V. Gisin and B. A. Malomed, J. Opt. Soc. Am. B 18, 1356 (2001).
    [CrossRef]
  7. A. Ciattoni, B. Crosignani, P. D. Porto, and A. Yariv, J. Opt. Soc. Am. B 22, 1384 (2005).
    [CrossRef]
  8. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Rep. 408, 131 (2005).
    [CrossRef]
  9. A. R. Davoyan, I. V. Shadrivov, and Yu. S. Kivshar, Opt. Express 16, 21209 (2008) and references therein.
    [CrossRef] [PubMed]
  10. G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
    [CrossRef]
  11. D. Mihalache, G. I. Stegeman, C. T. Seaton, E. M. Wright, R. Zanoni, A. D. Boardman, and T. Twardowski, Opt. Lett. 12, 187 (1987).
    [CrossRef] [PubMed]
  12. A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, Phys. Rev. A 35, 1159 (1987).
    [CrossRef] [PubMed]
  13. M. S. Kushwaha, Jpn. J. Appl. Phys. 29, L1826 (1990).
    [CrossRef]

2009 (1)

C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
[CrossRef] [PubMed]

2008 (1)

2005 (2)

A. Ciattoni, B. Crosignani, P. D. Porto, and A. Yariv, J. Opt. Soc. Am. B 22, 1384 (2005).
[CrossRef]

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

2001 (1)

2000 (1)

Yu. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

1994 (1)

1990 (1)

M. S. Kushwaha, Jpn. J. Appl. Phys. 29, L1826 (1990).
[CrossRef]

1987 (2)

1985 (1)

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

1974 (1)

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

Agrawal, G. P.

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

Ariyasu, J.

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

Boardman, A. D.

Chen, Y.

Ciattoni, A.

Crosignani, B.

Davoyan, A. R.

Gisin, B. V.

Hong, R. -C.

C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
[CrossRef] [PubMed]

Jeng, C. -C.

C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
[CrossRef] [PubMed]

Kivshar, Yu. S.

A. R. Davoyan, I. V. Shadrivov, and Yu. S. Kivshar, Opt. Express 16, 21209 (2008) and references therein.
[CrossRef] [PubMed]

Yu. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

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

Kushwaha, M. S.

M. S. Kushwaha, Jpn. J. Appl. Phys. 29, L1826 (1990).
[CrossRef]

Lee, R. -K.

C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
[CrossRef] [PubMed]

Lin, Y. Y.

C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
[CrossRef] [PubMed]

Malomed, B. A.

Maradudin, A. A.

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

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef] [PubMed]

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

Mihalache, D.

Mitchell, D. J.

Pelinovsky, D. E.

Yu. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

Porto, P. D.

Rubenchik, A. M.

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

Seaton, C. T.

D. Mihalache, G. I. Stegeman, C. T. Seaton, E. M. Wright, R. Zanoni, A. D. Boardman, and T. Twardowski, Opt. Lett. 12, 187 (1987).
[CrossRef] [PubMed]

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

Shadrivov, I. V.

Smolyaninov, I. I.

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

Snyder, A. W.

Stegeman, G. I.

D. Mihalache, G. I. Stegeman, C. T. Seaton, E. M. Wright, R. Zanoni, A. D. Boardman, and T. Twardowski, Opt. Lett. 12, 187 (1987).
[CrossRef] [PubMed]

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef] [PubMed]

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

Twardowski, T.

Wallis, R. F.

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

Wright, E. M.

Yariv, A.

Zakharov, V. E.

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

Zanoni, R.

Zayats, A. V.

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

J. Appl. Phys. (1)

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

J. Opt. Soc. Am. B (2)

Jpn. J. Appl. Phys. (1)

M. S. Kushwaha, Jpn. J. Appl. Phys. 29, L1826 (1990).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rep. (2)

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

Yu. S. Kivshar and D. E. Pelinovsky, Phys. Rep. 331, 117 (2000).
[CrossRef]

Phys. Rev. A (1)

A. D. Boardman, A. A. Maradudin, G. I. Stegeman, T. Twardowski, and E. M. Wright, Phys. Rev. A 35, 1159 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

C.-C. Jeng, Y. Y. Lin, R.-C. Hong, and R.-K. Lee, Phys. Rev. Lett. 102, 153905 (2009).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

Other (1)

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

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Figures (5)

Fig. 1
Fig. 1

(a) Spatial TM soliton. Shown are the electric field components u (solid curve) and v (dashed curve). (b) Partial powers P u and P v of the electric field components.

Fig. 2
Fig. 2

Spectrum of transverse instability for TM polarized spatial soliton for three values of the propagation constant: β = 1.1 , 1.3, and 1.5, respectively.

Fig. 3
Fig. 3

Examples of the dispersion relation ω ( β ) of nonlinear surface plasmons calculated analytically for x 0 = 0.1 (◇) and x 0 = 1 (△), and from direct numerical solutions x 0 = 0.1 (solid curve) and x 0 = 1 (dashed curve), respectively. Parameters are k = 1 and n 0 = 1 .

Fig. 4
Fig. 4

Nonlinear surface plasmon polaritons. Left, power dependence of the plasmon modes versus β for different frequencies ω ¯ = 0.05 (solid curve), ω ¯ = 0.1 (dashed curve) and analytical solution for ω ¯ = 0.1 (dotted-dashed curve), respectively. The inset is its blow up. Right, three examples of the nonlinear plasmons presented by their field components e z (dashed curve) and h y (solid curve), and marked as A, B, and C on the power dependencies.

Fig. 5
Fig. 5

Results of numerical simulations showing [(a),(b)] the development of transverse modulations for the TM polarized vector soliton; [(c),(d)] propagation of a nonlinear plasmon at a metal-dielectric interface, at Γ = 0 ; and [(e),(f)] propagation of a nonlinear plasmon for Γ = 10 4 . Shown are the field components H y (left) and E z (right) at the input ( z = 0 ) and after the propagation ( z = 10 ) , in columns. The propagation constant β = 1.1 (point A in Fig. 4).

Equations (6)

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[ 2 + k 2 n 2 ] E = [ E   ln   n 2 ] .
( d 2 d x 2 + k 2 n 2 β 2 ) u = d d x ( u d   ln   n 2 d x ) ,
( d 2 d x 2 + k 2 n 2 β 2 ) v = β u d   ln   n 2 d x ;
n 2 = n 0 2 + α ( | u | 2 + | v | 2 ) ,
[ β 2 ϵ M ( ω ) k 2 ] 1 / 2 ϵ 0 n 2 ( x 0 ) β ϵ M ( ω ) u ( x 0 ) = v ( x 0 ) .
ω ω p 1 k n 2 ( x 0 ) β 2 k 2 n 0 2   tanh ( β 2 k 2 n 0 2 x 0 ) ,

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