Abstract

We study propagation of polychromatic light near the edge of a nonlinear waveguide array. We describe simultaneous spatial and spectral beam reshaping associated with power and wavelength-dependent tunneling between the waveguides. We present experimental verifications of the effects predicted theoretically including the first observation of supercontinuum nonlinear surface modes.

© 2006 Optical Society of America

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  1. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30,2466-2468 (2005).
    [CrossRef] [PubMed]
  2. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-063904 (2006).
    [CrossRef] [PubMed]
  3. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96,073901-073904 (2006).
    [CrossRef] [PubMed]
  4. G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, "Observation of discrete quadratic surface solitons," Opt. Express 14,5508-5516 (2006).
    [CrossRef] [PubMed]
  5. C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97,083901-083904 (2006).
    [CrossRef] [PubMed]
  6. E. Smirnov, M. Stepic, C. E. Ruter, D. Kip, and V. Shandarov, "Observation of staggered surface solitary waves in one-dimensional waveguide arrays," Opt. Lett. 31,2338-2340 (2006).
    [CrossRef] [PubMed]
  7. K. Motzek, A. A. Sukhorukov, and Yu. S. Kivshar, "Polychromatic interface solitons in nonlinear photonic lattices," Opt. Lett. 31,3125-3127 (2006).
    [CrossRef] [PubMed]
  8. M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature 387,880-883 (1997).
    [CrossRef]
  9. H. Buljan, T. Schwartz, M. Segev, M. Soljacic, and D. N. Christodoulides, "Polychromatic partially spatially incoherent solitons in a noninstantaneous Kerr nonlinear medium," J. Opt. Soc. Am. B 21,397-404 (2004).
    [CrossRef]
  10. R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, "Incoherent white-light solitons in nonlinear periodic lattices," Phys. Rev. E 73,056608-9 (2006).
    [CrossRef]
  11. J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25,25-27 (2000).
    [CrossRef]
  12. P. St. J. Russell, "Photonic crystal fibers," Science 299,358-362 (2003).
    [CrossRef] [PubMed]
  13. M. Matuszewski, C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, A. Mitchell, M. Trippenbach, M. W. Austin, W. Krolikowski, and Yu. S. Kivshar, "Crossover from self-defocusing to discrete trapping in nonlinear waveguide arrays," Opt. Express 14,254-259 (2006).
    [CrossRef] [PubMed]
  14. P. Yeh, A. Yariv, and C. S. Hong, "Electromagnetic propagation in periodic stratified media.1. General theory," J. Opt. Soc. Am. 67,423-438 (1977).
    [CrossRef]
  15. P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32,104-105 (1978).
    [CrossRef]
  16. K. Motzek, A. A. Sukhorukov, Yu. S. Kivshar, and F. Kaiser, "Polychromatic multigap solitons in nonlinear photonic lattices," in Nonlinear Guided Waves and their applications, Post conference ed., OSA p. WD25 (Optical Society of America, Washington DC, 2005).
  17. K. Motzek, A. A. Sukhorukov, and Yu. S. Kivshar, "Self-trapping of polychromatic light in nonlinear periodic photonic structures," Opt. Express 14,9873-9878 (2006).
    [CrossRef] [PubMed]

2006

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-063904 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96,073901-073904 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97,083901-083904 (2006).
[CrossRef] [PubMed]

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, "Incoherent white-light solitons in nonlinear periodic lattices," Phys. Rev. E 73,056608-9 (2006).
[CrossRef]

M. Matuszewski, C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, A. Mitchell, M. Trippenbach, M. W. Austin, W. Krolikowski, and Yu. S. Kivshar, "Crossover from self-defocusing to discrete trapping in nonlinear waveguide arrays," Opt. Express 14,254-259 (2006).
[CrossRef] [PubMed]

G. A. Siviloglou, K. G. Makris, R. Iwanow, R. Schiek, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, "Observation of discrete quadratic surface solitons," Opt. Express 14,5508-5516 (2006).
[CrossRef] [PubMed]

E. Smirnov, M. Stepic, C. E. Ruter, D. Kip, and V. Shandarov, "Observation of staggered surface solitary waves in one-dimensional waveguide arrays," Opt. Lett. 31,2338-2340 (2006).
[CrossRef] [PubMed]

K. Motzek, A. A. Sukhorukov, and Yu. S. Kivshar, "Polychromatic interface solitons in nonlinear photonic lattices," Opt. Lett. 31,3125-3127 (2006).
[CrossRef] [PubMed]

K. Motzek, A. A. Sukhorukov, and Yu. S. Kivshar, "Self-trapping of polychromatic light in nonlinear periodic photonic structures," Opt. Express 14,9873-9878 (2006).
[CrossRef] [PubMed]

2005

2004

2003

P. St. J. Russell, "Photonic crystal fibers," Science 299,358-362 (2003).
[CrossRef] [PubMed]

2000

1997

M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature 387,880-883 (1997).
[CrossRef]

1978

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32,104-105 (1978).
[CrossRef]

1977

Austin, M. W.

Bartal, G.

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, "Incoherent white-light solitons in nonlinear periodic lattices," Phys. Rev. E 73,056608-9 (2006).
[CrossRef]

Buljan, H.

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, "Incoherent white-light solitons in nonlinear periodic lattices," Phys. Rev. E 73,056608-9 (2006).
[CrossRef]

H. Buljan, T. Schwartz, M. Segev, M. Soljacic, and D. N. Christodoulides, "Polychromatic partially spatially incoherent solitons in a noninstantaneous Kerr nonlinear medium," J. Opt. Soc. Am. B 21,397-404 (2004).
[CrossRef]

Cho, A. Y.

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32,104-105 (1978).
[CrossRef]

Christodoulides, D. N.

Fleischer, J. W.

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, "Incoherent white-light solitons in nonlinear periodic lattices," Phys. Rev. E 73,056608-9 (2006).
[CrossRef]

Hache, A.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-063904 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30,2466-2468 (2005).
[CrossRef] [PubMed]

Hong, C. S.

Iwanow, R.

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96,073901-073904 (2006).
[CrossRef] [PubMed]

Kip, D.

Kivshar, Yu. S.

Krolikowski, W.

M. Matuszewski, C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, A. Mitchell, M. Trippenbach, M. W. Austin, W. Krolikowski, and Yu. S. Kivshar, "Crossover from self-defocusing to discrete trapping in nonlinear waveguide arrays," Opt. Express 14,254-259 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97,083901-083904 (2006).
[CrossRef] [PubMed]

Makris, K. G.

Matuszewski, M.

Min, Y.

Mitchell, A.

M. Matuszewski, C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, A. Mitchell, M. Trippenbach, M. W. Austin, W. Krolikowski, and Yu. S. Kivshar, "Crossover from self-defocusing to discrete trapping in nonlinear waveguide arrays," Opt. Express 14,254-259 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97,083901-083904 (2006).
[CrossRef] [PubMed]

Mitchell, M.

M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature 387,880-883 (1997).
[CrossRef]

Molina, M. I.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97,083901-083904 (2006).
[CrossRef] [PubMed]

Morandotti, R.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-063904 (2006).
[CrossRef] [PubMed]

Motzek, K.

Neshev, D. N.

M. Matuszewski, C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, A. Mitchell, M. Trippenbach, M. W. Austin, W. Krolikowski, and Yu. S. Kivshar, "Crossover from self-defocusing to discrete trapping in nonlinear waveguide arrays," Opt. Express 14,254-259 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97,083901-083904 (2006).
[CrossRef] [PubMed]

Pezer, R.

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, "Incoherent white-light solitons in nonlinear periodic lattices," Phys. Rev. E 73,056608-9 (2006).
[CrossRef]

Ranka, J. K.

Rosberg, C. R.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97,083901-083904 (2006).
[CrossRef] [PubMed]

M. Matuszewski, C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, A. Mitchell, M. Trippenbach, M. W. Austin, W. Krolikowski, and Yu. S. Kivshar, "Crossover from self-defocusing to discrete trapping in nonlinear waveguide arrays," Opt. Express 14,254-259 (2006).
[CrossRef] [PubMed]

Russell, P. St. J.

P. St. J. Russell, "Photonic crystal fibers," Science 299,358-362 (2003).
[CrossRef] [PubMed]

Ruter, C. E.

Salamo, G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-063904 (2006).
[CrossRef] [PubMed]

Schiek, R.

Schwartz, T.

Segev, M.

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, "Incoherent white-light solitons in nonlinear periodic lattices," Phys. Rev. E 73,056608-9 (2006).
[CrossRef]

H. Buljan, T. Schwartz, M. Segev, M. Soljacic, and D. N. Christodoulides, "Polychromatic partially spatially incoherent solitons in a noninstantaneous Kerr nonlinear medium," J. Opt. Soc. Am. B 21,397-404 (2004).
[CrossRef]

M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature 387,880-883 (1997).
[CrossRef]

Shandarov, V.

Siviloglou, G. A.

Smirnov, E.

Sohler, W.

Soljacic, M.

Sorel, M.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-063904 (2006).
[CrossRef] [PubMed]

Stegeman, G. I.

Stentz, A. J.

Stepic, M.

Sukhorukov, A. A.

Suntsov, S.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-063904 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30,2466-2468 (2005).
[CrossRef] [PubMed]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96,073901-073904 (2006).
[CrossRef] [PubMed]

Trippenbach, M.

Vicencio, R. A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97,083901-083904 (2006).
[CrossRef] [PubMed]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96,073901-073904 (2006).
[CrossRef] [PubMed]

Windeler, R. S.

Yang, H.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-063904 (2006).
[CrossRef] [PubMed]

Yariv, A.

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32,104-105 (1978).
[CrossRef]

P. Yeh, A. Yariv, and C. S. Hong, "Electromagnetic propagation in periodic stratified media.1. General theory," J. Opt. Soc. Am. 67,423-438 (1977).
[CrossRef]

Yeh, P.

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32,104-105 (1978).
[CrossRef]

P. Yeh, A. Yariv, and C. S. Hong, "Electromagnetic propagation in periodic stratified media.1. General theory," J. Opt. Soc. Am. 67,423-438 (1977).
[CrossRef]

Appl. Phys. Lett.

P. Yeh, A. Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32,104-105 (1978).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Nature

M. Mitchell and M. Segev, "Self-trapping of incoherent white light," Nature 387,880-883 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

R. Pezer, H. Buljan, G. Bartal, M. Segev, and J. W. Fleischer, "Incoherent white-light solitons in nonlinear periodic lattices," Phys. Rev. E 73,056608-9 (2006).
[CrossRef]

Phys. Rev. Lett.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96,063901-063904 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96,073901-073904 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97,083901-083904 (2006).
[CrossRef] [PubMed]

Science

P. St. J. Russell, "Photonic crystal fibers," Science 299,358-362 (2003).
[CrossRef] [PubMed]

Other

K. Motzek, A. A. Sukhorukov, Yu. S. Kivshar, and F. Kaiser, "Polychromatic multigap solitons in nonlinear photonic lattices," in Nonlinear Guided Waves and their applications, Post conference ed., OSA p. WD25 (Optical Society of America, Washington DC, 2005).

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Figures (5)

Fig. 1.
Fig. 1.

(a,d) Refractive index profiles in waveguide arrays with (a) weaker (for w=7µm) and (d) stronger (for w=8.5µm) surface defects. Dashed line shows, for comparison, the refractive index in an infinite periodic structure. Corresponding (b,e) dynamics inside the arrays and (c,f) output spectra are shown for the input beam coupled to the surface waveguide. The input spectrum is constant for 400nm<λ<830nm.

Fig. 2.
Fig. 2.

(a–d) Nonlinear dynamics in the waveguide array (bottom) and corresponding output spectra (top) for increasing powers of the input beam coupled to the surface waveguide. Maximum changes of the nonlinear refractive index at the input (z=0) are |Δn nonl|×105≃0.3, 0.9, 1.6, 2.8. Other parameters correspond to Fig. 1(d).

Fig. 3.
Fig. 3.

(a–d) Linear dynamics inside the array (bottom) and corresponding output spectra (top) for different input beam positions. Parameters correspond to Fig. 1(a).

Fig. 4.
Fig. 4.

(a) Linear and (b–d) nonlinear dynamics inside the array (bottom) and output spectra (top) for increasing powers of the input beam coupled to the second (n=1) waveguide. Maximum nonlinear changes of refractive index at the input (z=0) are |Δn nonl|×105≃0, 1.6, 2.8, 6.2. Other parameters correspond to Fig. 1(a).

Fig. 5.
Fig. 5.

Experimental demonstration of interaction of a supercontinuum polychromatic light with a surface. Top row: Output spectrally resolved spatial distribution at low powers of 32µW (linear propagation) for input beam positioned at the first (n=0), second (n=1), … and the sixth (n=5) waveguide respectively. Bottom row: Excitation at the second waveguide. (a) Linear spectral distribution measured by a spectrometer. The position “zero” (n=0) indicates the edge waveguide of the array. The intensity is represented in logarithmic scale for better visualization. (b,c) Corresponding nonlinear localization (b) measured by a spectrometer and (c) spectrally resolved spatial distribution for input power of 1.25mW. (d) Output intensity distribution and the corresponding refractive index profile of the waveguide array. (e,f) Spectrally resolved spatial distribution at higher input powers of 6 and 11 mW, respectively.

Equations (1)

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i A m z + λ m z s 4 π n 0 x s 2 2 A m x 2 + 2 π z s λ m { ν ( x ) + γ M j = 1 M σ ( λ j ) A j 2 } A m = 0 ,

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