Abstract

In an array of nonlinear waveguides, a giant compression of the input beam can be achieved by exciting a rogue wave. Input field almost homogeneously distributed over hundreds of waveguides concentrates practically all the energy into a single waveguide at the output plane of the structure. We determine the required input profile of the electric field to achieve this. We illustrate the phenomenon by modeling the array by direct numerical simulations of the discrete nonlinear Schrödinger equation.

© 2009 Optical Society of America

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References

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  1. N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
    [CrossRef]
  2. P. Müller, Ch. Garrett, and A. Osborne, Oceanogr. 18, 185 (2005).
  3. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
    [CrossRef] [PubMed]
  4. D. H. Peregrine, J. Austral. Math. Soc 25, 16 (1983).
    [CrossRef]
  5. N. Akhmediev, J. M. Soto-Crespo, and A. Ankiewicz, Phys. Lett. A 373, 2137 (2009).
    [CrossRef]
  6. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  7. G. L. Alfimov, V. A. Brazhnyi, and V. V. Konotop, Physica D 194, 127 (2004).
    [CrossRef]
  8. F. Kh. Abdullaev, S. A. Darmanyan, and J. Garnier, in Progress in Optics, E.Wolf, ed. (Elsevier Science, 2002), Vol. 44, pp. 303-365.
    [CrossRef]

2009 (2)

N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, and A. Ankiewicz, Phys. Lett. A 373, 2137 (2009).
[CrossRef]

2007 (1)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef] [PubMed]

2005 (1)

P. Müller, Ch. Garrett, and A. Osborne, Oceanogr. 18, 185 (2005).

2004 (1)

G. L. Alfimov, V. A. Brazhnyi, and V. V. Konotop, Physica D 194, 127 (2004).
[CrossRef]

1988 (1)

1983 (1)

D. H. Peregrine, J. Austral. Math. Soc 25, 16 (1983).
[CrossRef]

Abdullaev, F. Kh.

F. Kh. Abdullaev, S. A. Darmanyan, and J. Garnier, in Progress in Optics, E.Wolf, ed. (Elsevier Science, 2002), Vol. 44, pp. 303-365.
[CrossRef]

Akhmediev, N.

N. Akhmediev, J. M. Soto-Crespo, and A. Ankiewicz, Phys. Lett. A 373, 2137 (2009).
[CrossRef]

N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
[CrossRef]

Alfimov, G. L.

G. L. Alfimov, V. A. Brazhnyi, and V. V. Konotop, Physica D 194, 127 (2004).
[CrossRef]

Ankiewicz, A.

N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, and A. Ankiewicz, Phys. Lett. A 373, 2137 (2009).
[CrossRef]

Brazhnyi, V. A.

G. L. Alfimov, V. A. Brazhnyi, and V. V. Konotop, Physica D 194, 127 (2004).
[CrossRef]

Christodoulides, D. N.

Darmanyan, S. A.

F. Kh. Abdullaev, S. A. Darmanyan, and J. Garnier, in Progress in Optics, E.Wolf, ed. (Elsevier Science, 2002), Vol. 44, pp. 303-365.
[CrossRef]

Garnier, J.

F. Kh. Abdullaev, S. A. Darmanyan, and J. Garnier, in Progress in Optics, E.Wolf, ed. (Elsevier Science, 2002), Vol. 44, pp. 303-365.
[CrossRef]

Garrett, Ch.

P. Müller, Ch. Garrett, and A. Osborne, Oceanogr. 18, 185 (2005).

Jalali, B.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef] [PubMed]

Joseph, R. I.

Konotop, V. V.

G. L. Alfimov, V. A. Brazhnyi, and V. V. Konotop, Physica D 194, 127 (2004).
[CrossRef]

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef] [PubMed]

Müller, P.

P. Müller, Ch. Garrett, and A. Osborne, Oceanogr. 18, 185 (2005).

Osborne, A.

P. Müller, Ch. Garrett, and A. Osborne, Oceanogr. 18, 185 (2005).

Peregrine, D. H.

D. H. Peregrine, J. Austral. Math. Soc 25, 16 (1983).
[CrossRef]

Ropers, C.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef] [PubMed]

Solli, D. R.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef] [PubMed]

Soto-Crespo, J. M.

N. Akhmediev, J. M. Soto-Crespo, and A. Ankiewicz, Phys. Lett. A 373, 2137 (2009).
[CrossRef]

Taki, M.

N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
[CrossRef]

J. Austral. Math. Soc (1)

D. H. Peregrine, J. Austral. Math. Soc 25, 16 (1983).
[CrossRef]

Nature (1)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef] [PubMed]

Oceanogr. (1)

P. Müller, Ch. Garrett, and A. Osborne, Oceanogr. 18, 185 (2005).

Opt. Lett. (1)

Phys. Lett. A (2)

N. Akhmediev, A. Ankiewicz, and M. Taki, Phys. Lett. A 373, 675 (2009).
[CrossRef]

N. Akhmediev, J. M. Soto-Crespo, and A. Ankiewicz, Phys. Lett. A 373, 2137 (2009).
[CrossRef]

Physica D (1)

G. L. Alfimov, V. A. Brazhnyi, and V. V. Konotop, Physica D 194, 127 (2004).
[CrossRef]

Other (1)

F. Kh. Abdullaev, S. A. Darmanyan, and J. Garnier, in Progress in Optics, E.Wolf, ed. (Elsevier Science, 2002), Vol. 44, pp. 303-365.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Contour plot of intensity | q n | 2 on the plane ( n , ζ ) . We used periodic boundary condition q n = q n + N with N = 101 and initial condition (2). Parameters are a, ϵ = 0.1, L = 100 ; b, ϵ = 0.2, L = 100 ; c, ϵ = 0.3, L = 100 ; d, ϵ = 0.1, L = 500 . The insets show input and output field profiles.

Fig. 2
Fig. 2

a, Contour plot of intensity | q n ( ζ ) | 2 obtained for N = 301 , ϵ = 0.1, and L = 500 . We used periodic boundary conditions and the initial profile (2). b, Output intensity in the central waveguide versus N.

Fig. 3
Fig. 3

a, Plot of intensity | q n | 2 on the ( n , ζ ) plane for ϵ = 0.1, N = 301 , L = 500 , obtained from Eq. (1) subject to the periodic boundary and fitted initial conditions. b, Fitted initial condition at ζ = 0 (solid green curve), input intensity (2) (dashed blue line) and the field profile at the middle line ζ = 500 (solid red curve).

Fig. 4
Fig. 4

a, Contour plot of intensity | q n | 2 in the ( n , ζ ) plane. We used the following: a, zero boundary condition q ( N + 1 ) 2 = q ( N + 1 ) 2 = 0 and the initial condition q n ( 0 ) = 1 4 n 2 ( N + 2 ) 2 Q n with Q n given by (2); b, traveling wave boundary conditions q ( N + 1 ) 2 = q ( N + 1 ) 2 = ϵ exp ( i ϵ 2 ζ ) and the fitted initial condition. Other parameters are ϵ =0.1, N = 301 , and L = 500 . The insets show the input and output field profiles.

Equations (2)

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i q ̇ n + q n + 1 + q n 1 2 q n + σ | q n | 2 q n = 0 .
q n ( 0 ) = Q n ϵ ( 1 4 1 2 i ϵ 2 L 1 + 2 ϵ 2 n 2 + 4 ϵ 4 L 2 ) e i ϵ 2 L

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