Abstract

We study the modulation instability in a two-dimensional nonlinear single feedback system with a photonic lattice and reveal a sharp transition in the instability regimes as the lattice strength is increased. For a shallow lattice, the instability modes are enhanced parallel to the lattice wave vector, while in stronger lattices, these modes are suppressed.

© 2010 Optical Society of America

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    [CrossRef]
  13. C. Denz, S. J. Jensen, M. Schwab, and T. Tschudi, J. Opt. B 1, 114 (1999).
    [CrossRef]

2009 (1)

N. Marsal, D. Wolfersberger, M. Sciamanna, G. Montemezzani, and D. N. Neshev, IEEE J. Quantum Electron. 45, 1380 (2009).
[CrossRef]

2008 (2)

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

N. Marsal, D. Wolfersberger, M. Sciamanna, G. Montemezzani, and D. N. Neshev, Opt. Lett. 33, 2509 (2008).
[CrossRef] [PubMed]

2007 (1)

2005 (1)

D. Gomila and G. L. Oppo, Phys. Rev. E 72, 016614 (2005).
[CrossRef]

2004 (1)

D. Gomila, R. Zambrini, and G. L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

2003 (1)

F. Pauly, O. Sandfuchs, F. Kaiser, and M. R. Belic, Opt. Commun. 218, 385 (2003).
[CrossRef]

2002 (1)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

2001 (1)

O. Sandfuchs, F. Kaiser, and M. R. Belic, Phys. Rev. A 64, 063809 (2001).
[CrossRef]

1999 (3)

C. Denz, S. J. Jensen, M. Schwab, and T. Tschudi, J. Opt. B 1, 114 (1999).
[CrossRef]

P. Y. Wang and M. Saffman, Opt. Lett. 24, 1118 (1999).
[CrossRef]

F. T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).
[CrossRef]

1996 (1)

Ackemann, T.

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).
[CrossRef]

Banerjee, P. P.

Belic, M. R.

F. Pauly, O. Sandfuchs, F. Kaiser, and M. R. Belic, Opt. Commun. 218, 385 (2003).
[CrossRef]

O. Sandfuchs, F. Kaiser, and M. R. Belic, Phys. Rev. A 64, 063809 (2001).
[CrossRef]

Boccaletti, S.

F. T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).
[CrossRef]

Christodoulides, D. N.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Denz, C.

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

C. Denz, S. J. Jensen, M. Schwab, and T. Tschudi, J. Opt. B 1, 114 (1999).
[CrossRef]

Efremidis, N. K.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Egorov, O. A.

Fleischer, J. W.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Gomila, D.

D. Gomila and G. L. Oppo, Phys. Rev. E 72, 016614 (2005).
[CrossRef]

D. Gomila, R. Zambrini, and G. L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

Honda, T.

Jensen, S. J.

C. Denz, S. J. Jensen, M. Schwab, and T. Tschudi, J. Opt. B 1, 114 (1999).
[CrossRef]

Kaiser, F.

F. Pauly, O. Sandfuchs, F. Kaiser, and M. R. Belic, Opt. Commun. 218, 385 (2003).
[CrossRef]

O. Sandfuchs, F. Kaiser, and M. R. Belic, Phys. Rev. A 64, 063809 (2001).
[CrossRef]

Kivshar, Yu. S.

Lederer, F.

Marsal, N.

N. Marsal, D. Wolfersberger, M. Sciamanna, G. Montemezzani, and D. N. Neshev, IEEE J. Quantum Electron. 45, 1380 (2009).
[CrossRef]

N. Marsal, D. Wolfersberger, M. Sciamanna, G. Montemezzani, and D. N. Neshev, Opt. Lett. 33, 2509 (2008).
[CrossRef] [PubMed]

Montemezzani, G.

N. Marsal, D. Wolfersberger, M. Sciamanna, G. Montemezzani, and D. N. Neshev, IEEE J. Quantum Electron. 45, 1380 (2009).
[CrossRef]

N. Marsal, D. Wolfersberger, M. Sciamanna, G. Montemezzani, and D. N. Neshev, Opt. Lett. 33, 2509 (2008).
[CrossRef] [PubMed]

Neshev, D. N.

N. Marsal, D. Wolfersberger, M. Sciamanna, G. Montemezzani, and D. N. Neshev, IEEE J. Quantum Electron. 45, 1380 (2009).
[CrossRef]

N. Marsal, D. Wolfersberger, M. Sciamanna, G. Montemezzani, and D. N. Neshev, Opt. Lett. 33, 2509 (2008).
[CrossRef] [PubMed]

Oppo, G. L.

D. Gomila and G. L. Oppo, Phys. Rev. E 72, 016614 (2005).
[CrossRef]

D. Gomila, R. Zambrini, and G. L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

Pauly, F.

F. Pauly, O. Sandfuchs, F. Kaiser, and M. R. Belic, Opt. Commun. 218, 385 (2003).
[CrossRef]

Radwell, N.

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

Ramazza, P.

F. T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).
[CrossRef]

Rose, P.

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

Saffman, M.

Sandfuchs, O.

F. Pauly, O. Sandfuchs, F. Kaiser, and M. R. Belic, Opt. Commun. 218, 385 (2003).
[CrossRef]

O. Sandfuchs, F. Kaiser, and M. R. Belic, Phys. Rev. A 64, 063809 (2001).
[CrossRef]

Schwab, M.

C. Denz, S. J. Jensen, M. Schwab, and T. Tschudi, J. Opt. B 1, 114 (1999).
[CrossRef]

Sciamanna, M.

N. Marsal, D. Wolfersberger, M. Sciamanna, G. Montemezzani, and D. N. Neshev, IEEE J. Quantum Electron. 45, 1380 (2009).
[CrossRef]

N. Marsal, D. Wolfersberger, M. Sciamanna, G. Montemezzani, and D. N. Neshev, Opt. Lett. 33, 2509 (2008).
[CrossRef] [PubMed]

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Segev, M.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Terhalle, B.

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

Tschudi, T.

C. Denz, S. J. Jensen, M. Schwab, and T. Tschudi, J. Opt. B 1, 114 (1999).
[CrossRef]

Wang, P. Y.

Wolfersberger, D.

N. Marsal, D. Wolfersberger, M. Sciamanna, G. Montemezzani, and D. N. Neshev, IEEE J. Quantum Electron. 45, 1380 (2009).
[CrossRef]

N. Marsal, D. Wolfersberger, M. Sciamanna, G. Montemezzani, and D. N. Neshev, Opt. Lett. 33, 2509 (2008).
[CrossRef] [PubMed]

Zambrini, R.

D. Gomila, R. Zambrini, and G. L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

B. Terhalle, N. Radwell, P. Rose, C. Denz, and T. Ackemann, Appl. Phys. Lett. 93, 151114 (2008).
[CrossRef]

IEEE J. Quantum Electron. (1)

N. Marsal, D. Wolfersberger, M. Sciamanna, G. Montemezzani, and D. N. Neshev, IEEE J. Quantum Electron. 45, 1380 (2009).
[CrossRef]

J. Opt. B (1)

C. Denz, S. J. Jensen, M. Schwab, and T. Tschudi, J. Opt. B 1, 114 (1999).
[CrossRef]

Opt. Commun. (1)

F. Pauly, O. Sandfuchs, F. Kaiser, and M. R. Belic, Opt. Commun. 218, 385 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rep. (1)

F. T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).
[CrossRef]

Phys. Rev. A (1)

O. Sandfuchs, F. Kaiser, and M. R. Belic, Phys. Rev. A 64, 063809 (2001).
[CrossRef]

Phys. Rev. E (2)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[CrossRef]

D. Gomila and G. L. Oppo, Phys. Rev. E 72, 016614 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

D. Gomila, R. Zambrini, and G. L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

(a) Schematic illustration of a PR feedback system with a photonic lattice. (b)–(d) Forward-wave intensity profiles for the stationary solutions. (e)–(g) Corresponding domains of instability, shown with black shading in the plane of transverse wave vectors ( k x , k y ) . The vertical dashed lines represent the edge of the lattice Brillouin zone. Parameters are (b), (e) Δ n p = 0 , Γ = 3.83 ; (c), (f) Δ n p = 10 5 , Γ = 3.75 ; and (d), (g) Δ n p = 4 × 10 5 , Γ = 3.95 .

Fig. 2
Fig. 2

Instability development for lattice parameters corresponding to Figs. 1b,1e; 1c,1f; and 1d,1g, respectively. Shown are the transverse Fourier spectral intensities for the reflected beam at the input crystal facet. (a)–(i) Numerical simulations of instability development at different stages: (a)–(c) initial, (d)–(f) intermediate, and (g)–(i) final. (j)–(l) Corresponding experimental results, following [5], with conditions closely matching the parameters of numerical simulations. The lattice has a period of 25 μm , such that the corresponding lattice wave vector in the far field is twice the one of the hexagonal pattern in (j). Circles indicate the wave vectors of beam diffraction on the lattice. Vertical dashed lines indicate the edge of the Brillouin zone. t / τ PR is the normalized time.

Equations (2)

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z F i D 2 F i V ( x , y ) F = Q B , z B + i D 2 B + i V ( x , y ) B = Q * F .
τ PR t Q + Q = Γ F B * / ( I + I d + I L ) .

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