Abstract

We show experimentally and theoretically that the interplay between a vortex-induced pattern rotation and an optical feedback nonlocality-induced pattern drift leads to new dynamics and geometries of optical pattern formation. First, the vortex-induced pattern rotation and the nonlocality-induced drift can annihilate each other, resulting in the formation of static zones in the near field of the otherwise drifting pattern. Second, increasing the external mirror tilt leads to new pattern solutions that are composed of wave vectors of different amplitudes and directions, resulting in a multistriped pattern geometry.

© 2013 Optical Society of America

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  1. F. T. Arecchi, S. Boccaletti, and P. Ramazza, Phys. Rep. 318, 1 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, Phys. Rev. A 54, 3472 (1996).
    [CrossRef]
  7. F. Papoff and R. Zambrini, Phys. Rev. Lett. 94, 243903 (2005).
    [CrossRef]
  8. E. Louvergneaux, C. Szwaj, G. Agez, P. Glorieux, and M. Taki, Phys. Rev. Lett. 92, 043901 (2004).
    [CrossRef]
  9. N. Marsal, D. Wolfersberger, M. Sciamanna, and G. Montemezzani, Phys. Rev. A 81, 031804 (2010).
    [CrossRef]
  10. V. Caullet, N. Marsal, D. Wolfersberger, and M. Sciamanna, Phys. Rev. Lett. 108, 263903 (2012).
    [CrossRef]
  11. M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, Nat. Phys. 8, 743 (2012).
    [CrossRef]
  12. V. Caullet, N. Marsal, D. Wolfersberger, and M. Sciamanna, Opt. Lett. 36, 2815 (2011).
    [CrossRef]
  13. S. Residori, A. Petrossian, and L. Gil, Phys. Rev. Lett. 88, 233901 (2002).
    [CrossRef]

2012

V. Caullet, N. Marsal, D. Wolfersberger, and M. Sciamanna, Phys. Rev. Lett. 108, 263903 (2012).
[CrossRef]

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, Nat. Phys. 8, 743 (2012).
[CrossRef]

2011

2010

N. Marsal, D. Wolfersberger, M. Sciamanna, and G. Montemezzani, Phys. Rev. A 81, 031804 (2010).
[CrossRef]

2008

2005

F. Papoff and R. Zambrini, Phys. Rev. Lett. 94, 243903 (2005).
[CrossRef]

2004

E. Louvergneaux, C. Szwaj, G. Agez, P. Glorieux, and M. Taki, Phys. Rev. Lett. 92, 043901 (2004).
[CrossRef]

2002

S. Residori, A. Petrossian, and L. Gil, Phys. Rev. Lett. 88, 233901 (2002).
[CrossRef]

1999

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

M. Schwab, C. Denz, and M. Saffman, Appl. Phys. B 69, 429 (1999).
[CrossRef]

R. Herrero, E. G. Westhoff, A. Aumann, T. Ackemann, Y. A. Logvin, and W. Lange, Phys. Rev. Lett. 82, 4627 (1999).
[CrossRef]

1998

A. V. Mamaev and M. Saffman, Phys. Rev. Lett. 80, 3499 (1998).
[CrossRef]

1996

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, Phys. Rev. A 54, 3472 (1996).
[CrossRef]

Ackemann, T.

R. Herrero, E. G. Westhoff, A. Aumann, T. Ackemann, Y. A. Logvin, and W. Lange, Phys. Rev. Lett. 82, 4627 (1999).
[CrossRef]

Agez, G.

E. Louvergneaux, C. Szwaj, G. Agez, P. Glorieux, and M. Taki, Phys. Rev. Lett. 92, 043901 (2004).
[CrossRef]

Arecchi, F. T.

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

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, Phys. Rev. A 54, 3472 (1996).
[CrossRef]

Aumann, A.

R. Herrero, E. G. Westhoff, A. Aumann, T. Ackemann, Y. A. Logvin, and W. Lange, Phys. Rev. Lett. 82, 4627 (1999).
[CrossRef]

Boccaletti, S.

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

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, Phys. Rev. A 54, 3472 (1996).
[CrossRef]

Caullet, V.

V. Caullet, N. Marsal, D. Wolfersberger, and M. Sciamanna, Phys. Rev. Lett. 108, 263903 (2012).
[CrossRef]

V. Caullet, N. Marsal, D. Wolfersberger, and M. Sciamanna, Opt. Lett. 36, 2815 (2011).
[CrossRef]

Denz, C.

M. Schwab, C. Denz, and M. Saffman, Appl. Phys. B 69, 429 (1999).
[CrossRef]

Dreischuh, A.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, Nat. Phys. 8, 743 (2012).
[CrossRef]

Giaquinta, A.

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, Phys. Rev. A 54, 3472 (1996).
[CrossRef]

Gil, L.

S. Residori, A. Petrossian, and L. Gil, Phys. Rev. Lett. 88, 233901 (2002).
[CrossRef]

Glorieux, P.

E. Louvergneaux, C. Szwaj, G. Agez, P. Glorieux, and M. Taki, Phys. Rev. Lett. 92, 043901 (2004).
[CrossRef]

Hansinger, P.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, Nat. Phys. 8, 743 (2012).
[CrossRef]

Herrero, R.

R. Herrero, E. G. Westhoff, A. Aumann, T. Ackemann, Y. A. Logvin, and W. Lange, Phys. Rev. Lett. 82, 4627 (1999).
[CrossRef]

Kern, C.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, Nat. Phys. 8, 743 (2012).
[CrossRef]

Lange, W.

R. Herrero, E. G. Westhoff, A. Aumann, T. Ackemann, Y. A. Logvin, and W. Lange, Phys. Rev. Lett. 82, 4627 (1999).
[CrossRef]

Logvin, Y. A.

R. Herrero, E. G. Westhoff, A. Aumann, T. Ackemann, Y. A. Logvin, and W. Lange, Phys. Rev. Lett. 82, 4627 (1999).
[CrossRef]

Louvergneaux, E.

E. Louvergneaux, C. Szwaj, G. Agez, P. Glorieux, and M. Taki, Phys. Rev. Lett. 92, 043901 (2004).
[CrossRef]

Mamaev, A. V.

A. V. Mamaev and M. Saffman, Phys. Rev. Lett. 80, 3499 (1998).
[CrossRef]

Marsal, N.

V. Caullet, N. Marsal, D. Wolfersberger, and M. Sciamanna, Phys. Rev. Lett. 108, 263903 (2012).
[CrossRef]

V. Caullet, N. Marsal, D. Wolfersberger, and M. Sciamanna, Opt. Lett. 36, 2815 (2011).
[CrossRef]

N. Marsal, D. Wolfersberger, M. Sciamanna, and G. Montemezzani, Phys. Rev. A 81, 031804 (2010).
[CrossRef]

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

Montemezzani, G.

N. Marsal, D. Wolfersberger, M. Sciamanna, and G. Montemezzani, Phys. Rev. A 81, 031804 (2010).
[CrossRef]

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

Neshev, D. N.

Pampaloni, E.

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, Phys. Rev. A 54, 3472 (1996).
[CrossRef]

Papoff, F.

F. Papoff and R. Zambrini, Phys. Rev. Lett. 94, 243903 (2005).
[CrossRef]

Petrossian, A.

S. Residori, A. Petrossian, and L. Gil, Phys. Rev. Lett. 88, 233901 (2002).
[CrossRef]

Ramazza, P.

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

Ramazza, P. L.

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, Phys. Rev. A 54, 3472 (1996).
[CrossRef]

Residori, S.

S. Residori, A. Petrossian, and L. Gil, Phys. Rev. Lett. 88, 233901 (2002).
[CrossRef]

Saffman, M.

M. Schwab, C. Denz, and M. Saffman, Appl. Phys. B 69, 429 (1999).
[CrossRef]

A. V. Mamaev and M. Saffman, Phys. Rev. Lett. 80, 3499 (1998).
[CrossRef]

Schwab, M.

M. Schwab, C. Denz, and M. Saffman, Appl. Phys. B 69, 429 (1999).
[CrossRef]

Sciamanna, M.

V. Caullet, N. Marsal, D. Wolfersberger, and M. Sciamanna, Phys. Rev. Lett. 108, 263903 (2012).
[CrossRef]

V. Caullet, N. Marsal, D. Wolfersberger, and M. Sciamanna, Opt. Lett. 36, 2815 (2011).
[CrossRef]

N. Marsal, D. Wolfersberger, M. Sciamanna, and G. Montemezzani, Phys. Rev. A 81, 031804 (2010).
[CrossRef]

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

Soria, S.

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, Phys. Rev. A 54, 3472 (1996).
[CrossRef]

Spielmann, C.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, Nat. Phys. 8, 743 (2012).
[CrossRef]

Szwaj, C.

E. Louvergneaux, C. Szwaj, G. Agez, P. Glorieux, and M. Taki, Phys. Rev. Lett. 92, 043901 (2004).
[CrossRef]

Taki, M.

E. Louvergneaux, C. Szwaj, G. Agez, P. Glorieux, and M. Taki, Phys. Rev. Lett. 92, 043901 (2004).
[CrossRef]

Westhoff, E. G.

R. Herrero, E. G. Westhoff, A. Aumann, T. Ackemann, Y. A. Logvin, and W. Lange, Phys. Rev. Lett. 82, 4627 (1999).
[CrossRef]

Wolfersberger, D.

V. Caullet, N. Marsal, D. Wolfersberger, and M. Sciamanna, Phys. Rev. Lett. 108, 263903 (2012).
[CrossRef]

V. Caullet, N. Marsal, D. Wolfersberger, and M. Sciamanna, Opt. Lett. 36, 2815 (2011).
[CrossRef]

N. Marsal, D. Wolfersberger, M. Sciamanna, and G. Montemezzani, Phys. Rev. A 81, 031804 (2010).
[CrossRef]

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

Zambrini, R.

F. Papoff and R. Zambrini, Phys. Rev. Lett. 94, 243903 (2005).
[CrossRef]

Zürch, M.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, Nat. Phys. 8, 743 (2012).
[CrossRef]

Appl. Phys. B

M. Schwab, C. Denz, and M. Saffman, Appl. Phys. B 69, 429 (1999).
[CrossRef]

Nat. Phys.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, Nat. Phys. 8, 743 (2012).
[CrossRef]

Opt. Lett.

Phys. Rep.

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

Phys. Rev. A

N. Marsal, D. Wolfersberger, M. Sciamanna, and G. Montemezzani, Phys. Rev. A 81, 031804 (2010).
[CrossRef]

P. L. Ramazza, S. Boccaletti, A. Giaquinta, E. Pampaloni, S. Soria, and F. T. Arecchi, Phys. Rev. A 54, 3472 (1996).
[CrossRef]

Phys. Rev. Lett.

F. Papoff and R. Zambrini, Phys. Rev. Lett. 94, 243903 (2005).
[CrossRef]

E. Louvergneaux, C. Szwaj, G. Agez, P. Glorieux, and M. Taki, Phys. Rev. Lett. 92, 043901 (2004).
[CrossRef]

R. Herrero, E. G. Westhoff, A. Aumann, T. Ackemann, Y. A. Logvin, and W. Lange, Phys. Rev. Lett. 82, 4627 (1999).
[CrossRef]

A. V. Mamaev and M. Saffman, Phys. Rev. Lett. 80, 3499 (1998).
[CrossRef]

V. Caullet, N. Marsal, D. Wolfersberger, and M. Sciamanna, Phys. Rev. Lett. 108, 263903 (2012).
[CrossRef]

S. Residori, A. Petrossian, and L. Gil, Phys. Rev. Lett. 88, 233901 (2002).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Scheme of our photorefractive feedback system. (a) Experimental vortex input beam. (b) Vortex wavefront. θ is the mirror tilt angle, and H is the feedback shift. H = L tan θ .

Fig. 2.
Fig. 2.

Experimental (top) and numerical (bottom) near-field patterns obtained without [panels (a) and c)] and with [panels (b) and (d)] a small mirror tilt. (a) and (b) Input intensities: I = 30 Wcm 2 . (c) and (d)  Γ L c = 4.2 .

Fig. 3.
Fig. 3.

Experimental (top) and numerical (bottom) patterns (near and far fields) for large mirror tilts. H > 1.5 μm . (a)–(f) Input intensities: I = 30 Wcm 2 . (g)–(l)  Γ L c = 4.2 . The yellow arrows represent the dynamics of the near-field patterns. The image of panel “a” is taken from the video available here at http://hal-supelec.archives-ouvertes.fr/hal-00815888.

Fig. 4.
Fig. 4.

Influence of nonlinearity on pattern formation in the case of a large mirror tilt. Experimentally [panels (a)–(d)], the feedback shift is fixed to H = 2.6 μm and the nonlinearity is driven by the input intensity I from 10 to 40 Wcm 2 . In the simulation [panels (e)–(l)], H = 1.6 μm and the nonlinearity is driven by the Γ L c coefficient from 4.2 to 4.7. The red and yellow shapes have been added to highlight particular pattern geometries.

Equations (3)

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z F + i f Δ 2 F = Q B ,
z B + i f Δ 2 B = Q * F ,
τ t Q + Q = Γ F B * | F | 2 + | B | 2 ,

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