Abstract

We demonstrate an original approach, to the best of our knowledge, to acquire nonlinear control over the angular momentum of a cluster of solitary waves. We show that the angular momentum can be adjusted by acting on the global excitation of the system. The effect is verified in liquid crystals by observing power-dependent rotation of a two-soliton cluster.

© 2007 Optical Society of America

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  1. A. D. Mcewan, Nature 260, 126 (1976).
    [CrossRef]
  2. R. J. van den Oord, M. C. de Lignie, J. J. M. Beenakker, and J. Korving, Phys. Rev. Lett. 59, 2907 (1987).
    [CrossRef] [PubMed]
  3. J. P. Torres, A. Alexandrescu, and L. Torner, Phys. Rev. A 68, 050301 (2003).
    [CrossRef]
  4. M. S. Bigelow, P. Zerom, and R. W. Boyd, Phys. Rev. Lett. 92, 083902 (2004).
    [CrossRef] [PubMed]
  5. W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
    [CrossRef]
  6. D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
    [CrossRef] [PubMed]
  7. M. R. Belic, A. Stepken, and F. Kaiser, Phys. Rev. Lett. 82, 544 (1999).
    [CrossRef]
  8. A. V. Buryak, Y. S. Kivshar, M.-f. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
    [CrossRef]
  9. M.-f. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
    [CrossRef]
  10. C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
    [CrossRef]
  11. A. S. Desyatnikov and Y. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
    [CrossRef] [PubMed]
  12. V. V. Steblina, Y. Kivshar, and A. V. Buryak, Opt. Lett. 23, 156 (1998).
    [CrossRef]
  13. C. Conti, Phys. Rev. E 72, 066620 (2005).
    [CrossRef]
  14. M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 31, 2030 (2006).
    [CrossRef] [PubMed]
  15. P. J. Olver, Applications of Lie Groups to Differential Equations (Springer-Verlag, 1986).
  16. M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Nature 432, 733 (2004).
    [CrossRef] [PubMed]
  17. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
    [CrossRef]
  18. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
    [CrossRef] [PubMed]
  19. V. E. Zakharov, What is Integrability? (Springer, 1990).
  20. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).
  21. D. N. Christodoulides and M. I. Carvalho, Opt. Lett. 19, 1714 (1994).
    [CrossRef] [PubMed]
  22. V. M. Perez-Garcia and V. Vekslerchik, Phys. Rev. E 67, 061804 (2003).
    [CrossRef]
  23. D. Kaup and A. Newell, Proc. R. Soc. London, Ser. A 361, 413 (1978).
    [CrossRef]

2006 (3)

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 31, 2030 (2006).
[CrossRef] [PubMed]

2005 (1)

C. Conti, Phys. Rev. E 72, 066620 (2005).
[CrossRef]

2004 (2)

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

M. S. Bigelow, P. Zerom, and R. W. Boyd, Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

2003 (3)

J. P. Torres, A. Alexandrescu, and L. Torner, Phys. Rev. A 68, 050301 (2003).
[CrossRef]

V. M. Perez-Garcia and V. Vekslerchik, Phys. Rev. E 67, 061804 (2003).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

2002 (2)

A. S. Desyatnikov and Y. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

1999 (2)

M. R. Belic, A. Stepken, and F. Kaiser, Phys. Rev. Lett. 82, 544 (1999).
[CrossRef]

A. V. Buryak, Y. S. Kivshar, M.-f. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

1998 (1)

1997 (2)

M.-f. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

1994 (1)

1987 (1)

R. J. van den Oord, M. C. de Lignie, J. J. M. Beenakker, and J. Korving, Phys. Rev. Lett. 59, 2907 (1987).
[CrossRef] [PubMed]

1978 (1)

D. Kaup and A. Newell, Proc. R. Soc. London, Ser. A 361, 413 (1978).
[CrossRef]

1976 (1)

A. D. Mcewan, Nature 260, 126 (1976).
[CrossRef]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Alexandrescu, A.

J. P. Torres, A. Alexandrescu, and L. Torner, Phys. Rev. A 68, 050301 (2003).
[CrossRef]

Alfassi, B.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

Assanto, G.

M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 31, 2030 (2006).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

Beenakker, J. J. M.

R. J. van den Oord, M. C. de Lignie, J. J. M. Beenakker, and J. Korving, Phys. Rev. Lett. 59, 2907 (1987).
[CrossRef] [PubMed]

Belic, M. R.

M. R. Belic, A. Stepken, and F. Kaiser, Phys. Rev. Lett. 82, 544 (1999).
[CrossRef]

Bigelow, M. S.

M. S. Bigelow, P. Zerom, and R. W. Boyd, Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Boyd, R. W.

M. S. Bigelow, P. Zerom, and R. W. Boyd, Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Buryak, A. V.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

A. V. Buryak, Y. S. Kivshar, M.-f. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

V. V. Steblina, Y. Kivshar, and A. V. Buryak, Opt. Lett. 23, 156 (1998).
[CrossRef]

Carvalho, M. I.

Christodoulides, D. N.

Cohen, O.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

Conti, C.

M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 31, 2030 (2006).
[CrossRef] [PubMed]

C. Conti, Phys. Rev. E 72, 066620 (2005).
[CrossRef]

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

de Lignie, M. C.

R. J. van den Oord, M. C. de Lignie, J. J. M. Beenakker, and J. Korving, Phys. Rev. Lett. 59, 2907 (1987).
[CrossRef] [PubMed]

Desyatnikov, A. S.

A. S. Desyatnikov and Y. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

Dyadyusha, A.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Firth, W. J.

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Kaczmarek, M.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Kaiser, F.

M. R. Belic, A. Stepken, and F. Kaiser, Phys. Rev. Lett. 82, 544 (1999).
[CrossRef]

Kaup, D.

D. Kaup and A. Newell, Proc. R. Soc. London, Ser. A 361, 413 (1978).
[CrossRef]

Kivshar, Y.

Kivshar, Y. S.

A. S. Desyatnikov and Y. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

A. V. Buryak, Y. S. Kivshar, M.-f. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Korving, J.

R. J. van den Oord, M. C. de Lignie, J. J. M. Beenakker, and J. Korving, Phys. Rev. Lett. 59, 2907 (1987).
[CrossRef] [PubMed]

Lederer, F.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Luca, A. D.

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

Malomed, B. A.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Mazilu, D.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Mcewan, A. D.

A. D. Mcewan, Nature 260, 126 (1976).
[CrossRef]

Mihalache, D.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Newell, A.

D. Kaup and A. Newell, Proc. R. Soc. London, Ser. A 361, 413 (1978).
[CrossRef]

Olver, P. J.

P. J. Olver, Applications of Lie Groups to Differential Equations (Springer-Verlag, 1986).

Peccianti, M.

M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 31, 2030 (2006).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

Perez-Garcia, V. M.

V. M. Perez-Garcia and V. Vekslerchik, Phys. Rev. E 67, 061804 (2003).
[CrossRef]

Rotschild, C.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

Salamo, G.

M.-f. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

Segev, M.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

A. V. Buryak, Y. S. Kivshar, M.-f. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

M.-f. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

Shih, M.-f.

A. V. Buryak, Y. S. Kivshar, M.-f. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

M.-f. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

Skryabin, D. V.

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Steblina, V. V.

Stepken, A.

M. R. Belic, A. Stepken, and F. Kaiser, Phys. Rev. Lett. 82, 544 (1999).
[CrossRef]

Torner, L.

J. P. Torres, A. Alexandrescu, and L. Torner, Phys. Rev. A 68, 050301 (2003).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Torres, J. P.

J. P. Torres, A. Alexandrescu, and L. Torner, Phys. Rev. A 68, 050301 (2003).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Towers, I.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Umeton, C.

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

van den Oord, R. J.

R. J. van den Oord, M. C. de Lignie, J. J. M. Beenakker, and J. Korving, Phys. Rev. Lett. 59, 2907 (1987).
[CrossRef] [PubMed]

Vekslerchik, V.

V. M. Perez-Garcia and V. Vekslerchik, Phys. Rev. E 67, 061804 (2003).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov, What is Integrability? (Springer, 1990).

Zerom, P.

M. S. Bigelow, P. Zerom, and R. W. Boyd, Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Nat. Phys. (2)

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

Nature (2)

A. D. Mcewan, Nature 260, 126 (1976).
[CrossRef]

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. Rev. A (1)

J. P. Torres, A. Alexandrescu, and L. Torner, Phys. Rev. A 68, 050301 (2003).
[CrossRef]

Phys. Rev. E (2)

C. Conti, Phys. Rev. E 72, 066620 (2005).
[CrossRef]

V. M. Perez-Garcia and V. Vekslerchik, Phys. Rev. E 67, 061804 (2003).
[CrossRef]

Phys. Rev. Lett. (9)

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

M. S. Bigelow, P. Zerom, and R. W. Boyd, Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

M. R. Belic, A. Stepken, and F. Kaiser, Phys. Rev. Lett. 82, 544 (1999).
[CrossRef]

A. V. Buryak, Y. S. Kivshar, M.-f. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

M.-f. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

R. J. van den Oord, M. C. de Lignie, J. J. M. Beenakker, and J. Korving, Phys. Rev. Lett. 59, 2907 (1987).
[CrossRef] [PubMed]

A. S. Desyatnikov and Y. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A (1)

D. Kaup and A. Newell, Proc. R. Soc. London, Ser. A 361, 413 (1978).
[CrossRef]

Other (3)

V. E. Zakharov, What is Integrability? (Springer, 1990).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

P. J. Olver, Applications of Lie Groups to Differential Equations (Springer-Verlag, 1986).

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Figures (3)

Fig. 1
Fig. 1

Sketch of the planar cell with NLCs: (a) front view and (b) top view with an indication of the molecular orientation (optic axis) in the plane ( y , z ) .

Fig. 2
Fig. 2

Summary of the experimental results: (a)–(d) evolution in the plane ( y , z ) and (e)–(h) output intensity profiles of the two-soliton cluster for increasing input powers P in [ 2.1 , 2.7 , 3.3 , 3.9 ] mW . The borders of the NLC cell are indicated with a solid line in (e)–(h).

Fig. 3
Fig. 3

(a), (b) Measured output spot size w of the two solitons normalized to w 0 = w ( 2.1 mW ) and (c) revolution angle δ versus input power P in .

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

L = 1 2 ( i ψ α * ψ α z + c.c. ) 1 2 ψ α * ψ α + 1 2 ψ α 2 Θ α β ψ β 2 ,
i ψ α z + 1 2 2 ψ α + ψ α Θ α β ψ β 2 = 0
M = d 2 r ( i ψ α * ψ α + c.c. ) ,
H = 1 2 d 2 r ( ψ α 2 Θ α β ψ β 2 ψ α * ψ α ) ,
A = d 2 r [ r × ( i ψ α * ψ α + c.c. ) ] ,
W = d 2 r ψ α 2 ,
z ψ α r ψ α = ψ α p ψ α ,
z ψ α p ψ α = ψ α Θ α ψ α ,
ψ α ( r ; z ) = ϕ ( r r α ) exp ( i μ z ) ,
m 2 q z 2 + q U ( q ) = 0 ,
U α β = d 2 r ϕ ( r q ) 2 Θ α ( r ) , α β .
E = m q ̇ q ̇ 2 + U ( q ) ,
L = m q × q ̇ .

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