Abstract

We demonstrate, theoretically and experimentally, incoherent surface solitons in a noninstantaneous nonlocal nonlinear media. These incoherent surface waves are located at the interface between a nonlinear medium with long-range nonlocality and a linear dielectric medium (air).

© 2007 Optical Society of America

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  9. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
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  19. W. Krolikowski, O. Bang, and J. Wyller, Phys. Rev. E 70, 036617 (2004).
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    [CrossRef]
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    [CrossRef]
  28. N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
    [CrossRef] [PubMed]
  29. C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
    [CrossRef]

2007 (2)

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Opt. Lett. 32, 154 (2007).
[CrossRef]

2006 (4)

M. Wu, P. Krivosik, B. A. Kalinikos, and C. E. Patton, Phys. Rev. Lett. 96, 227202 (2006).
[CrossRef] [PubMed]

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

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

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

2005 (4)

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef] [PubMed]

H. Buljan, M. Segev, and A. Vardi, Phys. Rev. Lett. 95, 180401 (2005).
[CrossRef] [PubMed]

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

2004 (4)

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, and J. Wyller, Phys. Rev. E 70, 036617 (2004).
[CrossRef]

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef] [PubMed]

2003 (2)

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 73901 (2003).
[CrossRef]

2001 (1)

1998 (1)

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

1997 (2)

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

M. Mitchell and M. Segev, Nature (London) 387, 880 (1997).
[CrossRef]

1996 (1)

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

1995 (2)

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

M. Cronin-Golomb, Opt. Lett. 20, 2075 (1995).
[CrossRef] [PubMed]

1986 (1)

S. K. Turitsyn, Theor. Math. Phys. 65, 797 (1986).

1980 (1)

1978 (1)

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

1968 (1)

F. W. Dabby and J. R. Whinnery, Appl. Phys. Lett. 13, 284 (1968).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich and D. L. Mills, Surface Polaritons (North-Holland, 1982).

Alfassi, B.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Opt. Lett. 32, 154 (2007).
[CrossRef]

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

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

Artigas, D.

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef] [PubMed]

Assanto, G.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 73901 (2003).
[CrossRef]

M. Peccianti and G. Assanto, Opt. Lett. 26, 1791 (2001).
[CrossRef]

Bang, O.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

W. Krolikowski, O. Bang, and J. Wyller, Phys. Rev. E 70, 036617 (2004).
[CrossRef]

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

Buljan, H.

H. Buljan, M. Segev, and A. Vardi, Phys. Rev. Lett. 95, 180401 (2005).
[CrossRef] [PubMed]

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Chen, Z.

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Cho, A. Y.

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Christiansen, P. L.

Christodoulides, D. N.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Opt. Lett. 32, 154 (2007).
[CrossRef]

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

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

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

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

Cohen, O.

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

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Conti, C.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 73901 (2003).
[CrossRef]

Coskun, T. H.

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

Cronin-Golomb, M.

Dabby, F. W.

F. W. Dabby and J. R. Whinnery, Appl. Phys. Lett. 13, 284 (1968).
[CrossRef]

Dreischuh, A.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

Edmundson, D.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

Garcia Quirino, G. S.

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Hache, A.

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

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

Haelterman, M.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef] [PubMed]

Kalinikos, B. A.

M. Wu, P. Krivosik, B. A. Kalinikos, and C. E. Patton, Phys. Rev. Lett. 96, 227202 (2006).
[CrossRef] [PubMed]

Krivosik, P.

M. Wu, P. Krivosik, B. A. Kalinikos, and C. E. Patton, Phys. Rev. Lett. 96, 227202 (2006).
[CrossRef] [PubMed]

Krolikowski, W.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, and J. Wyller, Phys. Rev. E 70, 036617 (2004).
[CrossRef]

Lange, C. H.

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

Lederer, F.

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

Makris, K. G.

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

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

Manela, O.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Opt. Lett. 32, 154 (2007).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Michaelis, D.

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

Millot, G.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef] [PubMed]

Mills, D. L.

V. M. Agranovich and D. L. Mills, Surface Polaritons (North-Holland, 1982).

Mitchell, M.

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

M. Mitchell and M. Segev, Nature (London) 387, 880 (1997).
[CrossRef]

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Neshev, D.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

Neshev, D. N.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

Nikolov, N. I.

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

Patton, C. E.

M. Wu, P. Krivosik, B. A. Kalinikos, and C. E. Patton, Phys. Rev. Lett. 96, 227202 (2006).
[CrossRef] [PubMed]

Peccianti, M.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 73901 (2003).
[CrossRef]

M. Peccianti and G. Assanto, Opt. Lett. 26, 1791 (2001).
[CrossRef]

Petersen, D. E.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

Picozzi, A.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef] [PubMed]

Pitois, S.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef] [PubMed]

Rasmussen, J. J.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

Rotschild, C.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Opt. Lett. 32, 154 (2007).
[CrossRef]

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

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Salamo, G.

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

Sanchez-Mondragon, J. J.

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Segev, M.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Opt. Lett. 32, 154 (2007).
[CrossRef]

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

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

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

H. Buljan, M. Segev, and A. Vardi, Phys. Rev. Lett. 95, 180401 (2005).
[CrossRef] [PubMed]

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

M. Mitchell and M. Segev, Nature (London) 387, 880 (1997).
[CrossRef]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997).
[CrossRef]

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Shih, M. F.

M. Mitchell, Z. Chen, M. F. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Sorel, M.

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

Stegeman, G. I.

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

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

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef] [PubMed]

Stepanov, S.

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Suntsov, S.

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

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Figures (3)

Fig. 1
Fig. 1

Normalized intensity distribution, I ( x ) , of an incoherent surface soliton comprised of three modes of weights d 1 = 0.8 , d 2 = 0.15 , and d 3 = 0.05 , and the induced index change, Δ n , for n 1 = 1.8 , n 2 = 1 , at maximal intensity of (a) 2.5 × 10 5 and (c) 2.5 × 10 7 [ W cm 2 ] . (b) Structures of the modes of the incoherent soliton shown in (a). (d) Incoherent surface soliton for n 1 = 1.8 , n 2 = 1.79998 , at maximal intensity of 2.5 × 10 5 [ W cm 2 ] .

Fig. 2
Fig. 2

Incoherent soliton of Fig. 1(a) (a) launched on its stable point and propagating on-axis, and (b) launched 70 μ m away from the interface, exhibiting self-bouncing.

Fig. 3
Fig. 3

Experimental photographs. (a) Incoherent input beam of 90 μ m FWHM and 30 μ m correlation distance launched near the interface. (b) At low power ( 100 mW ) the beam broadens to 230 μ m FWHM output. (c) At 2.5 W the beam forms an incoherent surface soliton, exiting the sample with the same width and location as the input. (d) 90 μ m FWHM incoherent beam launched with its center 100 μ m away from the interface. (e) At low power ( 100 mW ) the beam broadens to 230 μ m FWHM output, with its center 100 μ m away from the interface. (f) At 2.5 W the beam forms an incoherent surface soliton and is attracted to the interface, exiting the sample with a 90 μ m FWHM, and with its center 40 μ m away from the interface. (g) 90 μ m FWHM low power ( 100 mW ) spatially coherent beam launched near the interface, which (h) barely broadens within 8.3 cm propagation. (i) Cross section of the sample and temperature boundary conditions.

Equations (4)

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2 E + k 0 2 n 2 E = 0 .
d 2 u n ( x ) d x 2 + [ k 0 2 ( n 1 2 + 2 n 1 Δ n ) Γ n 2 ] u n ( x ) = 0 ,
d 2 u n ( x ) d x 2 + [ k 0 2 n 2 2 Γ n 2 ] u n ( x ) = 0 ,
d 2 Δ n ( x ) d x 2 = γ I ( x ) ,

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