Abstract

We present a numerical study of the giant Goos–Hänchen shifts (GHSs) obtained from an Airy beam impinging on a nonlinear interface. To avoid any angular restriction associated with the paraxial approximation, the analysis is based on the nonlinear Helmholtz equation. We report the existence of nonstandard nonlinear GHSs displaying an extreme sensitivity to the input intensity and the existence of multiple critical values. These intermittent and oscillatory regimes can be explained in terms of competition between critical coupling to a surface mode and soliton emission from the refracted beam component and how this interplay varies with localization of the initial Airy beam.

© 2014 Optical Society of America

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    [CrossRef]
  15. J. Sánchez-Curto, P. Chamorro-Posada, and G. S. McDonald, Opt. Lett. 36, 3605 (2011).
    [CrossRef]
  16. P. Chamorro-Posada and G. S. McDonald, J. Nonlinear Opt. Phys. Mater. 21, 1250031 (2012).
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    [CrossRef]
  19. H. Maaba, M. Faryadb, and A. Lakhtakiab, J. Mod. Opt. 60, 355 (2013).
    [CrossRef]

2013 (1)

H. Maaba, M. Faryadb, and A. Lakhtakiab, J. Mod. Opt. 60, 355 (2013).
[CrossRef]

2012 (2)

P. Chamorro-Posada and G. S. McDonald, J. Nonlinear Opt. Phys. Mater. 21, 1250031 (2012).

I. D. Chremmos and N. K. Efremidis, J. Opt. Soc. Am. A 29, 861 (2012).
[CrossRef]

2011 (2)

2010 (1)

2009 (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

2008 (1)

2007 (3)

2006 (1)

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

2001 (1)

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, Opt. Commun. 192, 1 (2001).
[CrossRef]

1998 (1)

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 45, 1111 (1998).
[CrossRef]

1989 (1)

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef]

1982 (1)

1979 (1)

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

1947 (1)

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).

Aceves, A. B.

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef]

Assanto, G.

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Opt. Lett. 32, 271 (2007).
[CrossRef]

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

Balazs, N. L.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Berry, M. V.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Broky, J.

Chamorro-Posada, P.

P. Chamorro-Posada and G. S. McDonald, J. Nonlinear Opt. Phys. Mater. 21, 1250031 (2012).

J. Sánchez-Curto, P. Chamorro-Posada, and G. S. McDonald, Opt. Lett. 36, 3605 (2011).
[CrossRef]

J. Sánchez-Curto, P. Chamorro-Posada, and G. S. McDonald, Opt. Lett. 32, 1126 (2007).
[CrossRef]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, Opt. Commun. 192, 1 (2001).
[CrossRef]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 45, 1111 (1998).
[CrossRef]

Chremmos, I. D.

Christodoulides, D. N.

Dogariu, A.

Dyadyusha, A.

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Opt. Lett. 32, 271 (2007).
[CrossRef]

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

Efremidis, N. K.

Faryadb, M.

H. Maaba, M. Faryadb, and A. Lakhtakiab, J. Mod. Opt. 60, 355 (2013).
[CrossRef]

Fattal, Y.

Gbur, G.

Goos, F.

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).

Gordon, J. P.

Gu, Y.

Hänchen, H.

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).

Kaczmarek, M.

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Opt. Lett. 32, 271 (2007).
[CrossRef]

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

Kaplan, A. E.

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

Lakhtakiab, A.

H. Maaba, M. Faryadb, and A. Lakhtakiab, J. Mod. Opt. 60, 355 (2013).
[CrossRef]

Maaba, H.

H. Maaba, M. Faryadb, and A. Lakhtakiab, J. Mod. Opt. 60, 355 (2013).
[CrossRef]

Marom, D. M.

McDonald, G. S.

P. Chamorro-Posada and G. S. McDonald, J. Nonlinear Opt. Phys. Mater. 21, 1250031 (2012).

J. Sánchez-Curto, P. Chamorro-Posada, and G. S. McDonald, Opt. Lett. 36, 3605 (2011).
[CrossRef]

J. Sánchez-Curto, P. Chamorro-Posada, and G. S. McDonald, Opt. Lett. 32, 1126 (2007).
[CrossRef]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, Opt. Commun. 192, 1 (2001).
[CrossRef]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 45, 1111 (1998).
[CrossRef]

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef]

New, G. H. C.

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, Opt. Commun. 192, 1 (2001).
[CrossRef]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 45, 1111 (1998).
[CrossRef]

Newell, A. C.

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef]

Peccianti, M.

M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Opt. Lett. 32, 271 (2007).
[CrossRef]

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

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

Rudnick, A.

Sánchez-Curto, J.

Siviloglou, G. A.

Smith, P. W.

Tomlinson, W. J.

Am. J. Phys. (1)

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Ann. Phys. (1)

F. Goos and H. Hänchen, Ann. Phys. 1, 333 (1947).

Appl. Opt. (1)

J. Mod. Opt. (2)

H. Maaba, M. Faryadb, and A. Lakhtakiab, J. Mod. Opt. 60, 355 (2013).
[CrossRef]

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, J. Mod. Opt. 45, 1111 (1998).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

P. Chamorro-Posada and G. S. McDonald, J. Nonlinear Opt. Phys. Mater. 21, 1250031 (2012).

J. Opt. Soc. Am. A (1)

Nat. Phys. (1)

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

Opt. Commun. (1)

P. Chamorro-Posada, G. S. McDonald, and G. H. C. New, Opt. Commun. 192, 1 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. A (1)

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef]

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

Other (1)

P. Chamorro-Posada, J. Sánchez-Curto, A. B. Aceves, and G. S. McDonald, “On the asymptotic evolution of finite energy Airy wavefunctions,” http://www.arxiv.org/abs/1305.3529 .

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Figures (5)

Fig. 1.
Fig. 1.

(a)–(c) Typical sequence in the critical coupling to a surface mode and giant GHS. (d)–(f) Typical soliton shedding sequence as α increases. In both cases a=0.1.

Fig. 2.
Fig. 2.

GHS for different values of ζ0 and (a) a=0.1 θ=1°, (b)–(d) a=0.2 θ=1°, (e) a=0.2 θ=2°, and (f) a=0.3 θ=1°.

Fig. 3.
Fig. 3.

Oscillations of giant GHS at θ=2°, a=0.2, and ζ0=5.

Fig. 4.
Fig. 4.

Setup of an intermittent GHS at a=0.3, θ=1°, and ζ0=6.

Fig. 5.
Fig. 5.

Intermittent GHS sequence for the second emitted soliton.

Equations (2)

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κ2uζ2+juζ+122uξ2Δl4κu+αl|u|2u=0,
u(ξ,ζ=0)=Ai(ξ+ξp)exp(a(ξ+ξp))

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