Abstract

We propose a new type of scalar wave-mixing optical solitons, Talbot solitons. The soliton consists of sinusoidal and uniform components that are mutually coherent and jointly trapped in one direction. The intensity structure of the soliton oscillates in the propagation direction as a result of the linear Talbot effect and periodic nonlinear energy exchange between the components. Talbot solitons induce a 1D waveguide and a 2D photonic lattice within the waveguide that may be used for quasi-phase matching of frequency conversion and as a tunable waveguide filter.

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References

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2006 (1)

2004 (1)

2003 (2)

M. Belic, Ph. Jander, A. Strinic, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, 025601 (2003).
[CrossRef]

J. R. Salgueiro, A. A. Sukhorukov, and Yu. S. Kivshar, Opt. Lett. 28, 1457 (2003).
[CrossRef] [PubMed]

2002 (3)

2000 (1)

C. Anastassiou, M. Soljacic, M. Segev, D. Kip, E. Eugenieva, D. N. Christodoulides, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (1)

M. Soljacic, S. Sears, and M. Segev, Phys. Rev. Lett. 81, 4851 (1998).
[CrossRef]

1997 (1)

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

1993 (1)

M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
[CrossRef]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

1985 (1)

A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

1974 (1)

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

1972 (1)

S. Somekh and A. Yariv, Appl. Phys. Lett. 21, 140 (1972).
[CrossRef]

Appl. Phys. Lett. (1)

S. Somekh and A. Yariv, Appl. Phys. Lett. 21, 140 (1972).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

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

Opt. Commun. (2)

A. Barthelemy, S. Maneuf, and C. Froehly, Opt. Commun. 55, 201 (1985).
[CrossRef]

M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Commun. 103, 145 (1993).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. E (1)

M. Belic, Ph. Jander, A. Strinic, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, 025601 (2003).
[CrossRef]

Phys. Rev. Lett. (4)

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacic, M. Segev, D. Kip, E. Eugenieva, D. N. Christodoulides, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

M. Soljacic, S. Sears, and M. Segev, Phys. Rev. Lett. 81, 4851 (1998).
[CrossRef]

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

Sov. Phys. JETP (1)

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

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Figures (3)

Fig. 1
Fig. 1

Talbot effect in ( 1 + 1 ) D nonlinear Kerr medium. (a) Maximum increase in the amplitude of the uniform field, normalized by its initial amplitude, as a function of the periodicity of the sinusoidal field. (b) Intensity versus propagation direction z and transversal dimension x. (c) Intensity oscillation owing to the Talbot effect at x = 0 and x = d 2 . (d) Numeric (solid curve) and analytic (dashed curve) calculations of the uniform field amplitude versus propagation direction. The oscillations result from nonlinear energy flow between the uniform and sinusoidal fields.

Fig. 2
Fig. 2

Talbot solitons wave functions. (a) Amplitude profiles of the uniform (solid curve) and sinusoidal (dashed curve) components of Talbot solitons with ϕ 2 ( 0 ) = 1 and ϕ 1 ( 0 ) = 0.2 . (b) Amplitude FWHM of the uniform (solid curve) and sinusoidal (dashed curve) components as a function of the uniform component peak amplitude. The peak amplitude of the sinusoidal component is fixed to 1.

Fig. 3
Fig. 3

Talbot soliton. (a) Intensity of the beam launched into the medium in the presence of 5% noise; intensity of the beam after propagation of (b) 5, (c) 10, and (d) 20 diffraction lengths, showing that the beam is trapped in the y direction. (e) Intensity oscillation due to the Talbot effect at ( x = 0 , y = 0 ) and ( x = d 2 , y = 0 ). (f) Numeric (solid curve) and analytic 1D model (dashed curve) calculation [Eq. (4)] of the uniform field amplitude versus propagation direction. The oscillations result from nonlinear energy flow between the uniform and sinusoidal fields.

Equations (7)

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i Ψ z + 2 Ψ x 2 + 2 Ψ y 2 + Ψ 2 Ψ = 0 .
Ψ = Ψ 0 sec h ( Ψ 0 y 3 8 ) cos ( k x ) exp [ i ( 3 Ψ 0 2 8 k 2 ) z ] ,
i Φ 1 z + Φ 1 y 2 + [ ϕ 1 2 + ϕ 2 2 2 ] Φ 1 = 2 ϕ 1 ϕ 2 cos ( δ z ) Φ 2 2 ,
i Φ 2 z + Φ 2 y 2 + [ ϕ 2 2 + 3 ϕ 1 2 4 k 2 ] Φ 2 = 2 ϕ 1 ϕ 2 cos ( δ z ) Φ 1 .
ϕ 1 ( z ) 2 = ϕ 1 ( 0 ) 2 C G [ ϕ 2 ( 0 ) 2 + ϕ 1 ( 0 ) 2 G ] ,
ϕ 1 y 2 + [ ϕ 1 2 + ϕ 2 2 2 ] ϕ 1 = α 1 ϕ 1 ,
ϕ 2 y 2 + [ ϕ 2 2 + 3 ϕ 1 2 4 k 2 ] ϕ 2 = α 2 ϕ 2 .

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