Abstract

We theoretically demonstrate that optical discrete X-waves are possible in normally dispersive nonlinear waveguide arrays. We show that such X-waves can be effectively excited for a wide range of initial conditions and in certain occasions can be generated in cascade. The possibility of observing this family of waves in AlGaAs array systems is investigated in terms of pertinent examples.

© 2005 Optical Society of America

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References

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IEEE Trans. Ultrason. Ferroelectr. Freq. (1)

J. Y. Lu and J. F. Greenleaf, �??Nondiffracting X waves-exact solutions to free-space scalar wave equation and their finite aperture realizations,�?? IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19 (1992).
[CrossRef] [PubMed]

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

Nature (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, �??Discretizing light behaviour in linear and nonlinear waveguide lattices,�?? Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, �??Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,�?? Nature 422, 147�??150 (2003).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. E (1)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, �??Discrete solitons in photorefractive optically induced photonic lattices,�?? Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Phys. Rev. Lett (1)

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, �??Spontaneously Generated X-Shaped Light Bullets,�?? Phys. Rev. Lett. 91, 093904 (2003).,�?? Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef] [PubMed]

Phys. Rev. Lett. (11)

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, �??Nonlinear Electromagnetic X Waves,�?? Phys. Rev. Lett. 90, 093904 (2003).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, �??Diffraction management,�?? Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, �??Dynamics of discrete solitons in optical waveguide arrays,�?? Phys. Rev. Lett. 83, 2726�??2729 (1999).
[CrossRef]

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, �??Discrete vector solitons in Kerr nonlinear waveguide arrays,�?? Phys. Rev. Lett. 91, 143907 (2003).J
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, �??Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,�?? Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, �??Observation of discrete quadratic solitons,�?? Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, �??Experimental observation of discrete modulational instability,�?? Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, �??Observation of discrete solitons in optically induced real time waveguide arrays,�?? Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, �??Gap solitons in waveguide arrays,�?? Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, �??Observation of vortex-ring �??discrete�?? solitons in 2D photonic lattices,�?? Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, and Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, �??Observation of discrete vortex solitons in optically induced photonic lattices,�?? Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Supplementary Material (1)

» Media 1: MOV (335 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Output intensity profile at z=1cm in an AlGaAs array, when the central channel is excited with a sech-pulse of 1ps duration (1.76ps FWHM) and 0.5kW peak-power; (a) contour plot and (b) three-dimensional depiction.

Fig. 2.
Fig. 2.

Output intensity profile at z=1cm in an AlGaAs array, when the central channel is excited with a sech-pulse of 1ps duration (1.76ps FWHM) and 0.7kW peak-power; (a) contour plot movie (336 KB) and (b) three-dimensional depiction. [Media 1]

Fig. 3.
Fig. 3.

Output intensity profile at z=1cm in an AlGaAs array, when the central channel is excited with a sech-pulse of 1ps duration (1.76ps FWHM) and 1.5kW peak-power; (a) contour plot and (b) three-dimensional depiction.

Fig. 4.
Fig. 4.

Output intensity profile at z=1cm in an AlGaAs array, when the central channel is excited with a sech-pulse of 200fs duration (352fs FWHM) and 1.5kW peak-power; (a) contour plot and (b) three-dimensional depiction.

Fig. 5.
Fig. 5.

Input (a) and output (b) intensity profile at z=1cm in an AlGaAs array, when the central channel is excited with a sech-type Gaussian beam of 1ps and 0.5kW peak-power at the central waveguide. The initial phase difference among excited waveguides is 0.

Fig. 6.
Fig. 6.

(a) Output intensity profile at z=1cm in an AlGaAs array, when the central channel is excited with a sech-type Gaussian beam of 1ps and 0.5kW peak-power at the central waveguide. The initial phase difference among excited waveguides is π. (b) Output intensity profile at z=1cm in an AlGaAs array, when the central channel is excited with a sech-type Gaussian beam of 1ps and 0.5kW peak-power at the central waveguide. The initial phase difference among excited waveguides is π/2.

Equations (2)

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i U n z β 2 2 2 U n t 2 + C [ U n + 1 + U n 1 ] + k 0 n 2 U n 2 U n = 0 ,
P = n + U n 2 d t , H = n + { β 2 2 U n t 2 γ 2 U n 4 C 0 ( U n * U n + 1 + U n U n + 1 * ) } d t

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