Abstract

Dynamical properties of counterpropagating (CP) mutually incoherent self-trapped beams in optically induced photonic lattices are investigated numerically. A local model with saturable Kerr-like nonlinearity is adopted for the photorefractive media, and an optically generated two-dimensional fixed photonic lattice introduced in the crystal. Different incident beam structures are considered, such as Gaussians and vortices of different topological charge. We observe spontaneous symmetry breaking of the head-on propagating Gaussian beams as the coupling strength is increased, resulting in the splitup transition of CP components. We see discrete diffraction, leading to the formation of discrete CP vector solitons. In the case of vortices, we find beam filamentation, as well as increased stability of the central vortex ring. A strong pinning of filaments to the lattice sites is noted. The angular momentum of vortices is not conserved, either along the propagation direction or in time, and, unlike the case without lattice, the rotation of filaments is not as readily observed.

© 2006 Optical Society of America

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References

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J. Opt. Soc. Am. B

Opt. Commun.

M. Haelterman, A. P. Sheppard, and A. W. Snyder, "Bimodal counterpropagating spatial solitary-waves," Opt. Commun. 103, 145 (1993).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Photonics News

Special Issue on solitons, Ed. M. Segev, Opt. Photonics News 13, No. 2 (2002).

Phys. Rev. E

M. Beli?, Ph. Jander, A. Strini?, A. Desyatnikov, and C. Denz, "Self-trapped bidirectional waveguides in a saturable photorefractive medium," Phys. Rev. E 68, 025601 (2003).
[CrossRef]

K. Motzek, Ph. Jander, A. Desyatnikov, M. Beli?, C. Denz, and F. Kaiser, "Dynamic counterpropagating vector solitons in saturable self-focusing media," Phys. Rev. E 68, 066611 (2003).
[CrossRef]

Phys. Rev. Lett.

M. Petrovi?, D. Jovi?, M. Beli?, J. Schröder, Ph. Jander, and C. Denz, "Two Dimensional Counterpropagating Spatial Solitons in Photorefractive Crystals," Phys. Rev. Lett. 95, 053901 (2005).
[CrossRef] [PubMed]

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odulov, "Collisions between optical spatial solitons propagating in opposite directions," Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, 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]

Prog. Opt.

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, "Optical vortices and vortex solitons," Prog. Opt. 47, (2005).
[CrossRef]

Other

S. Trillo, and W. Torruellas eds., Spatial Solitons (Springer, New York, 2001).

Y. S. Kivshar, and G. P. Agrawal, Optical Solitons (Academic Press, San Diego, 2003).

Supplementary Material (10)

» Media 1: MOV (767 KB)     
» Media 2: MOV (744 KB)     
» Media 3: MOV (601 KB)     
» Media 4: MOV (1088 KB)     
» Media 5: MOV (754 KB)     
» Media 6: MOV (603 KB)     
» Media 7: MOV (1603 KB)     
» Media 8: MOV (441 KB)     
» Media 9: MOV (497 KB)     
» Media 10: MOV (628 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Movies of the intensity distributions of the backward field at its output face, for various FWHM of input beams: (a) 11 μm (768 KB) [Media 1], (b) 9 μm (745 KB) [Media 2], (c) 7 μm (602 KB) [Media 3], (d) 5 μm (1.1 MB) [Media 4]. For FWHM=5 μm no steady state is observed. Parameters: lattice spacing 28 μm, FWHM of lattice beams 9 μm, maximum lattice intensity Ig =10Id , Γ=19.3, L=2LD =8 mm, |F0 | 2 =|BL | 2 =10.

Fig. 2.
Fig. 2.

Movies of the intensity distributions of the backward field at its output face for various coupling strengths: (a) Γ=16.6, L=1.3LD , (755 KB) [Media 5] (b) Γ=19.3, L=2.5LD (603 KB) [Media 6]. (c) Isosurface plots at 10% of maximum intensity for the case presented in Fig. 2(b) and in the steady state; green - forward beam, red - backward beam, white - lattice beams. Other parameters are as in Fig. 1(a).

Fig. 3.
Fig. 3.

Intensity (upper row) and phase (lower row) distributions of the backward field at its output face in the steady state, for different topological charges, recorded on the top of each figure. Parameters are as in Fig. 1, input FWHM of vortices is 26.2 μm.

Fig. 4.
Fig. 4.

Rotating vortex, backward field: (a) Movie of the intensity distribution in the real space (1.603 MB) [Media 7]. (b) Movie of the time evolution of the total angular momentum of the backward beam (441 KB) [Media 8]. (c) Movie of the time evolution of the sum of angular momenta of both fields (498 KB) [Media 9]. (d) Movie of the time evolution of the angular momentum of the total field F+B (629 KB) [Media 10]. Total angular momentum is normalized to the total beam intensity. Parameters: lattice spacing 28 μm, FWHM of lattice beams 9 μm, maximum lattice intensity Ig =5Id , Γ=16.55, L=2.5LD =10 mm, |F0 |2=|BL |2=5, input FWHM of vortices 26.2 μm.

Equations (3)

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i z F = Δ F + Γ EF , i z B = Δ B + Γ EB ,
τ t E + E = I 1 + I ,
τ t E + E = I + I g 1 + I + I g ,

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