Abstract

In this work, we numerically characterize the waveguide properties of the asymmetric collision between two bright spatial solitons in a nonlinear Kerr media. The results demonstrate that the energy carried by a probe beam guided by one soliton can be transferred after the collision to the waveguide created by the other soliton depending on the initial separation between the solitons, the angle of their collision, and in some cases, the particular soliton that initially guides the probe beam. The observed behavior is equivalent to that obtained for the symmetrical collision when there is an initial relative phase between the solitons.

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References

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  1. A. W. Synder and D. J. Mitchell, “Accessible solitons,” Science276(5318), 1538–1541 (1997).
    [CrossRef]
  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1989).
  3. Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic Press, 2003).
  4. R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett.13(15), 479–482 (1964).
    [CrossRef]
  5. B. Luther-Davies and Y. Xiaoping, “Waveguides and Y junctions formed in bulk media by using dark spatial solitons,” Opt. Lett.17(7), 496–498 (1992).
    [CrossRef] [PubMed]
  6. G. E. Torres-Cisneros, J. J. Sánchez-Mondragon, and V. A. Vysloukh, “Asymmetric optical Y junctions and switching of weak beams using bright spatial-soliton collisions,” Opt. Lett.18(16), 1299–1301 (1993).
    [CrossRef] [PubMed]
  7. B. L. Davies and X. Yang, “Steerable optical waveguides formed in self-defocusing media by using dark spatial solitons,” Opt. Lett.17, 496–498 (1992).
    [CrossRef] [PubMed]
  8. N. Akhmediev and A. Ankiewicz, “Spatial soliton X-junctions and couplers,” Opt. Commun.100(1-4), 186–192 (1993).
    [CrossRef]
  9. P. D. Miller and N. N. Akhmediev, “Transfer matrices for multiport devices made from solitons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics53(4), 4098–4106 (1996).
    [CrossRef] [PubMed]
  10. Y. Kodama and A. Hasegawa, “Effects of initial overlap on the propagation of optical solitons at different wavelengths,” Opt. Lett.16(4), 208–210 (1991).
    [CrossRef] [PubMed]
  11. M. Shalaby and A. Barthelemy, “Ultrafast photonic switching and splitting through cross-phase modulation with a spatial solitons couple,” Opt. Commun.94(5), 341–345 (1992).
    [CrossRef]
  12. J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. Smith, “Experimental observation of spatial soliton interactions,” Opt. Lett.16(1), 15–17 (1991).
    [CrossRef] [PubMed]
  13. J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. Smith, “Spatial optical solitons in planar glass waveguides,” J. Opt. Soc. Am. B8(6), 1290–1297 (1991).
    [CrossRef]
  14. M. Shalaby, F. Reynaud, and A. Barthelemy, “Experimental observation of spatial soliton interactions with a π/2 relative phase difference,” Opt. Lett.17(11), 778–780 (1992).
    [CrossRef] [PubMed]
  15. P. Chamorro-Posada and G. S. McDonald, “Spatial Kerr soliton collisions at arbitrary angles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(3), 036609 (2006).
    [CrossRef] [PubMed]
  16. K. Steiglitz and D. Rand, “Photon trapping and transfer with solitons,” Phys. Rev. A79(2), 021802 (2009).
    [CrossRef]
  17. K. Steiglitz, “Soliton-guided phase shifter and beam splitter,” Phys. Rev. A81(3), 033835 (2010).
    [CrossRef]
  18. K. Steiglitz, “Making beam splitters with dark soliton collisions,” Phys. Rev. A82(4), 043831 (2010).
    [CrossRef]
  19. D. Ramirez Martinez, M. M. Mendez Otero, M. L. Arroyo Carrasco, and M. D. Iturbe Castillo, “Alternative (1+1)-D dark spatial soliton-like distributions in Kerr media,” J. Phys. Sci. Appl.1, 196–203 (2011).

2011 (1)

D. Ramirez Martinez, M. M. Mendez Otero, M. L. Arroyo Carrasco, and M. D. Iturbe Castillo, “Alternative (1+1)-D dark spatial soliton-like distributions in Kerr media,” J. Phys. Sci. Appl.1, 196–203 (2011).

2010 (2)

K. Steiglitz, “Soliton-guided phase shifter and beam splitter,” Phys. Rev. A81(3), 033835 (2010).
[CrossRef]

K. Steiglitz, “Making beam splitters with dark soliton collisions,” Phys. Rev. A82(4), 043831 (2010).
[CrossRef]

2009 (1)

K. Steiglitz and D. Rand, “Photon trapping and transfer with solitons,” Phys. Rev. A79(2), 021802 (2009).
[CrossRef]

2006 (1)

P. Chamorro-Posada and G. S. McDonald, “Spatial Kerr soliton collisions at arbitrary angles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(3), 036609 (2006).
[CrossRef] [PubMed]

1997 (1)

A. W. Synder and D. J. Mitchell, “Accessible solitons,” Science276(5318), 1538–1541 (1997).
[CrossRef]

1996 (1)

P. D. Miller and N. N. Akhmediev, “Transfer matrices for multiport devices made from solitons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics53(4), 4098–4106 (1996).
[CrossRef] [PubMed]

1993 (2)

1992 (4)

1991 (3)

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett.13(15), 479–482 (1964).
[CrossRef]

Aitchison, J. S.

Akhmediev, N.

N. Akhmediev and A. Ankiewicz, “Spatial soliton X-junctions and couplers,” Opt. Commun.100(1-4), 186–192 (1993).
[CrossRef]

Akhmediev, N. N.

P. D. Miller and N. N. Akhmediev, “Transfer matrices for multiport devices made from solitons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics53(4), 4098–4106 (1996).
[CrossRef] [PubMed]

Ankiewicz, A.

N. Akhmediev and A. Ankiewicz, “Spatial soliton X-junctions and couplers,” Opt. Commun.100(1-4), 186–192 (1993).
[CrossRef]

Arroyo Carrasco, M. L.

D. Ramirez Martinez, M. M. Mendez Otero, M. L. Arroyo Carrasco, and M. D. Iturbe Castillo, “Alternative (1+1)-D dark spatial soliton-like distributions in Kerr media,” J. Phys. Sci. Appl.1, 196–203 (2011).

Barthelemy, A.

M. Shalaby, F. Reynaud, and A. Barthelemy, “Experimental observation of spatial soliton interactions with a π/2 relative phase difference,” Opt. Lett.17(11), 778–780 (1992).
[CrossRef] [PubMed]

M. Shalaby and A. Barthelemy, “Ultrafast photonic switching and splitting through cross-phase modulation with a spatial solitons couple,” Opt. Commun.94(5), 341–345 (1992).
[CrossRef]

Chamorro-Posada, P.

P. Chamorro-Posada and G. S. McDonald, “Spatial Kerr soliton collisions at arbitrary angles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(3), 036609 (2006).
[CrossRef] [PubMed]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett.13(15), 479–482 (1964).
[CrossRef]

Davies, B. L.

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett.13(15), 479–482 (1964).
[CrossRef]

Hasegawa, A.

Iturbe Castillo, M. D.

D. Ramirez Martinez, M. M. Mendez Otero, M. L. Arroyo Carrasco, and M. D. Iturbe Castillo, “Alternative (1+1)-D dark spatial soliton-like distributions in Kerr media,” J. Phys. Sci. Appl.1, 196–203 (2011).

Jackel, J. L.

Kodama, Y.

Leaird, D. E.

Luther-Davies, B.

McDonald, G. S.

P. Chamorro-Posada and G. S. McDonald, “Spatial Kerr soliton collisions at arbitrary angles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(3), 036609 (2006).
[CrossRef] [PubMed]

Mendez Otero, M. M.

D. Ramirez Martinez, M. M. Mendez Otero, M. L. Arroyo Carrasco, and M. D. Iturbe Castillo, “Alternative (1+1)-D dark spatial soliton-like distributions in Kerr media,” J. Phys. Sci. Appl.1, 196–203 (2011).

Miller, P. D.

P. D. Miller and N. N. Akhmediev, “Transfer matrices for multiport devices made from solitons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics53(4), 4098–4106 (1996).
[CrossRef] [PubMed]

Mitchell, D. J.

A. W. Synder and D. J. Mitchell, “Accessible solitons,” Science276(5318), 1538–1541 (1997).
[CrossRef]

Oliver, M. K.

Ramirez Martinez, D.

D. Ramirez Martinez, M. M. Mendez Otero, M. L. Arroyo Carrasco, and M. D. Iturbe Castillo, “Alternative (1+1)-D dark spatial soliton-like distributions in Kerr media,” J. Phys. Sci. Appl.1, 196–203 (2011).

Rand, D.

K. Steiglitz and D. Rand, “Photon trapping and transfer with solitons,” Phys. Rev. A79(2), 021802 (2009).
[CrossRef]

Reynaud, F.

Sánchez-Mondragon, J. J.

Shalaby, M.

M. Shalaby and A. Barthelemy, “Ultrafast photonic switching and splitting through cross-phase modulation with a spatial solitons couple,” Opt. Commun.94(5), 341–345 (1992).
[CrossRef]

M. Shalaby, F. Reynaud, and A. Barthelemy, “Experimental observation of spatial soliton interactions with a π/2 relative phase difference,” Opt. Lett.17(11), 778–780 (1992).
[CrossRef] [PubMed]

Silberberg, Y.

Smith, P. W.

Steiglitz, K.

K. Steiglitz, “Soliton-guided phase shifter and beam splitter,” Phys. Rev. A81(3), 033835 (2010).
[CrossRef]

K. Steiglitz, “Making beam splitters with dark soliton collisions,” Phys. Rev. A82(4), 043831 (2010).
[CrossRef]

K. Steiglitz and D. Rand, “Photon trapping and transfer with solitons,” Phys. Rev. A79(2), 021802 (2009).
[CrossRef]

Synder, A. W.

A. W. Synder and D. J. Mitchell, “Accessible solitons,” Science276(5318), 1538–1541 (1997).
[CrossRef]

Torres-Cisneros, G. E.

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett.13(15), 479–482 (1964).
[CrossRef]

Vysloukh, V. A.

Weiner, A. M.

Xiaoping, Y.

Yang, X.

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

J. Phys. Sci. Appl. (1)

D. Ramirez Martinez, M. M. Mendez Otero, M. L. Arroyo Carrasco, and M. D. Iturbe Castillo, “Alternative (1+1)-D dark spatial soliton-like distributions in Kerr media,” J. Phys. Sci. Appl.1, 196–203 (2011).

Opt. Commun. (2)

M. Shalaby and A. Barthelemy, “Ultrafast photonic switching and splitting through cross-phase modulation with a spatial solitons couple,” Opt. Commun.94(5), 341–345 (1992).
[CrossRef]

N. Akhmediev and A. Ankiewicz, “Spatial soliton X-junctions and couplers,” Opt. Commun.100(1-4), 186–192 (1993).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. A (3)

K. Steiglitz and D. Rand, “Photon trapping and transfer with solitons,” Phys. Rev. A79(2), 021802 (2009).
[CrossRef]

K. Steiglitz, “Soliton-guided phase shifter and beam splitter,” Phys. Rev. A81(3), 033835 (2010).
[CrossRef]

K. Steiglitz, “Making beam splitters with dark soliton collisions,” Phys. Rev. A82(4), 043831 (2010).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

P. Chamorro-Posada and G. S. McDonald, “Spatial Kerr soliton collisions at arbitrary angles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.74(3), 036609 (2006).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

P. D. Miller and N. N. Akhmediev, “Transfer matrices for multiport devices made from solitons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics53(4), 4098–4106 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett.13(15), 479–482 (1964).
[CrossRef]

Science (1)

A. W. Synder and D. J. Mitchell, “Accessible solitons,” Science276(5318), 1538–1541 (1997).
[CrossRef]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1989).

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

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Figures (8)

Fig. 1
Fig. 1

Asymmetric collision of two bright spatial solitons with V = 1.

Fig. 2
Fig. 2

Propagation of a probe beam in the waveguide photo-induced by soliton S2 with V = 1, and initial separations c: (a) 10.5, (b) 11.5, (c) 12.5, (d) 16.

Fig. 3
Fig. 3

Normalized confined energy E1 (square) for the waveguide photo-induced by soliton S1 and E2 (circle) for the waveguide photo-induced by soliton S2 as function of c, for an asymmetric collision with V = 1 when the probe beam was initially confined by S2.

Fig. 4
Fig. 4

Propagation of the probe beam given by the sum of a sech mode and a high order mode when was initially guided by S2 for the asymmetric collision of solitons with V = 1 and c = 8.

Fig. 5
Fig. 5

Propagation of the probe beam, with V = 2 and c = 8, when it was initially guided by: (a) S1 and (b) S2.

Fig. 6
Fig. 6

Propagation of a probe beam given by the sum of a sech mode and a high order mode for an asymmetric collision with V = 2 and c = 8 when the probe beam was initially guided by: (a) S1 and (b) S2.

Fig. 7
Fig. 7

Normalized confinement energy E1 (square) for the waveguide photoinduced by soliton S1, and E2 (circle) for the waveguide photo-induced by soliton S2 as function of c, for an asymmetric collision of solitons with V = 2, when the probe beam was initially guided by: (a) S1 and (b) S2. (c) Normalized confinement energy for each waveguide where the probe beam was initially guided by: S1 (square) and S2 (circle).

Fig. 8
Fig. 8

(a) Collision between three solitons: one with V = 1 and the other two with V = 0, separation between them of c = 8. (b) Behavior of the probe beam initially guided by the central soliton.

Equations (7)

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i q 1 Z = 1 4 2 q 1 X 2 ± L D L NL | q 1 | 2 q 1 ,
i q 2 Z = 1 4 r n r k 2 q 2 X 2 ± 2 L D r k L NL | q 1 | 2 q 2 ,
q 1 (X,Z)=sech( 2 X)exp(-iZ/2),
q 1 (X,Z)=tanh( 2 X)exp(-iZ).
q 1 (X)=sech( 2 1/2 X)+sech( 2 1/2 (X+c))exp(-iV(X+c)),
q 2 (X)=exp(-w X 2 ),
q 1 (X)=[sech( 2 1/2 (X+c))+(X+c)sech( 2 1/2 (X+c))]exp(-iV(X+c)).

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