Abstract

Spatial-soliton interactions with continuous waves (cw’s) are studied, with numerical simulations as well as a quasi-particle perturbation method, and the critical dependency of their features on the parameters of the cw is shown. The intentional mixing of appropriately launched cw’s with spatial solitons is proposed as a technique for the design and implementation of all-optical, dynamically reconfigurable devices.

© 2004 Optical Society of America

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  1. J. S. Aitchison, A. M. Weiner, Y. Silderberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, “Observation of spatial optical solitons in a nonlinear glass waveguide,” Opt. Lett. 15, 471–473 (1990).
    [CrossRef] [PubMed]
  2. E. Fazio, M. Zitelli, M. Bertolotti, A. Carrera, N. G. Sanvito, and G. Chiaretti, “Solitonic waveguides in planar glass structures,” Opt. Commun. 185, 331–336 (2000).
    [CrossRef]
  3. M. Peccianti and G. Assanto, “Signal readdressing by steering of spatial solitons in bulk nematic liquid crystals,” Opt. Lett. 26, 1690–1692 (2001).
    [CrossRef]
  4. A. Buryak, P. Di Traponi, D. Skryabin, and S. Trillo, “Opti-cal solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
    [CrossRef]
  5. L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, “Beamsteering by χ(2) trapping,” Opt. Lett. 20, 1952–1954 (1995).
    [CrossRef] [PubMed]
  6. A. W. Snyder and D. J. Mitchell, “Spatial solitons of the power-law nonlinearity,” Opt. Lett. 18, 101–103 (1993).
    [CrossRef] [PubMed]
  7. D. N. Christodoulides and M. I. Carvalho, “Bright, dark, and gray spatial solitons states in photorefractive media,” J. Opt. Soc. Am. B 12, 1628–1633 (1995).
    [CrossRef]
  8. A. W. Snyder, D. J. Mitchell, L. Poladian, and F. Ladouceur, “Self-induced optical fibers: spatial solitary waves,” Opt. Lett. 16, 21–23 (1991).
    [CrossRef] [PubMed]
  9. B. Luther-Davies and Y. Xiaoping, “Waveguides and Y-junctions formed in bulk media by using dark spatial solitons,” Opt. Lett. 17, 496–498 (1992).
    [CrossRef] [PubMed]
  10. N. N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fibre couplers,” Phys. Rev. Lett. 70, 2395–2398 (1993).
    [CrossRef] [PubMed]
  11. J. J. Rasmussen and K. Ripdal, “Blow-up in nonlinear Schrödinger equation. I. A general review,” Phys. Scr. 33, 481–497 (1986).
    [CrossRef]
  12. A. W. Snyder, A. V. Buryak, and D. J. Mitchell, “Beam splitting on weak illumination,” Opt. Lett. 23, 4–6 (1998).
    [CrossRef]
  13. A. Hasegawa and Y. Kodama, “Amplification and reshaping of optical solitons in a glass fiber. I,” Opt. Lett. 7, 285–287 (1982).
    [CrossRef] [PubMed]
  14. N. N. Akhmediev and S. Wabnitz, “Phase detecting of solitons by mixing with a continuous-wave background in an optical fiber,” J. Opt. Soc. Am. B 9, 236–242 (1992).
    [CrossRef]
  15. R. W. Boyd, Nonlinear Optics (Academic, New York, 1992).
  16. J. M. Harbold, F. Ö. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett. 27, 119–121 (2002).
    [CrossRef]
  17. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, Oxford, 1995).
  18. J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
    [CrossRef]
  19. R. Scharf and A. R. Bishop, “Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials,” Phys. Rev. E 47, 1375–1383 (1993).
    [CrossRef]

2002 (2)

A. Buryak, P. Di Traponi, D. Skryabin, and S. Trillo, “Opti-cal solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

J. M. Harbold, F. Ö. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett. 27, 119–121 (2002).
[CrossRef]

2001 (1)

2000 (2)

E. Fazio, M. Zitelli, M. Bertolotti, A. Carrera, N. G. Sanvito, and G. Chiaretti, “Solitonic waveguides in planar glass structures,” Opt. Commun. 185, 331–336 (2000).
[CrossRef]

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

1998 (1)

1995 (2)

1993 (3)

A. W. Snyder and D. J. Mitchell, “Spatial solitons of the power-law nonlinearity,” Opt. Lett. 18, 101–103 (1993).
[CrossRef] [PubMed]

R. Scharf and A. R. Bishop, “Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials,” Phys. Rev. E 47, 1375–1383 (1993).
[CrossRef]

N. N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fibre couplers,” Phys. Rev. Lett. 70, 2395–2398 (1993).
[CrossRef] [PubMed]

1992 (2)

1991 (1)

1990 (1)

1986 (1)

J. J. Rasmussen and K. Ripdal, “Blow-up in nonlinear Schrödinger equation. I. A general review,” Phys. Scr. 33, 481–497 (1986).
[CrossRef]

1982 (1)

Aggarwal, I. D.

Aitchison, J. S.

Akhmediev, N. N.

N. N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fibre couplers,” Phys. Rev. Lett. 70, 2395–2398 (1993).
[CrossRef] [PubMed]

N. N. Akhmediev and S. Wabnitz, “Phase detecting of solitons by mixing with a continuous-wave background in an optical fiber,” J. Opt. Soc. Am. B 9, 236–242 (1992).
[CrossRef]

Ankiewicz, A.

N. N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fibre couplers,” Phys. Rev. Lett. 70, 2395–2398 (1993).
[CrossRef] [PubMed]

Assanto, G.

Bertolotti, M.

E. Fazio, M. Zitelli, M. Bertolotti, A. Carrera, N. G. Sanvito, and G. Chiaretti, “Solitonic waveguides in planar glass structures,” Opt. Commun. 185, 331–336 (2000).
[CrossRef]

Bishop, A. R.

R. Scharf and A. R. Bishop, “Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials,” Phys. Rev. E 47, 1375–1383 (1993).
[CrossRef]

Buryak, A.

A. Buryak, P. Di Traponi, D. Skryabin, and S. Trillo, “Opti-cal solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Buryak, A. V.

Carrera, A.

E. Fazio, M. Zitelli, M. Bertolotti, A. Carrera, N. G. Sanvito, and G. Chiaretti, “Solitonic waveguides in planar glass structures,” Opt. Commun. 185, 331–336 (2000).
[CrossRef]

Carvalho, M. I.

Chiaretti, G.

E. Fazio, M. Zitelli, M. Bertolotti, A. Carrera, N. G. Sanvito, and G. Chiaretti, “Solitonic waveguides in planar glass structures,” Opt. Commun. 185, 331–336 (2000).
[CrossRef]

Christodoulides, D. N.

Di Traponi, P.

A. Buryak, P. Di Traponi, D. Skryabin, and S. Trillo, “Opti-cal solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Doran, N. J.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

Fazio, E.

E. Fazio, M. Zitelli, M. Bertolotti, A. Carrera, N. G. Sanvito, and G. Chiaretti, “Solitonic waveguides in planar glass structures,” Opt. Commun. 185, 331–336 (2000).
[CrossRef]

Forysiak, W.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

Harbold, J. M.

Hasegawa, A.

Ilday, F. Ö.

Jackel, J. L.

Kodama, Y.

Ladouceur, F.

Leaird, D. E.

Luther-Davies, B.

Menyuk, C. R.

Mitchell, D. J.

Nguyen, V. Q.

Nijhof, J. H. B.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

Oliver, M. K.

Peccianti, M.

Poladian, L.

Rasmussen, J. J.

J. J. Rasmussen and K. Ripdal, “Blow-up in nonlinear Schrödinger equation. I. A general review,” Phys. Scr. 33, 481–497 (1986).
[CrossRef]

Ripdal, K.

J. J. Rasmussen and K. Ripdal, “Blow-up in nonlinear Schrödinger equation. I. A general review,” Phys. Scr. 33, 481–497 (1986).
[CrossRef]

Sanghera, J. S.

Sanvito, N. G.

E. Fazio, M. Zitelli, M. Bertolotti, A. Carrera, N. G. Sanvito, and G. Chiaretti, “Solitonic waveguides in planar glass structures,” Opt. Commun. 185, 331–336 (2000).
[CrossRef]

Scharf, R.

R. Scharf and A. R. Bishop, “Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials,” Phys. Rev. E 47, 1375–1383 (1993).
[CrossRef]

Shaw, L. B.

Silderberg, Y.

Skryabin, D.

A. Buryak, P. Di Traponi, D. Skryabin, and S. Trillo, “Opti-cal solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Smith, P. W. E.

Snyder, A. W.

Stegeman, G. I.

Torner, L.

Torruellas, W. E.

Trillo, S.

A. Buryak, P. Di Traponi, D. Skryabin, and S. Trillo, “Opti-cal solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Vogel, E. M.

Wabnitz, S.

Weiner, A. M.

Wise, F. W.

Xiaoping, Y.

Zitelli, M.

E. Fazio, M. Zitelli, M. Bertolotti, A. Carrera, N. G. Sanvito, and G. Chiaretti, “Solitonic waveguides in planar glass structures,” Opt. Commun. 185, 331–336 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

E. Fazio, M. Zitelli, M. Bertolotti, A. Carrera, N. G. Sanvito, and G. Chiaretti, “Solitonic waveguides in planar glass structures,” Opt. Commun. 185, 331–336 (2000).
[CrossRef]

Opt. Lett. (9)

A. Hasegawa and Y. Kodama, “Amplification and reshaping of optical solitons in a glass fiber. I,” Opt. Lett. 7, 285–287 (1982).
[CrossRef] [PubMed]

J. S. Aitchison, A. M. Weiner, Y. Silderberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, “Observation of spatial optical solitons in a nonlinear glass waveguide,” Opt. Lett. 15, 471–473 (1990).
[CrossRef] [PubMed]

A. W. Snyder, D. J. Mitchell, L. Poladian, and F. Ladouceur, “Self-induced optical fibers: spatial solitary waves,” Opt. Lett. 16, 21–23 (1991).
[CrossRef] [PubMed]

B. Luther-Davies and Y. Xiaoping, “Waveguides and Y-junctions formed in bulk media by using dark spatial solitons,” Opt. Lett. 17, 496–498 (1992).
[CrossRef] [PubMed]

A. W. Snyder and D. J. Mitchell, “Spatial solitons of the power-law nonlinearity,” Opt. Lett. 18, 101–103 (1993).
[CrossRef] [PubMed]

L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, “Beamsteering by χ(2) trapping,” Opt. Lett. 20, 1952–1954 (1995).
[CrossRef] [PubMed]

A. W. Snyder, A. V. Buryak, and D. J. Mitchell, “Beam splitting on weak illumination,” Opt. Lett. 23, 4–6 (1998).
[CrossRef]

M. Peccianti and G. Assanto, “Signal readdressing by steering of spatial solitons in bulk nematic liquid crystals,” Opt. Lett. 26, 1690–1692 (2001).
[CrossRef]

J. M. Harbold, F. Ö. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As-S-Se glasses for all-optical switching,” Opt. Lett. 27, 119–121 (2002).
[CrossRef]

Phys. Rep. (1)

A. Buryak, P. Di Traponi, D. Skryabin, and S. Trillo, “Opti-cal solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Phys. Rev. E (1)

R. Scharf and A. R. Bishop, “Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials,” Phys. Rev. E 47, 1375–1383 (1993).
[CrossRef]

Phys. Rev. Lett. (1)

N. N. Akhmediev and A. Ankiewicz, “Novel soliton states and bifurcation phenomena in nonlinear fibre couplers,” Phys. Rev. Lett. 70, 2395–2398 (1993).
[CrossRef] [PubMed]

Phys. Scr. (1)

J. J. Rasmussen and K. Ripdal, “Blow-up in nonlinear Schrödinger equation. I. A general review,” Phys. Scr. 33, 481–497 (1986).
[CrossRef]

Other (2)

R. W. Boyd, Nonlinear Optics (Academic, New York, 1992).

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, Oxford, 1995).

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Figures (4)

Fig. 1
Fig. 1

Propagation of a soliton beam (a) without injection of cw and (b) with injection of a cw having amplitude a=0.1, transverse wave number kX=1, and initial phase ϕ=0, as obtained from direct numerical simulation of the NLS equation. (c) Illustration of the cw-controlled steering of an input spatial soliton (SS).

Fig. 2
Fig. 2

Interaction of a beam with cw having kX=±1, ϕ=0, and a=0.05, 0.10, and 0.15. (a) Contour plot of beam amplitude as obtained from direct numerical simulation of the NLS equation; (b) beam center X0 as obtained by numerical integration of the parameter evolution equations; (c), (d) beam amplitude oscillations as obtained from direct numerical simulation of the NLS equation (c) and by numerical integration of the parameter evolution equations (d) for a=0.05 (dark solid curve), a=0.10 (light semi-solid curve), a=0.15 (dotted curve); (e) chirp oscillations as obtained from direct numerical simulation of the NLS equation for a=0.05 (dark solid curve), a=0.10 (light semi-solid curve), and a=0.15 (dotted curve).

Fig. 3
Fig. 3

Beam mean transverse velocity 〈κ〉 versus the cw transverse wave number kX: (a), (b) Contour plots of the beam amplitude as obtained by direct numerical simulation of the NLS equation for beam interaction with a cw having ϕ=0, a=0.10, and kX=0.2, 0.5, 1, 1.5, 2, and 5; (c) 〈κ〉 versus kX obtained by numerical integration of the parameter evolution equations for a=0.05, 0.10, and 0.15. For comparison, results from the direct numerical simulations in (a) and (b) are indicated by solid circles.

Fig. 4
Fig. 4

Beam mean transverse velocity 〈κ〉 versus the initial phase difference ϕ between the cw and the beam: (a) Contour plots of the beam amplitude as obtained by direct numerical simulation of the NLS equation for a beam interacting with a cw having kX=1, a=0.15, and ϕ=0, π/3, π/2, 2π/3, and π; (b) 〈κ〉 versus ϕ obtained by numerical integration of the parameter evolution equations for a=0.05, 0.10, and 0.15. For comparison, results from the direct numerical simulations in (a) are indicated by solid circles.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

i uZ+12 2uX2+|u|2u=0,
|u|=kZa0ε0cn2I2 |E|=kZzdε0cn2I2 |E|,
|E|1kZa0 2ε0cn2I,
u=us+ucw.
i usZ+12 2usX2+|us|2us=R(us, ucw),
i ucwZ+12 2ucwX2=0,
dndZ=12aπ sechωπ2n2(ω2+1)sin(A),
dκdZ=-12aπω sechωπ2n2(ω2+1)sin(A),
dX0dZ=-κ-12aπ sechωπ2-π2 tanhωπ2(ω2+1)+2ωcos(A),
dσdZ=12(n2-κ2)+X0 dκdZ+12aπn sechωπ2×ωπ2tanhωπ2(ω2+1)+2cos(A),
ΔkZ=(1/2)n2.

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