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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 2 — Feb. 1, 2013
  • pp: 396–404

Stability and collisions of moving Bragg grating solitons in a cubic-quintic nonlinear medium

Sahan Dasanayaka and Javid Atai  »View Author Affiliations


JOSA B, Vol. 30, Issue 2, pp. 396-404 (2013)
http://dx.doi.org/10.1364/JOSAB.30.000396


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Abstract

The existence, stability, and collisions of moving solitons in Bragg gratings (BGs) in a cubic-quintic nonlinear medium are investigated. Two disjoint families of solitons that are separated by a border are identified. One family (Type 1) can be considered as the generalization of the moving solitons in BGs written in a cubic nonlinear medium. The other family (Type 2) occurs in regions where quintic nonlinearity dominates. Through systematic numerical stability analysis, the stability regions in the plane of quintic nonlinearity versus frequency have been determined. It is found that the stability regions are dependent on the velocity of solitons. The collisions of counterpropagating solitons have been systematically investigated. Collisions of in-phase Type 1 solitons can result in a variety of outcomes including forming two asymmetrically separating solitons and passing through each other and separating symmetrically with reduced, unchanged, or increased velocities. In certain parameter regions, solitons merge to form a quiescent one. An outcome that has not been reported previously for uniform gratings is the formation of a quiescent soliton and two symmetrically separating solitons. This outcome is found to be more robust than the merger.

© 2013 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(060.3735) Fiber optics and optical communications : Fiber Bragg gratings

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: September 12, 2012
Revised Manuscript: December 10, 2012
Manuscript Accepted: December 11, 2012
Published: January 22, 2013

Citation
Sahan Dasanayaka and Javid Atai, "Stability and collisions of moving Bragg grating solitons in a cubic-quintic nonlinear medium," J. Opt. Soc. Am. B 30, 396-404 (2013)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-2-396


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References

  1. R. Kashyap, Fiber Bragg Gratings (Academic, 1999).
  2. P. St. J. Russell, “Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures,” J. Mod. Opt. 38, 1599–1619 (1991). [CrossRef]
  3. C. M. de Sterke and J. E. Sipe, “Gap solitons,” Prog. Opt. 33, 203–260 (1994). [CrossRef]
  4. P. A. Krug, T. Stephens, G. Yoffe, F. Ouellette, P. Hill, and G. Dhosi, “Dispersion compensation over 270 km at 10  Gbit/s using an offset-core chirped fibre Bragg grating,” Electron. Lett. 31, 1091–1093 (1995). [CrossRef]
  5. N. M. Litchinitser, B. J. Eggleton, and D. B. Patterson, “Fiber Bragg gratings for dispersion compensation in transmission: theoretical model and design criteria for nearly ideal pulse recompression,” J. Lightwave Technol. 15, 1303–1313(1997). [CrossRef]
  6. W. H. Loh, R. I. Laming, N. Robinson, A. Cavaciuti, F. Vaninetti, C. J. Anderson, M. N. Zervas, and M. J. Cole, “Dispersion compensation over distances in excess of 500 km for 10  Gb/ssystems using chirped fiber gratings,” IEEE Photon. Technol. Lett. 8, 944–946 (1996). [CrossRef]
  7. H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979). [CrossRef]
  8. S. Radic, N. George, and G. P. Agrawal, “Theory of low-threshold optical switching in nonlinear phase-shifted periodic structures,” J. Opt. Soc. Am. B 12, 671–680 (1995). [CrossRef]
  9. N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “All-optical switching in a nonlinear periodic-waveguide structure,” Appl. Phys. Lett. 60, 1427–1429 (1992). [CrossRef]
  10. H. G. Winful, “Pulse compression in optical fiber filters,” Appl. Phys. Lett. 46, 527–529 (1985). [CrossRef]
  11. S. LaRochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibres,” Electron. Lett. 26, 1459–1460 (1990). [CrossRef]
  12. D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749 (1989). [CrossRef]
  13. A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–42 (1989). [CrossRef]
  14. J. E. Sipe and H. G. Winful, “Nonlinear Schrödinger solitons in a periodic structure,” Opt. Lett. 13, 132–133 (1988). [CrossRef]
  15. B. A. Malomed and R. S. Tasgal, “Vibration modes of a gap soliton in a nonlinear optical medium,” Phys. Rev. E 49, 5787–5796 (1994). [CrossRef]
  16. I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, “Vibrations and oscillatory instabilities of gap solitons,” Phys. Rev. Lett. 80, 5117–5120 (1998). [CrossRef]
  17. A. De Rossi, C. Conti, and S. Trillo, “Stability, multistability, and wobbling of optical gap solitons,” Phys. Rev. Lett. 81, 85–88 (1998). [CrossRef]
  18. B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993 (1997). [CrossRef]
  19. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996). [CrossRef]
  20. D. Taverner, N. G. R. Broderick, D. J. Richardson, R. I. Laming, and M. Ibsen, “Nonlinear self-switching and multiple gap-soliton formation in a fiber Bragg grating,” Opt. Lett. 23, 328–330 (1998). [CrossRef]
  21. C. M. de Sterke, B. J. Eggleton, and P. A. Krug, “High-intensity pulse propagation in uniform gratings and grating superstructures,” J. Lightwave Technol. 15, 1494–1502 (1997). [CrossRef]
  22. W. C. K. Mak, P. L. Chu, and B. A. Malomed, “Solitary waves in coupled nonlinear waveguides with Bragg gratings,” J. Opt. Soc. Am. B 15, 1685–1692 (1998). [CrossRef]
  23. J. Atai, and B. A. Malomed, “Bragg-grating solitons in a semilinear dual-core system,” Phys. Rev. E 62, 8713–8718 (2000). [CrossRef]
  24. J. Atai, and B. A. Malomed, “Solitary waves in systems with separated Bragg grating and nonlinearity,” Phys. Rev. E 64, 066617 (2001). [CrossRef]
  25. B. H. Baratali, and J. Atai, “Gap solitons in dual-core Bragg gratings with dispersive reflectivity,” J. Opt. 14, 065202 (2012). [CrossRef]
  26. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004). [CrossRef]
  27. J. Atai, and B. A. Malomed, “Gap solitons in Bragg gratings with dispersive reflectivity,” Phys. Lett. A 342, 404–412 (2005). [CrossRef]
  28. D. R. Neill, J. Atai, and B. A. Malomed, “Dynamics and collisions of moving solitons in Bragg gratings with dispersive reflectivity,” J. Opt. A 10, 085105 (2008). [CrossRef]
  29. D. V. Skryabin, “Coupled core-surface solitons in photonic crystal fibers,” Opt. Express 12, 4841–4846 (2004). [CrossRef]
  30. I. M. Merhasin and B. A. Malomed, “Gap solitons in a model of a hollow optical fiber,” Opt. Lett. 30, 1105–1107 (2005). [CrossRef]
  31. J. Atai, B. A. Malomed, and I. M. Merhasin, “Stability and collisions of gap solitons in a model of a hollow optical fiber,” Opt. Commun. 265, 342–348 (2006). [CrossRef]
  32. D. R. Neill, and J. Atai, “Gap solitons in a hollow optical fiber in the normal dispersion regime,” Phys. Lett. A 367, 73–82 (2007). [CrossRef]
  33. J. T. Mok, C. M. de Sterke, I. C. M. Littler, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys. 2, 775–780 (2006). [CrossRef]
  34. R. H. Goodman, R. E. Slusher, and M. I. Weinstein, “Stopping light on a defect,” J. Opt. Soc. Am. B 19, 1635–1652 (2002). [CrossRef]
  35. W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Formation of a standing-light pulse through collision of gap solitons,” Phys. Rev. E 68, 026609 (2003). [CrossRef]
  36. D. R. Neill and J. Atai, “Collision dynamics of gap solitons in Kerr media,” Phys. Lett. A 353, 416–421 (2006). [CrossRef]
  37. L. Tkeshelashvili, J. Niegemann, S. Pereira, and K. Busch, “Nonlinear wave interaction in photonic band gap materials,” Photon. Nanostr. Fundam. Appl. 4, 75–88 (2006). [CrossRef]
  38. Y. P. Shapira and M. Horowitz, “Optical AND gate based on soliton interaction in a fiber Bragg grating,” Opt. Lett. 32, 1211–1213 (2007). [CrossRef]
  39. C. Conti, S. Trillo, and G. Assanto, “Doubly resonant Bragg simultons via second-harmonic generation,” Phys. Rev. Lett. 78, 2341–2344 (1997). [CrossRef]
  40. H. He and P. D. Drummond, “Ideal soliton environment using parametric band gaps,” Phys. Rev. Lett. 78, 4311–4315 (1997). [CrossRef]
  41. W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Three-wave gap solitons in waveguides with quadratic nonlinearity,” Phys. Rev. E 58, 6708–6722 (1998). [CrossRef]
  42. J. Atai and B. A. Malomed, “Families of Bragg-grating solitons in a cubic–quintic medium,” Phys. Lett. A 284, 247–252 (2001). [CrossRef]
  43. J. Atai, “Interaction of Bragg grating solitons in a cubic–quintic medium,” J. Opt. B Quantum Semiclass. Opt. 6, S177–S181 (2004). [CrossRef]
  44. G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, and F. Sanchez, “Experimental and theoretical study of higher-order nonlinearities in chalcogenide glasses,” Opt. Commun. 219, 427–433 (2003). [CrossRef]
  45. C. Zhan, D. Zhang, D. Zhu, D. Wang, Y. Li, D. Li, Z. Lu, L. Zhao, and Y. Nie, “Third- and fifth-order optical nonlinearities in a new stilbazolium derivative,” J. Opt. Soc. Am. B 19, 369–375 (2002). [CrossRef]
  46. S. Dasanayaka and J. Atai, “Stability of Bragg grating solitons in a cubic–quintic nonlinear medium with dispersive reflectivity,” Phys. Lett. A 375, 225–229 (2010). [CrossRef]
  47. S. Dasanayaka and J. Atai, “Interactions of solitons in Bragg gratings with dispersive reflectivity in a cubic-quintic medium,” Phys. Rev. E 84, 026613 (2011). [CrossRef]
  48. W. Królikowski and S. A. Holmstrom, “Fusion and birth of spatial solitons upon collision,” Opt. Lett. 22, 369–371 (1997). [CrossRef]
  49. E. A. Ultanir, G. I. Stegeman, C. H. Lange, and F. Lederer, “Coherent interactions of dissipative spatial solitons,” Opt. Lett. 29, 283–285 (2004). [CrossRef]
  50. J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Nonlinear optical beam interactions in waveguide arrays,” Phys. Rev. Lett. 93, 093903 (2004). [CrossRef]
  51. J. Cuevas and J. C. Eilbeck, “Discrete soliton collisions in a waveguide array with saturable nonlinearity,” Phys. Lett. A 358, 15–20 (2006). [CrossRef]
  52. I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, “Soliton collisions in the discrete nonlinear Schrödinger equation,” Phys. Rev. E 68, 046604 (2003). [CrossRef]

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