OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 25, Iss. 3 — Mar. 1, 2008
  • pp: 302–309

Stability and collisions of traveling solitons in Bragg-grating superstructures

Kobi Levy and Boris A. Malomed  »View Author Affiliations


JOSA B, Vol. 25, Issue 3, pp. 302-309 (2008)
http://dx.doi.org/10.1364/JOSAB.25.000302


View Full Text Article

Enhanced HTML    Acrobat PDF (571 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We investigate stability of moving solitons in a nonlinear optical fiber with short segments of a relatively strong Bragg grating (BG) periodically inserted into it. The model is related to a class of composite and artificial optical media that have recently attracted much interest. The analysis is focused on moving solitons, as this is relevant to the experiment. By means of systematic simulations, we find that, in accordance with a qualitative consideration, the stability region for moving solitons first increases with velocity c but then decreases (in contrast to the uniform fiber BG, where the stability of the solitons depends very weakly on c). As well as in the uniform system, solitons do not exist for c exceeding the group velocity of light in the fiber, nor may they be stable with negative intrinsic frequencies. Collisions between solitons moving in opposite directions are also studied in a systematic way. A difference from the situation in the uniform fiber BG is strong shrinkage and eventual disappearance of a region where the collision results in a merger of the two solitons into a single one, which is explained too. Fiber waveguides with BG superstructures being currently available, moving solitons can be created in them by means of experimental techniques similar to those that have helped to generate solitons in uniform fiber gratings.

© 2008 Optical Society of America

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(230.1480) Optical devices : Bragg reflectors

ToC Category:
Nonlinear Optics

History
Original Manuscript: August 15, 2007
Revised Manuscript: November 3, 2007
Manuscript Accepted: November 6, 2007
Published: February 13, 2008

Citation
Kobi Levy and Boris A. Malomed, "Stability and collisions of traveling solitons in Bragg-grating superstructures," J. Opt. Soc. Am. B 25, 302-309 (2008)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-25-3-302


Sort:  Year  |  Journal  |  Reset  

References

  1. A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68, 4309-4341 (1997). [CrossRef]
  2. R. Kashyap, Fiber Bragg Gratings (Academic, 1999).
  3. F. Ouelette, P. A. Krug, T. Stephens, G. Dhosi, and B. Eggleton, “Broad-band and WDM dispersion compensationusing chirped sampled fiber Bragg gratings,” Electron. Lett. 31, 899-901 (1995). [CrossRef]
  4. B. J. Eggleton, A. Ahuja, P. S. Westbrook, J. A. Rogers, P. Kuo, T. N. Nielsen, and B. Mikkelsen, “Integrated tunable fiber gratings for dispersion management in high-bit rate systems,” J. Lightwave Technol. 18, 1418-1432 (2000). [CrossRef]
  5. 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]
  6. Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, “Stationary waves in nonlinear, periodically modulated media with large group retardation,” Zh. Tekh. Fiz. 51, 902 (1981) Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin,[Sov. Phys. Tech. Phys. 26, 541 (1981)].
  7. W. Chen and D. L. Mills, “Gap solitons and the nonlinear-optical response of superlattices,” Phys. Rev. Lett. 58, 160-163 (1987). [CrossRef] [PubMed]
  8. C. M. de Sterke and J. E. Sipe, “Gap solitons,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1994), Vol. XXXIII, Chap. III, pp. 203-260.
  9. Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).
  10. D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structure,” Phys. Rev. Lett. 62, 1746-1749 (1989). [CrossRef] [PubMed]
  11. A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37-42 (1989). [CrossRef]
  12. 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]
  13. 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]
  14. A. De Rossi, C. Conti, and S. Trillo, “Stability, multistability, and wobbling of optical gap solitons,” Phys. Rev. Lett. 81, 85-88 (1998). [CrossRef]
  15. 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] [PubMed]
  16. B. J. Eggleton, C. M. De Sterke, and R. E. Slusher, “Bragg solitons in the nonlinear Schrödinger limit: experiment and theory,” J. Opt. Soc. Am. B 16, 587-599 (1999). [CrossRef]
  17. J. T. Mok, C. M. de Sterke, I. C. M. Litte, and B. J. Eggleton, “Dispersionless slow light using gap solitons,” Nat. Phys. 2, 775-780 (2006). [CrossRef]
  18. A. A. Sukhorukov and Yu. S. Kivshar, “Discrete gap solitons in modulated waveguide arrays,” Opt. Lett. 27, 2112-2114 (2002). [CrossRef]
  19. P. G. Kevrekidis, B. A. Malomed, and Z. Musslimani, “Discrete gap solitons in a diffraction-managed waveguide array,” Eur. Phys. J. D 23, 421-236 (2003). [CrossRef]
  20. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,” Phys. Rev. Lett. 90, 053902 (2003). [CrossRef] [PubMed]
  21. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004). [CrossRef] [PubMed]
  22. R. Morandotti, D. Mandelik, Y. Silberberg, J. S. Aitchison, M. Sorel, D. N. Christodoulides, A. A. Sukhorukov, and Y. S. Kivshar, “Observation of discrete gap solitons in binary waveguide arrays,” Opt. Lett. 29, 2890-2892 (2004). [CrossRef]
  23. F. Chen, M. Stepic, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, “Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays,” Opt. Express 13, 4314-4324 (2005). [CrossRef] [PubMed]
  24. 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]
  25. D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Yu. S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 (2004). [CrossRef] [PubMed]
  26. 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]
  27. G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express 13, 1780-1796 (2005). [CrossRef] [PubMed]
  28. P. St. J. Russell, “Optical superlattices for modulation and deflection of light,” J. Appl. Phys. 59, 3344-3355 (1986). [CrossRef]
  29. N. G. R. Broderick and C. M. de Sterke, “Theory of grating superstructures,” Phys. Rev. E 55, 3634-3646 (1977). [CrossRef]
  30. 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]
  31. D. R. Neill and J. Atai, “Collision dynamics of gap solitons in Kerr media,” Phys. Lett. A 353, 416-421 (2006). [CrossRef]
  32. K. Yagasaki, I. M. Merhasin, B. A. Malomed, T. Wagenknecht, and A. R. Champneys, “Gap solitons in Bragg gratings with a harmonic superlattice,” Europhys. Lett. 74, 1006-1012 (2006). [CrossRef]
  33. P. Y. P. Chen, B. A. Malomed, and P. L. Chu, “Trapping Bragg solitons by a pair of defects,” Phys. Rev. E 71, 066601 (2005). [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, “Interaction of a soliton with a localized gain in a fiber Bragg grating,” Phys. Rev. E 67, 026608 (2003). [CrossRef]
  36. W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Interaction of a soliton with a local defect in a fiber Bragg grating,” J. Opt. Soc. Am. B 20, 725-735 (2003). [CrossRef]
  37. C. Kittel, Introduction to Solid State Physics (Wiley, 1995).
  38. W. Li and A. Smerzi, Phys. Rev. E 70, 016605 (2004). [CrossRef]
  39. I. M. Merhasin, B. V. Gisin, R. Driben, and B. A. Malomed, “Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity,” Phys. Rev. E 71, 016613 (2005). [CrossRef]
  40. B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).
  41. L. Torner, “Walkoff-compensated dispersion-mapped quadratic solitons,” IEEE Photon. Technol. Lett. 11, 1268-1270 (1999). [CrossRef]
  42. R. Driben and B. A. Malomed, “Split-step solitons in long fiber links,” Opt. Commun. 185, 439-456 (2000). [CrossRef]
  43. R. Driben and B. A. Malomed, “Suppression of crosstalk between solitons in a multi-channel split-step system,” Opt. Commun. 197, 481-489 (2001). [CrossRef]
  44. J. Atai and B. A. Malomed, “Spatial solitons in a medium composed of self-focusing and self-defocusing layers,” Phys. Lett. A 298, 140-148 (2002). [CrossRef]
  45. N. C. Panoiu, R. M. Osgood, and B. A. Malomed, “Semi-discrete composite solitons in arrays of quadratically nonlinear waveguides,” Opt. Lett. 31, 1097-1099 (2006). [CrossRef] [PubMed]
  46. M. J. Ablowitz and H. Segur, Solitons and Inverse Scattering Transform (SIAM, 1981). [CrossRef]
  47. D. B. Duncan, J. C. Eilbeck, H. Feddersen, and J. A. D. Wattis, “Solitons on lattices,” Physica D 68, 1-11 (1993). [CrossRef]
  48. M. J. Ablowitz, Z. H. Musslimani, and G. Biondini, “Methods for discrete solitons in nonlinear lattices,” Phys. Rev. E 65, 026602 (2002). [CrossRef]
  49. 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]
  50. S. Flach, Y. Zolotaryuk, and K. Kladko, “Moving lattice kinks and pulses: An inverse method,” Phys. Rev. E 59, 6105-6115 (1999). [CrossRef]
  51. P. G. Kevrekidis, “On a class of discretizations of Hamiltonian nonlinear partial differential equations,” Physica D 183, 68-86 (2003). [CrossRef]
  52. D. E. Pelinovsky and V. M. Rothos, “Bifurcations of travelling wave solutions in the discrete NLS equations,” Physica D 202, 16-36 (2005). [CrossRef]
  53. O. F. Oxtoby, D. E. Pelinovsky, and I. V. Barashenkov, “Travelling kinks in discrete phi(4) models,” Nonlinearity 19, 217-235 (2006). [CrossRef]
  54. B. A. Malomed, J. Fujioka, A. Espinosa-Ceron, R. F. Rodriguez, and S. González, “Moving embedded lattice solitons,” Chaos 16, 013112 (2006). [CrossRef] [PubMed]
  55. W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Slowdown and splitting of gap solitons in apodized Bragg Gratings,” J. Mod. Opt. 51, 2141-2158 (2004). [CrossRef]
  56. N. M. Litchinitser, B. J. Eggleton, C. M. de Sterke, A. B. Aceves, and G. P. Agrawal, “Interaction of Bragg solitons in fiber gratings,” J. Opt. Soc. Am. B 16, 18-23 (1999). [CrossRef]
  57. H. Sakaguchi and B. A. Malomed, “Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps,” J. Phys. B 37, 1443-1459 (2004). [CrossRef]
  58. I. Carrusotto, D. Embriaco, and G. C. La Rocca, “Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices,” Phys. Rev. A 65, 053611 (2002). [CrossRef]
  59. B. B. Baizakov, V. V. Konotop, and M. Salerno, “Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability,” J. Phys. B 35, 5105-5119 (2002). [CrossRef]
  60. E. A. Ostrovskaya and Yu. S. Kivshar, “Matter-wave gap solitons in atomic band-gap structures,” Phys. Rev. Lett. 90, 160407 (2003). [CrossRef] [PubMed]
  61. B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, “Bright Bose-Einstein gap solitons of atoms with repulsive interaction,” Phys. Rev. Lett. 92, 230401 (2004). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited