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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 27, Iss. 5 — May. 1, 2010
  • pp: 1051–1064

Sudden spontaneous acceleration and deceleration of gap-acoustic solitons

Richard S. Tasgal, R. Shnaiderman, and Y. B. Band  »View Author Affiliations


JOSA B, Vol. 27, Issue 5, pp. 1051-1064 (2010)
http://dx.doi.org/10.1364/JOSAB.27.001051


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Abstract

Gap-acoustic solitons (GASs) are stable pulses that exist in nonlinear Bragg waveguides. They are a mathematical generalization of gap solitons, in which the model includes the dependence of the refractive index on the material density. We derive unified dynamical equations for gap solitons along with Brillouin scattering, which also results from the dependence of the refractive index on the material density. We find accurate values of the coefficients for fused silica. The analysis of the GAS conserved quantities—Hamiltonian, momentum, photon energy (or number of photons), and material mass—shows dramatic differences compared to the model neglecting the dependence of the refractive index on the material density. In particular, subsonic GASs in fused silica have far more momentum at low velocities than at high velocities. The dependence of the GAS momentum on velocity due to acoustic effects is dramatic up to approximately 1% of the speed of light. These momentum-connected effects mean that instability of a slow GAS may make it suddenly accelerate to high speeds, and also that an unstable high-speed GAS can abruptly decelerate to close to zero velocity. The predictions are confirmed by a direct numerical simulation.

© 2010 Optical Society of America

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(190.3100) Nonlinear optics : Instabilities and chaos
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(230.1040) Optical devices : Acousto-optical devices
(290.5830) Scattering : Scattering, Brillouin
(060.3735) Fiber optics and optical communications : Fiber Bragg gratings

ToC Category:
Nonlinear Optics

History
Original Manuscript: November 5, 2009
Revised Manuscript: February 9, 2010
Manuscript Accepted: February 21, 2010
Published: April 28, 2010

Citation
Richard S. Tasgal, R. Shnaiderman, and Y. B. Band, "Sudden spontaneous acceleration and deceleration of gap-acoustic solitons," J. Opt. Soc. Am. B 27, 1051-1064 (2010)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-5-1051


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References

  1. W. E. Thirring, “A soluble relativistic field theory,” Ann. Phys. (N.Y.) 3, 91–112 (1958). [CrossRef]
  2. E. A. Kuznetsov and A. V. Mikhailov, “On the complete integrability of the two-dimensional classical Thirring model,” Theor. Math. Phys. 30, 193–200 (1977). [CrossRef]
  3. D. J. Kaup and A. C. Newell, “On the Coleman correspondence and the soliton of the massive Thirring model,” Lett. Nuovo Cimento 20, 325–331 (1977). [CrossRef]
  4. B. J. Eggleton, C. Martijn 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]
  5. W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987). [CrossRef] [PubMed]
  6. D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749 (1989). [CrossRef] [PubMed]
  7. A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–42 (1989). [CrossRef]
  8. 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]
  9. M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413, 273–276 (2001). [CrossRef] [PubMed]
  10. R. W. Boyd and D. J. Gauthier, “‘Slow’ and ‘fast’ light,” Prog. Opt. 43, 497–530 (2002). [CrossRef]
  11. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003). [CrossRef] [PubMed]
  12. K. Y. Song, M. G. Herraez, and L. Thevenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82–88 (2005). [CrossRef] [PubMed]
  13. D. Dahan and G. Eisenstein, “Tunable all optical delay via slow and fast light propagation in a Raman assisted fiber optical parametric amplifier: a route to all optical buffering,” Opt. Express 13, 6234–6249 (2005). [CrossRef] [PubMed]
  14. Y. Zhang, W. Qui, J. Ye, N. Wang, J. Wang, H. Tian, and P. Yuan, “Controllable ultraslow light propagation in highly-doped erbium fiber,” Opt. Commun. 281, 2633–2637 (2008). [CrossRef]
  15. R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074–1077 (2009). [CrossRef] [PubMed]
  16. 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]
  17. 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]
  18. I. V. Barashenkov and E. V. Zemlyanaya, “Oscillatory instabilities of gap solitons: a numerical study,” Comput. Phys. Commun. 126, 22–27 (2000). [CrossRef]
  19. A. De Rossi, C. Conti, and S. Trillo, “Stability, multistability, and wobbling of optical gap solitons,” Phys. Rev. Lett. 81, 85–88 (1998). [CrossRef]
  20. R. S. Tasgal, Y. B. Band, and B. A. Malomed, “Optoacoustic solitons in Bragg gratings,” Phys. Rev. Lett. 98, 243902 (2007). [CrossRef] [PubMed]
  21. E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. N. Starodumov, “Electrostriction mechanism of soliton interaction in optical fibers,” Opt. Lett. 15, 314–316 (1990). [CrossRef] [PubMed]
  22. A. A. Zabolotskii, “Generation of pulses upon nonresonant acousto-electromagnetic interaction,” Opt. Spectrosc. 97, 936–944 (2004). [CrossRef]
  23. T. Iizuka and Y. S. Kivshar, “Optical gap solitons in nonresonant quadratic media,” Phys. Rev. E 59, 7148–7151 (1999). [CrossRef]
  24. S. V. Sazonov, “Optical-acoustic soliton under the conditions of slow light and stimulated Mandelstam–Brillouin scattering,” JETP Lett. 81, 201–204 (2005). [CrossRef]
  25. J. D. Jackson, Classical Electrodynamics (Wiley, 1975).
  26. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).
  27. R. W. Boyd, Nonlinear Optics (Academic, 2003).
  28. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2006).
  29. D. T. Hon, “Pulse compression by stimulated Brillouin scattering,” Opt. Lett. 5, 516–518 (1980). [CrossRef] [PubMed]
  30. I. Bongrand, C. Montes, E. Picholle, J. Botineau, A. Picozzi, G. Cheval, and D. Bahloul, “Soliton compression in Brillouin fiber lasers,” Opt. Lett. 26, 1475–1477 (2001). [CrossRef]
  31. P. Maák, G. Kurdi, A. Barócsi, K. Osvay, A. P. Kovács, L. Jakab, and P. Richter, “Shaping of ultrashort pulses using bulk acousto-optic filter,” Appl. Phys. B 82, 283–287 (2006). [CrossRef]
  32. E. Rat, M. Foret, G. Massiera, R. Vialla, M. Arai, R. Vacher, and E. Courtens, “Anharmonic versus relaxational sound damping in glasses. I. Brillouin scattering in densified silica,” Phys. Rev. B 72, 214204 (2005). [CrossRef]
  33. K. Smith and L. F. Mollenauer, “Experimental observation of soliton interaction over long fiber paths: discovery of a long-range interaction,” Opt. Lett. 14, 1284–1286 (1989). [CrossRef] [PubMed]
  34. E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, “Long-range interaction of picosecond solitons through excitation of acoustic waves in optical fibers,” Appl. Phys. B 54, 175–180 (1992). [CrossRef]
  35. P. J. Thomas, N. L. Rowell, H. M. van Driel, and G. I. Stegeman, “Normal acoustic modes and Brillouin scattering in single-mode optical fibers,” Phys. Rev. B 19, 4986–4998 (1979). [CrossRef]
  36. R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244–5252 (1985). [CrossRef]
  37. D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” Appl. Opt. 37, 546–550 (1998). [CrossRef]
  38. P. J. Hardman, P. D. Townsend, A. J. Poustie, and K. J. Blow, “Experimental investigation of resonant enhancement of the acoustic interaction of optical pulses in an optical fiber,” Opt. Lett. 21, 393–395 (1996). [CrossRef] [PubMed]
  39. E. L. Buckland and R. W. Boyd, “Electrostrictive contribution to the intensity-dependent refractive index of optical fibers,” Opt. Lett. 21, 1117–1119 (1996). [CrossRef] [PubMed]
  40. E. L. Buckland and R. W. Boyd, “Measurement of the frequency response of the electrostrictive nonlinearity in optical fibers,” Opt. Lett. 22, 676–678 (1997). [CrossRef] [PubMed]
  41. A. Fellegara, A. Melloni, and M. Martinelli, “Measurement of the frequency response induced by electrostriction in optical fibers,” Opt. Lett. 22, 1615–1617 (1997). [CrossRef]
  42. A. Melloni, M. Frasca, A. Garavaglia, A. Tonini, and M. Martinelli, “Direct measurement of electrostriction in optical fibers,” Opt. Lett. 23, 691–693 (1998). [CrossRef]
  43. E. L. Buckland, “Mode-profile dependence of the electrostrictive response in fibers,” Opt. Lett. 24, 872–874 (1999). [CrossRef]
  44. E. M. Dianov, M. E. Sukharev, and A. S. Biriukov, “Electrostrictive response in single-mode ring-index-profile fibers,” Opt. Lett. 25, 390–392 (2000). [CrossRef]
  45. S. Afshar V., V. P. Kalosha, X. Bao, and L. Chen, “Enhancement of stimulated Brillouin scattering of higher-order acoustic modes in single-mode optical fiber,” Opt. Lett. 30, 2685–2687 (2005). [CrossRef]
  46. J. Feng and F. K. Kneubuhl, “Solitons in a periodic structure with Kerr nonlinearity,” IEEE J. Quantum Electron. 29, 590–597 (1993). [CrossRef]
  47. V. E. Zakharov, “Collapse of Langmuir waves,” Zh. Eksp. Teor. Fiz. 62, 1745–1751 (1972) V. E. Zakharov, “[Sov. Phys. JETP 35, 908–914 (1972)].
  48. A. S. Davydov, “Solitons in molecular systems,” Phys. Scr. 20, 387–394 (1979). [CrossRef]
  49. L. Stenflo, “Nonlinear equations for acoustic gravity waves,” Phys. Scr. 33, 156–158 (1986). [CrossRef]
  50. H. Hadouaj, B. A. Malomed, and G. A. Maugin, “Dynamics of a soliton in a generalized Zakharov system with dissipation,” Phys. Rev. A 44, 3925–3931 (1991). [CrossRef] [PubMed]
  51. H. Hadouaj, B. A. Malomed, and G. A. Maugin, “Soliton–soliton collisions in a generalized Zakharov system,” Phys. Rev. A 44, 3932–3940 (1991). [CrossRef] [PubMed]
  52. G. A. Maugin, H. Hadouaj, and B. A. Malomed, “Nonlinear coupling between shear horizontal surface solitons and Rayleigh waves on elastic structures,” Phys. Rev. B 45, 9688–9694 (1992). [CrossRef]
  53. I. L. Fabelinskii, Molecular Scattering of Light (Plenum, 1968).

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