OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 29, Iss. 10 — Oct. 1, 2012
  • pp: 2741–2748

Stabilizing single- and two-color vortex beams in quadratic media by a trapping potential

Hidetsugu Sakaguchi and Boris A. Malomed  »View Author Affiliations


JOSA B, Vol. 29, Issue 10, pp. 2741-2748 (2012)
http://dx.doi.org/10.1364/JOSAB.29.002741


View Full Text Article

Enhanced HTML    Acrobat PDF (520 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We consider two-dimensional (2D) localized modes in the second-harmonic-generating (χ(2)) system with the harmonic-oscillator (HO) trapping potential. In addition to its realization in optics, the system describes the mean-field dynamics of mixed atomic-molecular Bose–Einstein condensates (BECs). The existence and stability of various modes is determined by their total power, N, topological charge, m/2 [m is the intrinsic vorticity of the second-harmonic (SH) field], and χ(2) mismatch, q. The analysis is carried out in a numerical form and, in parallel, by means of the variational approximation (VA), which produces results that agree well with numerical findings. Below a certain power threshold, NNc(m)(q), all trapped modes are of the single-color type, represented by the SH component only, while the fundamental frequency (FF) one is absent. In contrast with the usual situation, where such modes are always unstable, we demonstrate that they are stable, for m=0, 1, 2 (the mode with m=1 may be formally considered as a semivortex with topological charge m/2=1/2), at NNc(m)(q), and unstable above this threshold. On the other hand, Nc(m)(q)0 at qqmax (in our notation, qmax=1); hence the single-color modes are unstable in the latter case. At N=Nc(m), the modes with m=0 and m=2 undergo a pitchfork bifurcation, which gives rise to two-color states, which remain completely stable for m=0. The two-color vortices with m=2 (topological charge 1) have an upper stability border, N=Nc2(q). Above the border, they exhibit periodic splittings and recombinations, while keeping their vorticity. The semivortex does not bifurcate; at N=Nc(m=1), it exhibits quasi-chaotic oscillations and a rotating “groove” resembling a screw-edge dislocation induced by the semi-integer vorticity.

© 2012 Optical Society of America

OCIS Codes
(190.3100) Nonlinear optics : Instabilities and chaos
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(020.1475) Atomic and molecular physics : Bose-Einstein condensates
(190.6135) Nonlinear optics : Spatial solitons

ToC Category:
Nonlinear Optics

History
Original Manuscript: June 6, 2012
Revised Manuscript: July 30, 2012
Manuscript Accepted: August 16, 2012
Published: September 13, 2012

Citation
Hidetsugu Sakaguchi and Boris A. Malomed, "Stabilizing single- and two-color vortex beams in quadratic media by a trapping potential," J. Opt. Soc. Am. B 29, 2741-2748 (2012)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-10-2741


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996). [CrossRef]
  2. C. Etrich, F. Lederer, B. A. Malomed, T. Peschel, and U. Peschel, “Optical solitons in media with a quadratic nonlinearity,” Prog. Opt. 41, 483–568 (2000). [CrossRef]
  3. A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002). [CrossRef]
  4. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005). [CrossRef]
  5. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  6. A. A. Kanashov and A. M. Rubenchik, “On diffraction and dispersion effect on three wave interaction,” Physica D 4, 122–134 (1981). [CrossRef]
  7. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995). [CrossRef]
  8. B. A. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, “Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity,” Phys. Rev. E 56, 4725–4735 (1997). [CrossRef]
  9. X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999). [CrossRef]
  10. X. Liu, K. Beckwitt, and F. Wise, “Two-dimensional optical spatiotemporal solitons in quadratic media,” Phys. Rev. E 62, 1328–1340 (2000). [CrossRef]
  11. F. A. Bovino, M. Braccini, and C. Sibilia, “Orbital angular momentum in noncollinear second-harmonic generation by off-axis vortex beams,” J. Opt. Soc. Am. B 28, 2806–2811 (2011). [CrossRef]
  12. W. J. Firth and D. V. Skryabin, “Optical solitons carrying orbital angular momentum,” Phys. Rev. Lett. 79, 2450–2453 (1997). [CrossRef]
  13. L. Torner and D. V. Petrov, “Azimuthal instabilities and self-breaking of beams into sets of solitons in bulk second-harmonic generation,” Electron. Lett. 33, 608–610 (1997). [CrossRef]
  14. D. V. Skryabin and W. J. Firth, “Instabilities of higher-order parametric solitons: Filamentation versus coalescence,” Phys. Rev. E 58, R1252–R1255 (1998). [CrossRef]
  15. J. P. Torres, J. M. Soto-Crespo, L. Torner, and D. V. Petrov, “Solitary-wave vortices in quadratic nonlinear media,” J. Opt. Soc. Am. B 15, 625–627 (1998). [CrossRef]
  16. D. V. Petrov, L. Torner, J. Martorell, R. Vilaseca, J. P. Torres, and C. Cojocaru, “Observation of azimuthal modulational instability and formation of patterns of optical solitons in a quadratic nonlinear crystal,” Opt. Lett. 23, 1444–1446 (1998). [CrossRef]
  17. J. P. Torres, J. M. Soto-Crespo, L. Torner, and D. V. Petrov, “Solitary-wave vortices in type II second-harmonic generation,” Opt. Commun. 149, 77–83 (1998). [CrossRef]
  18. G. Molina-Terriza, E. M. Wright, and L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26, 163–165 (2001). [CrossRef]
  19. V. I. Kruglov, Y. A. Logvin, and V. M. Volkov, “The theory of spiral laser-beams in nonlinear media,” J. Mod. Opt. 39, 2277–2291 (1992). [CrossRef]
  20. C. J. Pethick and H. Smith, Bose-Einstein Condensate in Dilute Gas (Cambridge University, 2008).
  21. F. Dalfovo and S. Stringari, “Bosons in anisotropic traps: ground state and vortices,” Phys. Rev. A 53, 2477–2485 (1996). [CrossRef]
  22. R. J. Dodd, “Approximate solutions of the nonlinear Schrödinger equation for ground and excited states of Bose-Einstein condensates,” J. Res. Natl. Inst. Stand. Technol. 101, 545–552 (1996). [CrossRef]
  23. T. J. Alexander and L. Bergé, “Ground states and vortices of matter-wave condensates and optical guided waves,” Phys. Rev. E 65, 026611 (2002). [CrossRef]
  24. L. D. Carr and C. W. Clark, “Vortices in attractive Bose-Einstein condensates in two dimensions,” Phys. Rev. Lett. 97, 010403 (2006). [CrossRef]
  25. D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, “Vortex stability in nearly-two-dimensional Bose-Einstein condensates with attraction,” Phys. Rev. A 73, 043615 (2006). [CrossRef]
  26. L. D. Carr and C. W. Clark, “Vortices and ring solitons in Bose-Einstein condensates,” Phys. Rev. A 74, 043613 (2006). [CrossRef]
  27. G. Herring, L. D. Carr, R. Carretero-González, P. G. Kevrekidis, and D. J. Frantzeskakis, “Radially symmetric nonlinear states of harmonically trapped Bose-Einstein condensates,” Phys. Rev. A 77, 043607 (2008). [CrossRef]
  28. F. Du, Y. W. Lu, and S. T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett. 85, 2181–2183(2004). [CrossRef]
  29. F. Luan, A. K. George, T. D. Hedeley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. S. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett. 29, 2369–2371 (2004). [CrossRef]
  30. P. D. Drummond, K. V. Kheruntsyan, and H. He, “Coherent molecular solitons in Bose-Einstein condensates,” Phys. Rev. Lett. 81, 3055–3058 (1998). [CrossRef]
  31. D. J. Heinzen, R. Wynar, P. D. Drummond, and K. V. Kheruntsyan, “Superchemistry: Dynamics of coupled atomic and molecular Bose-Einstein condensates,” Phys. Rev. Lett. 84, 5029–5033 (2000). [CrossRef]
  32. J. J. Hope and M. K. Olsen, “Quantum superchemistry: Dynamical quantum effects in coupled atomic and molecular Bose-Einstein condensates,” Phys. Rev. Lett. 86, 3220–3223 (2001). [CrossRef]
  33. T. Hornung, S. Gordienko, R. de Vivie-Riedle, and B. J. Verhaar, “Optimal conversion of an atomic to a molecular Bose-Einstein condensate,” Phys. Rev. A 66, 043607 (2002). [CrossRef]
  34. Z. Y. Xu, Y. V. Kartashov, L. C. Crasovan, D. Mihalache, and L. Torner, “Multicolor vortex solitons in two-dimensional photonic lattices,” Phys. Rev. E 71, 016616 (2005). [CrossRef]
  35. M. J. Werner and P. D. Drummond, “Strongly coupled nonlinear parametric solitary waves,” Opt. Lett. 19, 613–615 (1994). [CrossRef]
  36. D. Mihalache, D. Mazilu, L. C. Crasovan, I. Towers, B. A. Malomed, A. V. Buryak, L. Torner, and F. Lederer, “Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities,” Phys. Rev. E 66, 016613 (2002). [CrossRef]

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