Journal of the Optical Society of Korea

Optical Society of Korea (한국광학회)
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Three-dimensional Spatiotemporal Accessible Solitons in a PT-symmetric Potential

  • Zhong, Wei-Ping (Department of Electronic and Information Engineering, Shunde Polytechnic) ;
  • Belic, Milivoj R. (Texas A&M University at Qatar) ;
  • Huang, Tingwen (Texas A&M University at Qatar)
  • Received : 2012.08.17
  • Accepted : 2012.10.11
  • Published : 2012.12.25
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Abstract

Utilizing the three-dimensional Snyder-Mitchell model with a PT-symmetric potential, we study the influence of PT symmetry on beam propagation in strongly nonlocal nonlinear media. The complex Coulomb potential is used as the PT-symmetric potential. A localized spatiotemporal accessible soliton solution of the model is obtained. Specific values of the modulation depth for different soliton parameters are discussed. Our results reveal that in these media the localized solitons can exist in various shapes, such as single-layer and multi-layer disk-shaped structures, as well as vortex-ring and necklace patterns.

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References

  1. C. M. Bender and S. Boettcher, "Real spectra in non- Hermitian Hamiltonians having PT symmetry," Phys. Rev. Lett. 80, 5243-5246 (1998). https://doi.org/10.1103/PhysRevLett.80.5243
  2. R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, "Theory of coupled optical PT-symmetric structures," Opt. Lett. 32, 2632-2634 (2007). https://doi.org/10.1364/OL.32.002632
  3. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature (London) 424, 817-823 (2003). https://doi.org/10.1038/nature01936
  4. F. Kh. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, "Solitons in PT-symmetric nonlinear lattices," Phys. Rev. A 83, 041805-1-041805-4 (2011). https://doi.org/10.1103/PhysRevA.83.041805
  5. C. E. Ruter, K. G. Makris, R. EI-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, "Observation of parity-time symmetry in optics," Nat. Phys. 6, 192-195 (2010). https://doi.org/10.1038/nphys1515
  6. A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, "Observation of PT-symmetry breaking in complex optical potentials," Phys. Rev. Lett. 103, 093902-1-093902-4 (2009). https://doi.org/10.1103/PhysRevLett.103.093902
  7. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, "PT-symmetric optical lattices," Phys. Rev. A 81, 063807-1-063807-10 (2010). https://doi.org/10.1103/PhysRevA.81.063807
  8. Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, "Optical solitons in PT periodic potentials," Phys. Rev. Lett. 100, 030402-1-030402-4 (2008). https://doi.org/10.1103/PhysRevLett.100.030402
  9. M. Znojil and G. Levai, "The Coulomb-harmonic oscillator correspondence in PT symmetric quantum mechanics," Phys. Lett. A 271, 327 (2000). https://doi.org/10.1016/S0375-9601(00)00400-X
  10. G. Levai, "Spontaneous breakdown of PT symmetry in the complex Coulomb potential," Pramana 73, 329-335 (2009). https://doi.org/10.1007/s12043-009-0125-5
  11. G. Lévai, P. Siegl, and M. Znojil, "Scattering in the PTsymmetric Coulomb potential," J. Phys. A 42, 295201 (2009). https://doi.org/10.1088/1751-8113/42/29/295201
  12. W. P. Zhong and L. Yi, "Two-dimensional Laguerre- Gaussian soliton family in strongly nonlocal nonlinear media," Phys. Rev. A 75, 061801-1-061801-4 (2007). https://doi.org/10.1103/PhysRevA.75.061801
  13. W. P. Zhong, L. Yi, R. H. Xie, M. Belic, and G. Chen, "Robust three-dimensional spatial soliton clusters in strongly nonlocal media," J. Phys. B: At. Mol. Opt. Phys. 41, 025402 (2008). https://doi.org/10.1088/0953-4075/41/2/025402
  14. O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media," Phys. Rev. E 66, 046619-1-046619-5 (2002). https://doi.org/10.1103/PhysRevE.66.046619
  15. D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, "Spiraling multivortex solitons in nonlocal nonlinear media," Opt. Lett. 33, 198-200 (2008). https://doi.org/10.1364/OL.33.000198
  16. A. Snyder and J. Mitchell, "Accessible solitons," Science 276, 1538-1541 (1997). https://doi.org/10.1126/science.276.5318.1538
  17. C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901-1-073901-4 (2003). https://doi.org/10.1103/PhysRevLett.91.073901
  18. C. Conti, M. Peccianti, and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium," Phys. Rev. Lett. 92, 113902-1-113902-4 (2004). https://doi.org/10.1103/PhysRevLett.92.113902
  19. Y. Silberberg, "Collapse of optical pulses," Opt. Lett. 15, 1282-1284 (1990). https://doi.org/10.1364/OL.15.001282
  20. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, "Spatiotemporal optical solitons," J. Opt. B: Quantum Semiclassical Opt. 7, R53-R72 (2005). https://doi.org/10.1088/1464-4266/7/5/R02
  21. F. K. Abdullaev and V. V. Konotop (eds.), Nonlinear Waves: Classical and Quantum Aspects (Kluwer Academic Publishers, Dordrecht, Netherlands, 2004).
  22. W. P. Zhong, M. Belić, R. Xie, T. Huang, and Y. Lu, "Three-dimensional spatiotemporal solitary waves in strongly nonlocal media," Opt. Commun. 283, 5213-5217 (2010). https://doi.org/10.1016/j.optcom.2010.08.004
  23. W. P. Zhong, M. Belić, G. Assanto, B. A. Malomed, and T. Huang, "Light bullets in the spatiotemporal nonlinear Schrödinger equation with a variable negative diffraction coefficient," Phys. Rev. A 84, 043801-1-043801-8 (2011). https://doi.org/10.1103/PhysRevA.84.043801
  24. D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007). https://doi.org/10.1364/OE.15.013077
  25. W. P. Zhong and M. Belic, "Three-dimensional optical vortex and necklace solitons in highly nonlocal nonlinear media," Phys. Rev. A 79, 023804-1-023804-6 (2009). https://doi.org/10.1103/PhysRevA.79.023804
  26. M. Znojil, "Quasi-exactly solvable quartic potentials with centrifugal and Coulombic terms," arXiv:math-ph/0002036v2 (2000). https://doi.org/10.1088/0305-4470/33/22/320

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