Solitons and vortices in nonlinear two-dimensional photonic crystals of the Kronig-Penney type |
Optics Express, Vol. 19, Issue 18, pp. 17834-17851 (2011)
http://dx.doi.org/10.1364/OE.19.017834
Acrobat PDF (2498 KB)
Abstract
Solitons in the model of nonlinear photonic crystals with the transverse structure based on two-dimensional (2D) quadratic- or rhombic-shaped Kronig-Penney (KP) lattices are studied by means of numerical methods. The model can also applies to a Bose-Einstein condensate (BEC) trapped in a superposition of linear and nonlinear 2D periodic potentials. The analysis is chiefly presented for the self-repulsive nonlinearity, which gives rise to several species of stable fundamental gap solitons, dipoles, four-peak complexes, and vortices in two finite bandgaps of the underlying spectrum. Stable solitons with complex shapes are found, in particular, in the second bandgap of the KP lattice with the rhombic structure. The stability of the localized modes is analyzed in terms of eigenvalues of small perturbations, and tested in direct simulations. Depending on the value of the KP’s duty cycle (DC, i.e., the ratio of the void’s width to the lattice period), an internal stability boundary for the solitons and vortices may exist inside of the first bandgap. Otherwise, the families of the localized modes are entirely stable or unstable in the bandgaps. With the self-attractive nonlinearity, only unstable solitons and vortices are found in the semi-infinite gap.
© 2011 OSA
1. Introduction and the model
3. J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russel, “Photonic band cap guidance in optical fibers,” Science 282, 1476–1478 (1998). [CrossRef] [PubMed]
11. S. Arismar Cerqueira Jr., “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys. 73, 024401 (2010). [CrossRef]
14. J. P. Dowling and C. M. Bowden, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41, 345–351 (1994). [CrossRef]
17. D. Hennig and G. P. Tsironis, “Wave transmission in nonlinear lattices,” Phys. Rep. 307, 333–432 (1999). [CrossRef]
18. A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear localized waves in a periodic medium,” Phys. Rev. Lett. 87, 083901 (2001). [CrossRef] [PubMed]
24. T. Mayteevarunyoo and B. A. Malomed, “Solitons in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 25, 1854–1863 (2008). [CrossRef]
25. B. T. Seaman, L. D. Carr, and M. J. Holland, “Nonlinear band structure in Bose-Einstein condensates: nonlinear Schrödinger equation with a Kronig-Penney potential,” Phys. Rev. A 71, 033622 (2005). [CrossRef]
26. A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, “Matter-wave solitons with a periodic, piecewise-constant scattering length,” Phys. Rev. A 78, 013611 (2008). [CrossRef]
12. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett. 29, 2369–2371 (2004). [CrossRef] [PubMed]
27. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and M. Douay, “Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region ¡ 20 dB/km) around 1550 nm,” Opt. Express 13, 8452–8459 (2005). [CrossRef] [PubMed]
13. T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express 11, 2589–2596 (2003). [CrossRef] [PubMed]
28. F. Du, Y. Q. Lu, and S. T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett. 85, 2181–2183 (2004). [CrossRef]
31. C. R. Rosberg, F. H. Bennet, D. N. Neshev, P. D. Rasmussen, O. Bang, W. Królikowski, A. Bjarklev, and Y. S. Kivshar, “Tunable diffraction and self-defocusing in liquid-filled photonic crystal fibers,” Opt. Express 15, 12145 (2007). [CrossRef] [PubMed]
28. F. Du, Y. Q. Lu, and S. T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett. 85, 2181–2183 (2004). [CrossRef]
29. M. W. Haakestad, T. T. Alkeskjold, M. D. Nielsen, L. Scolari, J. Riishede, H. E. Engan, and A. Bjarklev, “Electrically tunable photonic bandgap guidance in a liquid-crystal-filled photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 819–821 (2005). [CrossRef]
32. Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–306 (2011). [CrossRef]
33. J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D 36, R1 (2003). [CrossRef]
34. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete propagation and spatial solitons in nematic liquid crystals,” Opt. Lett. 29, 1530–1532 (2004). [CrossRef] [PubMed]
35. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009). [CrossRef]
36. D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988). [CrossRef] [PubMed]
39. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008). [CrossRef]
40. B. Maes, P. Bienstman, and R. Baets, “Bloch modes and self-localized waveguides in nonlinear photonic crystals,” J. Opt. Soc. Am. B 22, 613–619 (2005). [CrossRef]
41. R. Driben, B. A. Malomed, A. Gubeskys, and J. Zyss, “Cubic-quintic solitons in the checkerboard potential,” Phys. Rev. E 76, 066604 (2007). [CrossRef]
42. R. Driben and B. A. Malomed, “Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials,” Eur. Phys. J. D 50, 317–323 (2008). [CrossRef]
43. H. L. Stormer, L. N. Pfeiffer, K. W. Baldwin, K. W. West, and J.Spector, atomically precise superlattice potential imposed on a 2-dimensional electron gas,” Appl. Phys. Lett. 58, 726–728 (1991). [CrossRef]
44. Y. Li, B. A. Malomed, M. Feng, and J. Zhou, “Arrayed and checkerboard optical waveguides controlled by the electromagnetically induced transparency,” Phys. Rev. A 82, 633813 (2010). [CrossRef]
45. S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, “Permanent magnetic lattices for ultracold atoms and quantum degenerate gases,” J. Phys. B 39, 847 (2006). [CrossRef]
46. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108 (1998). [CrossRef]
47. M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature 415, 39 (2002). [CrossRef] [PubMed]
48. P. O. Fedichev, Y. Kagan, G. V. Shlyapnikov, and J. T. M. Walraven, “Influence of nearly resonant light on the scattering length in low-temperature atomic gases,” Phys. Rev. Lett. 77, 2913–2916 (1996). [CrossRef] [PubMed]
49. M. Theis, M., G. Thalhammer, K. Winkler, M. Hellwig, G. Ruff, R. Grimm, and J. H. Denschlag, “Tuning the scattering length with an optically induced Feshbach resonance,” Phys. Rev. Lett. 93, 123001 (2004). [CrossRef] [PubMed]
5. P. Xie, Z.-Q. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasiperiodic photonic crystals,” Phys. Rev. E 67, 026607 (2003). [CrossRef]
6. A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, and J. A. Monsoriu, “Spatial soliton formation in photonic crystal fibers,” Opt. Express 11, 452–459 (2003). [CrossRef] [PubMed]
7. Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, “Soliton topology versus discrete symmetry in optical lattices,” Phys. Rev. Lett. 95, 123902 (2005). [CrossRef] [PubMed]
8. A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, and J. A. Monsoriu, “Vortex solitons in photonic crystal fibers,” Opt. Express 12, 817–822 (2004). [CrossRef] [PubMed]
2. The framework of the analysis
2.1. Stationary solutions and the bandgap spectrum
50. J. Yang, “Newton-conjugate gradient methods for solitary wave computations,” J. Comput. Phys. 228, 7007–7024 (2009). [CrossRef]
2.2. The linear-stability analysis of solitons
51. J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, 2010). [CrossRef]
3. Photonic crystals with the square transverse structure
3.1. Fundamental solitons and their bound states
52. T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno, “Matter-wave vortices and solitons in anisotropic optical lattices,” Physica D 238, 1439–1448 (2009). [CrossRef]
3.2. Vortices
53. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quant. Semiclass. Opt. 7, R53–R72 (2005). [CrossRef]
35. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009). [CrossRef]
52. T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno, “Matter-wave vortices and solitons in anisotropic optical lattices,” Physica D 238, 1439–1448 (2009). [CrossRef]
4. Photonic crystals with the rhombic transverse structure
4.1. Simple and complex gap solitons
4.2. Vortices
4.3. The self-focusing nonlinearity
53. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quant. Semiclass. Opt. 7, R53–R72 (2005). [CrossRef]
5. Conclusion
54. H. Sakaguchi and B. A. Malomed, “Two-dimensional loosely and tightly bound solitons in optical lattices and inverted traps,” J. Phys. B 37, 2225–2239 (2004). [CrossRef]
55. R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Królikowski, C. Denz, and Y. S. Kivshar, “Reduced-symmetry two-dimensional solitons in photonic lattices,” Phys. Rev. Lett.96, 023905 (2006). [CrossRef] [PubMed]
55. R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Królikowski, C. Denz, and Y. S. Kivshar, “Reduced-symmetry two-dimensional solitons in photonic lattices,” Phys. Rev. Lett.96, 023905 (2006). [CrossRef] [PubMed]
52. T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno, “Matter-wave vortices and solitons in anisotropic optical lattices,” Physica D 238, 1439–1448 (2009). [CrossRef]
Acknowledgment
References and links
1. | J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008). |
2. | M. Skorobogatiy and J. Yang, Fundamentals of Photonic Crystals Guiding (Cambridge University Press, 2009). |
3. | J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russel, “Photonic band cap guidance in optical fibers,” Science 282, 1476–1478 (1998). [CrossRef] [PubMed] |
4. | B. J. Eggleton, B. J., C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, “Microstructured optical fiber devices,” Opt. Express 9, 698–713 (2001). [CrossRef] [PubMed] |
5. | P. Xie, Z.-Q. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasiperiodic photonic crystals,” Phys. Rev. E 67, 026607 (2003). [CrossRef] |
6. | A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, and J. A. Monsoriu, “Spatial soliton formation in photonic crystal fibers,” Opt. Express 11, 452–459 (2003). [CrossRef] [PubMed] |
7. | Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, “Soliton topology versus discrete symmetry in optical lattices,” Phys. Rev. Lett. 95, 123902 (2005). [CrossRef] [PubMed] |
8. | A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, and J. A. Monsoriu, “Vortex solitons in photonic crystal fibers,” Opt. Express 12, 817–822 (2004). [CrossRef] [PubMed] |
9. | T. M. Monro and D. J. Richardson, “Holey optical fibres: Fundamental properties and device applications,” C. R. Physique 4, 175–186 (2003). [CrossRef] |
10. | P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24, 4729–4749 (2006). [CrossRef] |
11. | S. Arismar Cerqueira Jr., “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys. 73, 024401 (2010). [CrossRef] |
12. | F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett. 29, 2369–2371 (2004). [CrossRef] [PubMed] |
13. | T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express 11, 2589–2596 (2003). [CrossRef] [PubMed] |
14. | J. P. Dowling and C. M. Bowden, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt. 41, 345–351 (1994). [CrossRef] |
15. | Q. Li, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Wave propagation in nonlinear photonic band-gap materials,” Phys. Rev. B 53, 15577–15585 (1996). [CrossRef] |
16. | E. Lidorikis, Q. Li, and C. M. Soukoulis, “Wave propagation in nonlinear multilayer structures,” Phys. Rev. B 54, 10249–10252 (1996). [CrossRef] |
17. | D. Hennig and G. P. Tsironis, “Wave transmission in nonlinear lattices,” Phys. Rep. 307, 333–432 (1999). [CrossRef] |
18. | A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear localized waves in a periodic medium,” Phys. Rev. Lett. 87, 083901 (2001). [CrossRef] [PubMed] |
19. | W. Li and A. Smerzi, “Nonlinear Krönig-Penney model,” Phys. Rev. E 70, 016605 (2004). [CrossRef] |
20. | 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] |
21. | Y. Kominis, “Analytical solitary wave solutions of the nonlinear Kronig-Penney model in photonic structures,” Phys. Rev. E 73, 066619 (2006). [CrossRef] |
22. | Y. Kominis and K. Hizanidis, “Lattice solitons in self-defocusing optical media: analytical solutions of the nonlinear Kronig-Penney model,” Opt. Lett. 31, 2888–2890 (2006). [CrossRef] [PubMed] |
23. | Y. Kominis, A. Papadopoulos, and K. Hizanidis, “Surface solitons in waveguide arrays: Analytical solutions,” Opt. Express 15, 10041–10051 (2007). [CrossRef] [PubMed] |
24. | T. Mayteevarunyoo and B. A. Malomed, “Solitons in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 25, 1854–1863 (2008). [CrossRef] |
25. | B. T. Seaman, L. D. Carr, and M. J. Holland, “Nonlinear band structure in Bose-Einstein condensates: nonlinear Schrödinger equation with a Kronig-Penney potential,” Phys. Rev. A 71, 033622 (2005). [CrossRef] |
26. | A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, “Matter-wave solitons with a periodic, piecewise-constant scattering length,” Phys. Rev. A 78, 013611 (2008). [CrossRef] |
27. | G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and M. Douay, “Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region ¡ 20 dB/km) around 1550 nm,” Opt. Express 13, 8452–8459 (2005). [CrossRef] [PubMed] |
28. | F. Du, Y. Q. Lu, and S. T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett. 85, 2181–2183 (2004). [CrossRef] |
29. | M. W. Haakestad, T. T. Alkeskjold, M. D. Nielsen, L. Scolari, J. Riishede, H. E. Engan, and A. Bjarklev, “Electrically tunable photonic bandgap guidance in a liquid-crystal-filled photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 819–821 (2005). [CrossRef] |
30. | A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, “Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers,” Opt. Lett. 30, 830 (2005). [CrossRef] [PubMed] |
31. | C. R. Rosberg, F. H. Bennet, D. N. Neshev, P. D. Rasmussen, O. Bang, W. Królikowski, A. Bjarklev, and Y. S. Kivshar, “Tunable diffraction and self-defocusing in liquid-filled photonic crystal fibers,” Opt. Express 15, 12145 (2007). [CrossRef] [PubMed] |
32. | Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–306 (2011). [CrossRef] |
33. | J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D 36, R1 (2003). [CrossRef] |
34. | A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete propagation and spatial solitons in nematic liquid crystals,” Opt. Lett. 29, 1530–1532 (2004). [CrossRef] [PubMed] |
35. | Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt. 52, 63–148 (2009). [CrossRef] |
36. | D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988). [CrossRef] [PubMed] |
37. | J. 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] |
38. | D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003). [CrossRef] [PubMed] |
39. | F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep. 463, 1–126 (2008). [CrossRef] |
40. | B. Maes, P. Bienstman, and R. Baets, “Bloch modes and self-localized waveguides in nonlinear photonic crystals,” J. Opt. Soc. Am. B 22, 613–619 (2005). [CrossRef] |
41. | R. Driben, B. A. Malomed, A. Gubeskys, and J. Zyss, “Cubic-quintic solitons in the checkerboard potential,” Phys. Rev. E 76, 066604 (2007). [CrossRef] |
42. | R. Driben and B. A. Malomed, “Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials,” Eur. Phys. J. D 50, 317–323 (2008). [CrossRef] |
43. | H. L. Stormer, L. N. Pfeiffer, K. W. Baldwin, K. W. West, and J.Spector, atomically precise superlattice potential imposed on a 2-dimensional electron gas,” Appl. Phys. Lett. 58, 726–728 (1991). [CrossRef] |
44. | Y. Li, B. A. Malomed, M. Feng, and J. Zhou, “Arrayed and checkerboard optical waveguides controlled by the electromagnetically induced transparency,” Phys. Rev. A 82, 633813 (2010). [CrossRef] |
45. | S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, “Permanent magnetic lattices for ultracold atoms and quantum degenerate gases,” J. Phys. B 39, 847 (2006). [CrossRef] |
46. | D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108 (1998). [CrossRef] |
47. | M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature 415, 39 (2002). [CrossRef] [PubMed] |
48. | P. O. Fedichev, Y. Kagan, G. V. Shlyapnikov, and J. T. M. Walraven, “Influence of nearly resonant light on the scattering length in low-temperature atomic gases,” Phys. Rev. Lett. 77, 2913–2916 (1996). [CrossRef] [PubMed] |
49. | M. Theis, M., G. Thalhammer, K. Winkler, M. Hellwig, G. Ruff, R. Grimm, and J. H. Denschlag, “Tuning the scattering length with an optically induced Feshbach resonance,” Phys. Rev. Lett. 93, 123001 (2004). [CrossRef] [PubMed] |
50. | J. Yang, “Newton-conjugate gradient methods for solitary wave computations,” J. Comput. Phys. 228, 7007–7024 (2009). [CrossRef] |
51. | J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, 2010). [CrossRef] |
52. | T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno, “Matter-wave vortices and solitons in anisotropic optical lattices,” Physica D 238, 1439–1448 (2009). [CrossRef] |
53. | B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quant. Semiclass. Opt. 7, R53–R72 (2005). [CrossRef] |
54. | H. Sakaguchi and B. A. Malomed, “Two-dimensional loosely and tightly bound solitons in optical lattices and inverted traps,” J. Phys. B 37, 2225–2239 (2004). [CrossRef] |
55. | R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Królikowski, C. Denz, and Y. S. Kivshar, “Reduced-symmetry two-dimensional solitons in photonic lattices,” Phys. Rev. Lett.96, 023905 (2006). [CrossRef] [PubMed] |
OCIS Codes
(020.1475) Atomic and molecular physics : Bose-Einstein condensates
(060.5295) Fiber optics and optical communications : Photonic crystal fibers
(050.5298) Diffraction and gratings : Photonic crystals
(190.6135) Nonlinear optics : Spatial solitons
ToC Category:
Photonic Crystals
History
Original Manuscript: August 5, 2011
Revised Manuscript: August 13, 2011
Manuscript Accepted: August 14, 2011
Published: August 25, 2011
Citation
Thawatchai Mayteevarunyoo, Boris A. Malomed, and Athikom Roeksabutr, "Solitons and vortices in nonlinear two-dimensional photonic crystals of the Kronig-Penney type," Opt. Express 19, 17834-17851 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-17834
Sort: Year | Journal | Reset
References
- J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).
- M. Skorobogatiy and J. Yang, Fundamentals of Photonic Crystals Guiding (Cambridge University Press, 2009).
- J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russel, “Photonic band cap guidance in optical fibers,” Science282, 1476–1478 (1998). [CrossRef] [PubMed]
- B. J. Eggleton, B. J., C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, “Microstructured optical fiber devices,” Opt. Express9, 698–713 (2001). [CrossRef] [PubMed]
- P. Xie, Z.-Q. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasiperiodic photonic crystals,” Phys. Rev. E67, 026607 (2003). [CrossRef]
- A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, and J. A. Monsoriu, “Spatial soliton formation in photonic crystal fibers,” Opt. Express11, 452–459 (2003). [CrossRef] [PubMed]
- Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, “Soliton topology versus discrete symmetry in optical lattices,” Phys. Rev. Lett.95, 123902 (2005). [CrossRef] [PubMed]
- A. Ferrando, M. Zacarés, P. F. de Córdoba, D. Binosi, and J. A. Monsoriu, “Vortex solitons in photonic crystal fibers,” Opt. Express12, 817–822 (2004). [CrossRef] [PubMed]
- T. M. Monro and D. J. Richardson, “Holey optical fibres: Fundamental properties and device applications,” C. R. Physique4, 175–186 (2003). [CrossRef]
- P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol.24, 4729–4749 (2006). [CrossRef]
- S. Arismar Cerqueira, “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys.73, 024401 (2010). [CrossRef]
- F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. St. J. Russell, “All-solid photonic bandgap fiber,” Opt. Lett.29, 2369–2371 (2004). [CrossRef] [PubMed]
- T. T. Larsen, A. Bjarklev, D. S. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express11, 2589–2596 (2003). [CrossRef] [PubMed]
- J. P. Dowling and C. M. Bowden, “Anomalous index of refraction in photonic bandgap materials,” J. Mod. Opt.41, 345–351 (1994). [CrossRef]
- Q. Li, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Wave propagation in nonlinear photonic band-gap materials,” Phys. Rev. B53, 15577–15585 (1996). [CrossRef]
- E. Lidorikis, Q. Li, and C. M. Soukoulis, “Wave propagation in nonlinear multilayer structures,” Phys. Rev. B54, 10249–10252 (1996). [CrossRef]
- D. Hennig and G. P. Tsironis, “Wave transmission in nonlinear lattices,” Phys. Rep.307, 333–432 (1999). [CrossRef]
- A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear localized waves in a periodic medium,” Phys. Rev. Lett.87, 083901 (2001). [CrossRef] [PubMed]
- W. Li and A. Smerzi, “Nonlinear Krönig-Penney model,” Phys. Rev. E70, 016605 (2004). [CrossRef]
- 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. E71, 016613 (2005). [CrossRef]
- Y. Kominis, “Analytical solitary wave solutions of the nonlinear Kronig-Penney model in photonic structures,” Phys. Rev. E73, 066619 (2006). [CrossRef]
- Y. Kominis and K. Hizanidis, “Lattice solitons in self-defocusing optical media: analytical solutions of the nonlinear Kronig-Penney model,” Opt. Lett.31, 2888–2890 (2006). [CrossRef] [PubMed]
- Y. Kominis, A. Papadopoulos, and K. Hizanidis, “Surface solitons in waveguide arrays: Analytical solutions,” Opt. Express15, 10041–10051 (2007). [CrossRef] [PubMed]
- T. Mayteevarunyoo and B. A. Malomed, “Solitons in one-dimensional photonic crystals,” J. Opt. Soc. Am. B25, 1854–1863 (2008). [CrossRef]
- B. T. Seaman, L. D. Carr, and M. J. Holland, “Nonlinear band structure in Bose-Einstein condensates: nonlinear Schrödinger equation with a Kronig-Penney potential,” Phys. Rev. A71, 033622 (2005). [CrossRef]
- A. S. Rodrigues, P. G. Kevrekidis, M. A. Porter, D. J. Frantzeskakis, P. Schmelcher, and A. R. Bishop, “Matter-wave solitons with a periodic, piecewise-constant scattering length,” Phys. Rev. A78, 013611 (2008). [CrossRef]
- G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and M. Douay, “Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region ¡ 20 dB/km) around 1550 nm,” Opt. Express13, 8452–8459 (2005). [CrossRef] [PubMed]
- F. Du, Y. Q. Lu, and S. T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett.85, 2181–2183 (2004). [CrossRef]
- M. W. Haakestad, T. T. Alkeskjold, M. D. Nielsen, L. Scolari, J. Riishede, H. E. Engan, and A. Bjarklev, “Electrically tunable photonic bandgap guidance in a liquid-crystal-filled photonic crystal fiber,” IEEE Photon. Technol. Lett.17, 819–821 (2005). [CrossRef]
- A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, “Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers,” Opt. Lett.30, 830 (2005). [CrossRef] [PubMed]
- C. R. Rosberg, F. H. Bennet, D. N. Neshev, P. D. Rasmussen, O. Bang, W. Królikowski, A. Bjarklev, and Y. S. Kivshar, “Tunable diffraction and self-defocusing in liquid-filled photonic crystal fibers,” Opt. Express15, 12145 (2007). [CrossRef] [PubMed]
- Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys.83, 247–306 (2011). [CrossRef]
- J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D36, R1 (2003). [CrossRef]
- A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete propagation and spatial solitons in nematic liquid crystals,” Opt. Lett.29, 1530–1532 (2004). [CrossRef] [PubMed]
- Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Opt.52, 63–148 (2009). [CrossRef]
- D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett.13, 794–796 (1988). [CrossRef] [PubMed]
- J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature422, 147–150 (2003). [CrossRef] [PubMed]
- D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424, 817–823 (2003). [CrossRef] [PubMed]
- F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008). [CrossRef]
- B. Maes, P. Bienstman, and R. Baets, “Bloch modes and self-localized waveguides in nonlinear photonic crystals,” J. Opt. Soc. Am. B22, 613–619 (2005). [CrossRef]
- R. Driben, B. A. Malomed, A. Gubeskys, and J. Zyss, “Cubic-quintic solitons in the checkerboard potential,” Phys. Rev. E76, 066604 (2007). [CrossRef]
- R. Driben and B. A. Malomed, “Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials,” Eur. Phys. J. D50, 317–323 (2008). [CrossRef]
- H. L. Stormer, L. N. Pfeiffer, K. W. Baldwin, K. W. West, and J.Spector, atomically precise superlattice potential imposed on a 2-dimensional electron gas,” Appl. Phys. Lett.58, 726–728 (1991). [CrossRef]
- Y. Li, B. A. Malomed, M. Feng, and J. Zhou, “Arrayed and checkerboard optical waveguides controlled by the electromagnetically induced transparency,” Phys. Rev. A82, 633813 (2010). [CrossRef]
- S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, “Permanent magnetic lattices for ultracold atoms and quantum degenerate gases,” J. Phys. B39, 847 (2006). [CrossRef]
- D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett.81, 3108 (1998). [CrossRef]
- M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature415, 39 (2002). [CrossRef] [PubMed]
- P. O. Fedichev, Y. Kagan, G. V. Shlyapnikov, and J. T. M. Walraven, “Influence of nearly resonant light on the scattering length in low-temperature atomic gases,” Phys. Rev. Lett.77, 2913–2916 (1996). [CrossRef] [PubMed]
- M. Theis, M., G. Thalhammer, K. Winkler, M. Hellwig, G. Ruff, R. Grimm, and J. H. Denschlag, “Tuning the scattering length with an optically induced Feshbach resonance,” Phys. Rev. Lett.93, 123001 (2004). [CrossRef] [PubMed]
- J. Yang, “Newton-conjugate gradient methods for solitary wave computations,” J. Comput. Phys.228, 7007–7024 (2009). [CrossRef]
- J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, 2010). [CrossRef]
- T. Mayteevarunyoo, B. A. Malomed, B. B. Baizakov, and M. Salerno, “Matter-wave vortices and solitons in anisotropic optical lattices,” Physica D238, 1439–1448 (2009). [CrossRef]
- B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quant. Semiclass. Opt.7, R53–R72 (2005). [CrossRef]
- H. Sakaguchi and B. A. Malomed, “Two-dimensional loosely and tightly bound solitons in optical lattices and inverted traps,” J. Phys. B37, 2225–2239 (2004). [CrossRef]
- R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Królikowski, C. Denz, and Y. S. Kivshar, “Reduced-symmetry two-dimensional solitons in photonic lattices,” Phys. Rev. Lett.96, 023905 (2006). [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.
Figures
Fig. 1 | Fig. 2 | Fig. 3 |
Fig. 4 | Fig. 5 | Fig. 6 |
Fig. 7 | Fig. 8 | Fig. 9 |
Fig. 10 | Fig. 11 | Fig. 12 |
Fig. 13 | Fig. 14 | |
« Previous Article | Next Article »
OSA is a member of CrossRef.