Collisions between discrete spatiotemporal dissipative Ginzburg-Landau solitons in two-dimensional photonic lattices

• Autorzy: Dumitru Mihalache , Dumitru Mazilu , Falk Lederer
• Języki publikacji: EN

Abstrakty

EN

Systematic results of collisions between discrete spatiotemporal dissipative Ginzburg-Landau solitons in two-dimensional photonic lattices are reported. The generic outcomes are identified for (i) the collision of two identical solitons located in the corner, at the edge, and in the center of the photonic lattice, and for (ii) the collision of two non-identical corner and edge solitons located at different distances from the boundaries of the photonic lattice. Depending on the values of the kick (collision momentum) and of the nonlinear (cubic) gain, the collision scenarios include soliton merging, creation of an extra soliton, soliton bouncing, soliton spreading, and quasi-elastic (symmetric) interactions.

Słowa kluczowe

EN

discrete spatiotemporal optical solitons; dissipative Ginzburg-Landau solitons; photonic lattices

• Czasopismo: Open Physics
• Rocznik: 2010
• Tom: 8
• Numer: 1
• Strony: 77-86

Daty

wydano

2010-02-01

online

2009-11-15

Twórcy

autor

Dumitru Mihalache

• Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest, 077125, Romania,

autor

Dumitru Mazilu

• Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest, 077125, Romania

autor

Falk Lederer

• Institute of Solid State Theory and Theoretical Optics, Friedrich-Schiller Universität Jena, Max-Wien-Platz 1, D-07743, Jena, Germany

Bibliografia

• [1] W. J. Tomlinson, Opt. Lett. 5, 323 (1980) http://dx.doi.org/10.1364/OL.5.000323[Crossref]
• [2] V. M. Agranovich, V. S. Babichenko, V. Y. Chernyak, JETP Lett.+ 32, 512 (1980)
• [3] V. K. Fedyanin, D. Mihalache, Z. Phys. B 47, 167 (1982) http://dx.doi.org/10.1007/BF01441299[Crossref]
• [4] D. Mihalache, R. G. Nazmitdinov, V. K. Fedyanin, Phys. Scripta 29, 269 (1984) http://dx.doi.org/10.1088/0031-8949/29/3/014[Crossref]
• [5] U. Langbein, F. Lederer, H.-E. Ponath, Opt. Commun. 46, 167 (1983) http://dx.doi.org/10.1016/0030-4018(83)90270-5[Crossref]
• [6] G. I. Stegeman, C. T. Seaton, J. Chilwell, S. D. Smith, Appl. Phys. Lett. 44, 830 (1984) http://dx.doi.org/10.1063/1.94956[Crossref]
• [7] N. N. Akhmediev, V. I. Korneyev, Y. V. Kuzmenko, Zh. Eksp. Teor. Fiz.+ 88, 107 (1985)
• [8] N. N. Akhmediev, V. I. Korneyev, Y. V. Kuzmenko, Sov. Phys. JETP-USSR 61, 62 (1985)
• [9] F. Lederer, D. Mihalache, Solid State Commun. 59, 151 (1986) http://dx.doi.org/10.1016/0038-1098(86)90198-5[Crossref]
• [10] D. Mihalache, D. Mazilu, F. Lederer, Opt. Commun. 59, 391 (1986) http://dx.doi.org/10.1016/0030-4018(86)90364-0[Crossref]
• [11] D. Mihalache et al., Opt. Lett. 12, 187 (1987) http://dx.doi.org/10.1364/OL.12.000187[Crossref]
• [12] D. Mihalache, M. Bertolotti, C. Sibilia, Prog. Optics 27, 229 (1989)
• [13] A. D. Boardman, P. Egan, F. Lederer, U. Langbein, D. Mihalache, In: Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath, G. I. Stegeman (Eds.) (Elsevier Science Publishers B. V., Amsterdam, 1991) 73
• [14] F. Lederer et al., Opt. Commun. 99, 95 (1993) http://dx.doi.org/10.1016/0030-4018(93)90711-D[Crossref]
• [15] K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, A. Haché, Opt. Lett. 30, 2466 (2005) http://dx.doi.org/10.1364/OL.30.002466[Crossref]
• [16] S. Suntsov et al., Phys. Rev. Lett. 96, 063901 (2006) http://dx.doi.org/10.1103/PhysRevLett.96.063901[Crossref]
• [17] C. R. Rosberg et al., Phys. Rev. Lett. 97, 083901 (2006) http://dx.doi.org/10.1103/PhysRevLett.97.083901[Crossref]
• [18] M. I. Molina, R. A. Vicencio, Yu.S. Kivshar, Opt. Lett. 31, 1693 (2006) http://dx.doi.org/10.1364/OL.31.001693[Crossref]
• [19] Yu. S. Kivshar, G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003)
• [20] Y. V. Kartashov, L. Torner, V. A. Vysloukh, Opt. Lett. 31, 2595 (2006) http://dx.doi.org/10.1364/OL.31.002595[Crossref]
• [21] Y. V. Kartashov, F. Ye, V. A. Vysloukh, L. Torner, Opt. Lett. 32, 2260 (2007) http://dx.doi.org/10.1364/OL.32.002260[Crossref]
• [22] Y. V. Kartashov, V. A. Vysloukh, L. Torner, Phys. Rev. A 76, 013831 (2007) http://dx.doi.org/10.1103/PhysRevA.76.013831[Crossref]
• [23] Y. Kominis, A. Papadopoulos, K. Hizanidis, Opt. Express 15, 10041 (2007) http://dx.doi.org/10.1364/OE.15.010041[Crossref]
• [24] Y. Kominis, K. Hizanidis, Phys. Rev. Lett. 102, 133903 (2009) http://dx.doi.org/10.1103/PhysRevLett.102.133903[Crossref]
• [25] M. I. Molina, Y. V. Kartashov, L. Torner, Yu. S. Kivshar, Opt. Lett. 32, 2668 (2007) http://dx.doi.org/10.1364/OL.32.002668[Crossref]
• [26] I. L. Garanovich, A. A. Sukhorukhov, Y. S. Kivshar, Cent. Eur. J. Phys. 6, 593 (2008) http://dx.doi.org/10.2478/s11534-008-0047-8[Crossref]
• [27] Z. Xu, Yu. S. Kivshar, Opt. Lett. 33, 2551 (2008) http://dx.doi.org/10.1364/OL.33.002551[Crossref]
• [28] E. Smirnov, M. Stepić, C. E. Rütter, D. Kip, V. Shandarov, Opt. Lett. 31, 2338 (2006) http://dx.doi.org/10.1364/OL.31.002338[Crossref]
• [29] B. Alfassi, C. Rotschild, O. Manela, M. Segev, D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007) http://dx.doi.org/10.1103/PhysRevLett.98.213901[Crossref]
• [30] A. Szameit, Y. V. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, V.A. Vysloukh, L. Torner, Opt. Lett. 33, 1132 (2008) http://dx.doi.org/10.1364/OL.33.001132[Crossref]
• [31] X. Wang, A. Samodurov, Z. Chen, Opt. Lett. 33, 1240 (2008) http://dx.doi.org/10.1364/OL.33.001240[Crossref]
• [32] S. Suntsov et al., J. Nonlinear Opt. Phys. 16, 401 (2007) http://dx.doi.org/10.1142/S0218863507003834[Crossref]
• [33] F. Lederer et al., Phys. Rep. 463, 1 (2008) http://dx.doi.org/10.1016/j.physrep.2008.04.004[Crossref]
• [34] Yu. S. Kivshar, Laser Phys. Lett. 5, 703 (2008) http://dx.doi.org/10.1002/lapl.200810062[Crossref]
• [35] D. Mihalache, D. Mazilu, F. Lederer, Yu. S. Kivshar, Opt. Express 15, 589 (2007) http://dx.doi.org/10.1364/OE.15.010718[Crossref]
• [36] D. Mihalache, D. Mazilu, F. Lederer, Yu. S. Kivshar, Opt. Lett. 32, 2091 (2007) http://dx.doi.org/10.1364/OL.32.002091[Crossref]
• [37] A. B. Aceves, C. De Angelis, A. M. Rubenchik, S. K. Turitsyn, Opt. Lett. 19, 329 (1994) http://dx.doi.org/10.1364/OL.19.000329[Crossref]
• [38] E. W. Laedke, K. H. Spatschek, S. K. Turitsyn, Phys. Rev. Lett. 73, 1055 (1994) http://dx.doi.org/10.1103/PhysRevLett.73.1055[Crossref]
• [39] A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik, S. K. Turitsyn, Phys. Rev. Lett. 75, 73 (1995) http://dx.doi.org/10.1103/PhysRevLett.75.73[Crossref]
• [40] A. V. Buryak, N. N. Akhmediev, IEEE J. Quantum Elect. 31, 682 (1995) http://dx.doi.org/10.1109/3.371943[Crossref]
• [41] Z. Xu, Y. V. Kartashov, L. C. Crasovan, D. Mihalache, L. Torner, Phys. Rev. E 70, 066618 (2004) http://dx.doi.org/10.1103/PhysRevE.70.066618[Crossref]
• [42] N. K. Efremidis, D. N. Christodoulides, Phys. Rev. E 67, 026606 (2003) http://dx.doi.org/10.1103/PhysRevE.67.026606[Crossref]
• [43] E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, F. Lederer, Phys. Rev. Lett. 90, 253903 (2003) http://dx.doi.org/10.1103/PhysRevLett.90.253903[Crossref]
• [44] U. Peschel, O. Egorov, F. Lederer, Opt. Lett. 29, 1909 (2004) http://dx.doi.org/10.1364/OL.29.001909[Crossref]
• [45] N. K. Efremidis, D. N. Christodoulides, K. Hizanidis, Phys. Rev. A 76, 043839 (2007) http://dx.doi.org/10.1103/PhysRevA.76.043839[Crossref]
• [46] D. Mihalache, D. Mazilu, F. Lederer, Yu.S. Kivshar, Phys. Rev. A 77, 043828 (2008) http://dx.doi.org/10.1103/PhysRevA.77.043828[Crossref]
• [47] D. Mihalache, D. Mazilu, F. Lederer, Yu.S. Kivshar, Phys. Rev. E 78, 056602 (2008) http://dx.doi.org/10.1103/PhysRevE.78.056602[Crossref]
• [48] Yu. V. Bludov, V. V. Konotop, Phys. Rev. E 76, 046604 (2007) http://dx.doi.org/10.1103/PhysRevE.76.046604[Crossref]
• [49] Q. E. Hoq et al., Phys. Rev. E 78, 036605 (2008) http://dx.doi.org/10.1103/PhysRevE.78.036605[Crossref]
• [50] C. J. Benton, A. V. Gorbach, D. V. Skryabin, Phys. Rev. A 78, 033818 (2008) http://dx.doi.org/10.1103/PhysRevA.78.033818[Crossref]
• [51] H. Leblond, B. A. Malomed, D. Mihalache, Phys. Rev. A 77, 063804 (2008) http://dx.doi.org/10.1103/PhysRevA.77.063804[Crossref]
• [52] H. Leblond, B. A. Malomed, D. Mihalache, Phys. Rev. A 79, 033841 (2009) http://dx.doi.org/10.1103/PhysRevA.79.033841[Crossref]
• [53] N. C. Panoiu, R. M. Osgood, Jr., B. A. Malomed, Opt. Lett. 31, 1097 (2006) http://dx.doi.org/10.1364/OL.31.001097[Crossref]
• [54] N. C. Panoiu, B. A. Malomed, R. M. Osgood, Phys. Rev. A 78, 013801 (2008) http://dx.doi.org/10.1103/PhysRevA.78.013801[Crossref]
• [55] F. Kh. Abdullaev, Yu. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, V.V. Konotop, Phys. Rev. E 77, 016604 (2008) http://dx.doi.org/10.1103/PhysRevE.77.016604[Crossref]
• [56] I. S. Aranson, L. Kramer, Rev. Mod. Phys. 74, 99 (2002) http://dx.doi.org/10.1103/RevModPhys.74.99[Crossref]
• [57] N. Akhmediev, A. Ankiewicz (Eds.), Lect. Notes Phys. 661 (2005)
• [58] N. Akhmediev, A. Ankiewicz (Eds.), Lect. Notes Phys. 751 (2008)
• [59] B. A. Malomed, Physica D 29, 155 (1987) http://dx.doi.org/10.1016/0167-2789(87)90052-2[Crossref]
• [60] O. Thual, S. Fauve, J. Phys. (Paris) 49, 1829 (1988)
• [61] S. Fauve, O. Thual, Phys. Rev. Lett. 64, 282 (1990) http://dx.doi.org/10.1103/PhysRevLett.64.282[Crossref]
• [62] W. van Saarloos, P.C. Hohenberg, Phys. Rev. Lett. 64, 749 (1990) http://dx.doi.org/10.1103/PhysRevLett.64.749[Crossref]
• [63] V. Hakim, P. Jakobsen, Y. Pomeau, Europhys. Lett. 11, 19 (1990) http://dx.doi.org/10.1209/0295-5075/11/1/004[Crossref]
• [64] B. A. Malomed, A. A. Nepomnyashchy, Phys. Rev. A 42, 6009 (1990) http://dx.doi.org/10.1103/PhysRevA.42.6009[Crossref]
• [65] P. Marcq, H. Chaté, R. Conte, Physica D 73, 305 (1994) http://dx.doi.org/10.1016/0167-2789(94)90102-3[Crossref]
• [66] N. Akhmediev, V. V. Afanasjev, Phys. Rev. Lett. 75, 2320 (1995) http://dx.doi.org/10.1103/PhysRevLett.75.2320[Crossref]
• [67] H. R. Brand, R. J. Deissler, Phys. Rev. Lett. 63, 2801 (1989) http://dx.doi.org/10.1103/PhysRevLett.63.2801[Crossref]
• [68] V. V. Afanasjev, N. Akhmediev, J. M. Soto-Crespo, Phys. Rev. E 53, 1931 (1996) http://dx.doi.org/10.1103/PhysRevE.53.1931[Crossref]
• [69] J. M. Soto-Crespo, N. Akhmediev, A. Ankiewicz, Phys. Rev. Lett. 85, 2937 (2000) http://dx.doi.org/10.1103/PhysRevLett.85.2937[Crossref]
• [70] W. Chang, A. Ankiewicz, N. Akhmediev, Phys. Lett. A 362, 31 (2007) http://dx.doi.org/10.1016/j.physleta.2006.10.003[Crossref]
• [71] A. Ankiewicz, N. Devine, N. Akhmediev, J. M. Soto-Crespo, Phys. Lett. A 370, 454 (2007) http://dx.doi.org/10.1016/j.physleta.2007.06.001[Crossref]
• [72] D. Mihalache et al., Phys. Rev. Lett. 97, 073904 (2006) http://dx.doi.org/10.1103/PhysRevLett.97.073904[Crossref]
• [73] D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, B. A. Malomed, Phys. Rev. A 75, 033811 (2007) http://dx.doi.org/10.1103/PhysRevA.75.033811[Crossref]
• [74] D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, B. A. Malomed, Phys. Rev. A 76, 045803 (2007) http://dx.doi.org/10.1103/PhysRevA.76.045803[Crossref]
• [75] D. Mihalache, Cent. Eur. J. Phys. 6, 582 (2008) http://dx.doi.org/10.2478/s11534-008-0083-4[Crossref]
• [76] D. Mihalache, Romanian Reports in Physics 60, 749 (2008)
• [77] D. V. Skryabin, A. G. Vladimirov, Phys. Rev. Lett. 89, 044101 (2002) http://dx.doi.org/10.1103/PhysRevLett.89.044101[Crossref]
• [78] N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, Berlin, 2002)
• [79] N. N. Rosanov, S. V. Fedorov, A. N. Shatsev, Phys. Rev. Lett. 95, 053903 (2005) http://dx.doi.org/10.1103/PhysRevLett.95.053903[Crossref]
• [80] Y. Silberberg, Opt. Lett. 15, 1282 (1990) http://dx.doi.org/10.1364/OL.15.001282[Crossref]
• [81] B. A. Malomed, D. Mihalache, F. Wise, L. Torner, J. Opt. B-Quantum S. O. 7, R53 (2005) http://dx.doi.org/10.1088/1464-4266/7/5/R02[Crossref]
• [82] D. Mihalache, D. Mazilu, Yu. S. Kivshar, F. Lederer, Opt. Express 15, 10718 (2007) http://dx.doi.org/10.1364/OE.15.010718[Crossref]
• [83] D. Mihalache, D. Mazilu, F. Lederer, Yu. S. Kivshar, Opt. Lett. 32, 3173 (2007) http://dx.doi.org/10.1364/OL.32.003173[Crossref]
• [84] J. M. Ortega, W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York, 1970) 182
• [85] S. Gatz, J. Herrmann, IEEE J. Quantum Elect. 28, 1732 (1992) http://dx.doi.org/10.1109/3.142561[Crossref]
• [86] W. C. K. Mak, B. A. Malomed, P. L. Chu, Phys. Rev. E 68, 026609 (2003) http://dx.doi.org/10.1103/PhysRevE.68.026609[Crossref]
• [87] D. Royston Neill, J. Atai, B. A. Malomed, J. Opt. APure Appl. Op. 10, 085105 (2008)
• [88] D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, B. A. Malomed, Phys. Rev. A 77, 033817 (2008) http://dx.doi.org/10.1103/PhysRevA.77.033817[Crossref]
• [89] D. Mihalache, D. Mazilu, F. Lederer, Yu. S. Kivshar, Phys. Rev. A 79, 013811 (2009) http://dx.doi.org/10.1103/PhysRevA.79.013811[Crossref]
• [90] N. Akhmediev, J. M. Soto-Crespo, P. Grelu, Chaos, 17, 037112 (2007) http://dx.doi.org/10.1063/1.2746830[Crossref]
• [91] J. M. Soto-Crespo, P. Grelu, N. Akhmediev, Opt. Express 14, 4013 (2006) http://dx.doi.org/10.1364/OE.14.004013[Crossref]
• [92] E. A. Ultanir, G. I. Stegeman, C. H. Lange, F. Lederer, Opt. Lett. 29, 283 (2004) http://dx.doi.org/10.1364/OL.29.000283[Crossref]
• [93] R. H. Goodman, R. Haberman, Phys. Rev. Lett. 98, 104103 (2007) http://dx.doi.org/10.1103/PhysRevLett.98.104103[Crossref]
• [94] S. V. Dmitriev, P. G. Kevrekidis, Y. S. Kivshar, Phys. Rev. E 78, 046604 (2008) http://dx.doi.org/10.1103/PhysRevE.78.046604[Crossref]
• [95] S. V. Dmitriev, T. Shigenari, Chaos 12, 324 (2002) http://dx.doi.org/10.1063/1.1476951[Crossref]
• [96] Y. Nishiura, T. Teramoto, K. I. Ueda, Phys. Rev. E 67, 056210 (2003) http://dx.doi.org/10.1103/PhysRevE.67.056210[Crossref]
• [97] X. Yuan, T. Teramoto, Y. Nishiura, Phys. Rev. E 75, 036220 (2007) http://dx.doi.org/10.1103/PhysRevE.75.036220[Crossref]

Identyfikatory

DOI

10.2478/s11534-009-0078-9