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Propagation of beams in strongly nonlocal nonlinear medium with an elliptically symmetric response is investigated. The result shows that the propagation of beams in this type of medium can be regarded as two-dimensional asynchronous fractional Fourier transform. With this powerful mathematical tool, the analytical solution and the propagation properties of beams can be conveniently obtained. Based on the properties of the two-dimensional asynchronous fractional Fourier transform, the general propagation properties of beams are discussed, the formation conditions of solitons and two-dimensional asynchronous breathers are analyzed, and the law for interaction among solitons and/or breathers is obtained.
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Keywords:
- elliptically symmetric response /
- strongly nonlocal nonlinearity /
- soliton /
- breather
[1] Snyder A W, Mitchell D J 1997 Science 276 1538
[2] Yakimenko A I, Lashkin V M, Prikhodko O O 2006 Phys. Rev. E 73 066605
[3] Buccoliero D, Desyatnikov A S, Królikowski W, Kivshar Y S 2008 Opt. Lett. 33 198
[4] Buccoliero D, Desyatnikov A S, Królikowski W, Kivshar Y S 2007 Phys. Rev. Lett. 98 053901
[5] Zhong W P, Lin Y 2007 Phys. Rev. A 75 061801
[6] Peccianti M, Conti C, Assanto G, Luca A D, Umeton C 2002 Appl. Phys. Lett. 81 3335
[7] Lopez-Aguayo S, Desyatnikov A S, Kivshar Y S 2006 Opt. Express 14 7903
[8] Wang Y Q, Guo Q 2008 Chin. Phys. B 17 2527
[9] Królikowski W, Bang O 2000 Phys. Rev. E 63 016610
[10] Deng D M, Guo Q 2007 Opt. Lett. 32 3206
[11] Mamaev A V, Zozulya A A, Mezentsev V K, Anderson D Z, Saffman M 1997 Phys. Rev. A 56 R1110
[12] Nikolov N I, Neshev D, Królikowski W, Bang O, Rasmussen J J, Christiansen P L 2004 Opt. Lett. 29 286
[13] Lopez-Aguayo S, Gutiérrez-Vega J C 2007 Opt. Express 15 18326
[14] Ouyang S G, Hu W, Guo Q 2007 Phys. Rev. A 76 053832
[15] Guo Q, Luo B, Yi F, Chi S, Xie Y 2004 Phys. Rev. E 69 016602
[16] Guo Q, Zhang X P, Hu W, Shou Q 2006 Acta Phys. Sin. 55 1832 (in Chinese) [郭旗, 张霞萍, 胡巍, 寿倩 2006 55 1832]
[17] Bai Z Y, Deng D M, Guo Q 2012 Chin. Phys. B 21 64218
[18] Conti C, Peccianti M, Assanto G 2004 Phys. Rev. Lett. 92 113902
[19] Peccianti M, Brzdakiewicz K A, Assanto G 2002 Opt. Lett. 27 1460
[20] Rotschild C, Segev M, Xu Z Y, Kartashov Y V, Torner L, Cohen O 2006 Opt. Lett. 31 3312
[21] Dreischuh A, Neshev D N, Petersen D E, Bang O, Krolikowski W 2006 Phys. Rev. Lett. 96 043901
[22] Qin X J, Guo Q, Hu W, Lan S 2006 Acta Phys. Sin. 55 1237 (in Chinese) [秦晓娟, 郭旗, 胡巍, 兰胜 2006 55 1237]
[23] Rotschild C, Cohen O, Manela O, Segev M, Carmon T 2005 Phys. Rev. Lett. 95 213904
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[1] Snyder A W, Mitchell D J 1997 Science 276 1538
[2] Yakimenko A I, Lashkin V M, Prikhodko O O 2006 Phys. Rev. E 73 066605
[3] Buccoliero D, Desyatnikov A S, Królikowski W, Kivshar Y S 2008 Opt. Lett. 33 198
[4] Buccoliero D, Desyatnikov A S, Królikowski W, Kivshar Y S 2007 Phys. Rev. Lett. 98 053901
[5] Zhong W P, Lin Y 2007 Phys. Rev. A 75 061801
[6] Peccianti M, Conti C, Assanto G, Luca A D, Umeton C 2002 Appl. Phys. Lett. 81 3335
[7] Lopez-Aguayo S, Desyatnikov A S, Kivshar Y S 2006 Opt. Express 14 7903
[8] Wang Y Q, Guo Q 2008 Chin. Phys. B 17 2527
[9] Królikowski W, Bang O 2000 Phys. Rev. E 63 016610
[10] Deng D M, Guo Q 2007 Opt. Lett. 32 3206
[11] Mamaev A V, Zozulya A A, Mezentsev V K, Anderson D Z, Saffman M 1997 Phys. Rev. A 56 R1110
[12] Nikolov N I, Neshev D, Królikowski W, Bang O, Rasmussen J J, Christiansen P L 2004 Opt. Lett. 29 286
[13] Lopez-Aguayo S, Gutiérrez-Vega J C 2007 Opt. Express 15 18326
[14] Ouyang S G, Hu W, Guo Q 2007 Phys. Rev. A 76 053832
[15] Guo Q, Luo B, Yi F, Chi S, Xie Y 2004 Phys. Rev. E 69 016602
[16] Guo Q, Zhang X P, Hu W, Shou Q 2006 Acta Phys. Sin. 55 1832 (in Chinese) [郭旗, 张霞萍, 胡巍, 寿倩 2006 55 1832]
[17] Bai Z Y, Deng D M, Guo Q 2012 Chin. Phys. B 21 64218
[18] Conti C, Peccianti M, Assanto G 2004 Phys. Rev. Lett. 92 113902
[19] Peccianti M, Brzdakiewicz K A, Assanto G 2002 Opt. Lett. 27 1460
[20] Rotschild C, Segev M, Xu Z Y, Kartashov Y V, Torner L, Cohen O 2006 Opt. Lett. 31 3312
[21] Dreischuh A, Neshev D N, Petersen D E, Bang O, Krolikowski W 2006 Phys. Rev. Lett. 96 043901
[22] Qin X J, Guo Q, Hu W, Lan S 2006 Acta Phys. Sin. 55 1237 (in Chinese) [秦晓娟, 郭旗, 胡巍, 兰胜 2006 55 1237]
[23] Rotschild C, Cohen O, Manela O, Segev M, Carmon T 2005 Phys. Rev. Lett. 95 213904
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