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Based on the nonlocal nonlinear Schrdinger equation and Poisson equation of thermal diffusion, using the slip-step Fourier algorithm and multi-grid method, we numerically investigated the propagation properties of Hermite-Guassian beams in the nonlocal thermal media. The results show that low-order Hermite-Gaussian beams can propagate stably, in contrast with the unstable propagation of high-order Hermite-Gaussian beams. The worse the stability is, the higher the order is. The effect of the boundary of the sample with different cross sections on the propagation properties of Hermite-Guassian beam is also discussed in detail. We found that propagation properties in square geometry are in agreement with those in Snyder-Mitchell model. However, in rectangular sample, the evolution of intensity distribution of Hermite-Gaussian beams differs seriously from that in the square sample.
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Keywords:
- nonlocal nonlinear media /
- Hermite-Gaussian beams /
- beam propagation
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[2] Suter D, Blasberg T 1983 Phys. Rev. A 48 4583
[3] Desyatnikov A S, Sukhorukov A A, Kivshar Y S 2005 Phys. Rev. Lett. 95 203904
[4] Kip D, Soljajic M, Segev M, Eugenieva E, Christodoulides D N 2000 Science 290 495
[5] Snyder A W, Mitchell D J 1997 Science 276 1538
[6] Guo Q, Luo B, Yi F, Chi S, Xie Y 2004 Phys. Rev. E 69 016602
[7] Zhu Y Q, Long X W, Hu W, Cao L G, Yang P B 2008 Acta Phys. Sin. 57 2260 (in Chinese) [朱叶青、 龙学文、 胡 巍、 曹龙贵、 杨平保 2008 57 2260]
[8] Yang P B, Cao L G, Hu W, Zhu Y Q, Guo Q, Yang X B 2008 Acta Phys. Sin. 57 285 (in Chinese) [杨平保、 曹龙贵、 胡 巍、 朱叶青、 郭 旗、 杨湘波 2008 57 285]
[9] Shao Y Q, Guo Q 2006 Acta Phys. Sin. 55 2751 (in Chinese) [邵毅全、 郭 旗 2006 55 2751]
[10] 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]
[11] Zheng Y J, Xuan W T, Lu D Q, OuYang S G, Hu W, Guo Q 2010 Acta Phys. Sin. 59 1075 (in Chinese) [郑亚建、 宣文涛、 陆大全、 欧阳世根、 胡 巍、 郭 旗 2010 59 1075]
[12] Chen L X, Lu D Q, Hu W, Yang Z J, Cao W W, Zheng R, Guo Q 2010 Acta Phys. Sin. 59 327 (in Chinese) [陈利霞、 陆大全、 胡 巍、 杨振军、 曹伟文、 郑 睿、 郭 旗 2010 59 327]
[13] Rotschild C, Segev M, Xu Z, Kartashov Y V, Torner L, Cohen O 2006 Opt. Lett. 31 3312
[14] Rotschild C, Alfassi B, Cohen O, Segev M 2006 Nature Physics 2 769
[15] Dreischuh A, Neshev D N, Petersen D E, Bang O, Krolikowski W 2006 Phys. Rev. Lett. 96 043901
[16] Rotschild C, Cohen O, Manela O, Segev M, Carmon T 2005 Phys. Rev. Lett. 95 213904
[17] Liang Y B, Zheng Y J, Yang P B, Cao L G, Lu D Q, Hu W, Guo Q 2008 Acta Phys. Sin. 57 5690 (in Chinese) [梁炎斌、 郑亚建、 杨平保、 曹龙贵、 陆大全、 胡 巍、 郭 旗 2008 57 5690]
[18] Iturbe-Castillo M D, Stepanov S, Sanchz-Mondragon J J 1996 Opt. Lett. 21 1622
[19] Agrawal G P Translated by Jia D F, Yu Z H, Tan B, Hu Z Y 2002 Nonlinear Fiber Optics and Application of Nonlinear Fiber Optic (Beijing: Electronic Industry Press) pp34, 35 (in Chinese)
[20] Teukolsky S A, Vetterling W T, Flannery B P Translated by Fu Z Y, Zhao M N, Ding Y 1995 Numerical Recips in C: The Art of Scientific Computing (Beijing: Electronic Industry Press) pp734—749 (in Chinese )
[21] Strinic A I, Petrovic M, Timotijevic D V, Aleksic N B, Belic M R 2009 Opt. Express 17 11698
[22] Lu D Q, Hu W, Zheng Y J, Liang Y B, Cao L G, Lan S, Guo Q 2008 Phys. Rev. A 78 043815
[23] Garcia-Ripoll J J, Perez-Garcia V M, Ostrovskaya E A, Kivshar Y S 2000 Phys. Rev. Lett. 85 82
[24] Garcia-Reimbert C, Minzoni A A, Marchant T R, Smyth N F, Worthy A L 2008 Physica D 237 1088
[25] Ye F W, Kartashov Y V, Torner L 2008 Phys. Rev. A 77 043821
[26] Deng D M, Zhao X, Guo Q, Lan S 2007 J. Opt. Soc. Am. B 24 2537
[27] Buccoliero D, Desyatnikov A S, Krolikowski W, Kivshar Y S 2007 Phys. Rev. Lett. 98 053901
[28] Buccoliero D, Desyatnikov A S 2009 Opt. Express 17 9609
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[1] Hasegawa A, Tappert F 1973 Appl. Phys. Lett. 23 142
[2] Suter D, Blasberg T 1983 Phys. Rev. A 48 4583
[3] Desyatnikov A S, Sukhorukov A A, Kivshar Y S 2005 Phys. Rev. Lett. 95 203904
[4] Kip D, Soljajic M, Segev M, Eugenieva E, Christodoulides D N 2000 Science 290 495
[5] Snyder A W, Mitchell D J 1997 Science 276 1538
[6] Guo Q, Luo B, Yi F, Chi S, Xie Y 2004 Phys. Rev. E 69 016602
[7] Zhu Y Q, Long X W, Hu W, Cao L G, Yang P B 2008 Acta Phys. Sin. 57 2260 (in Chinese) [朱叶青、 龙学文、 胡 巍、 曹龙贵、 杨平保 2008 57 2260]
[8] Yang P B, Cao L G, Hu W, Zhu Y Q, Guo Q, Yang X B 2008 Acta Phys. Sin. 57 285 (in Chinese) [杨平保、 曹龙贵、 胡 巍、 朱叶青、 郭 旗、 杨湘波 2008 57 285]
[9] Shao Y Q, Guo Q 2006 Acta Phys. Sin. 55 2751 (in Chinese) [邵毅全、 郭 旗 2006 55 2751]
[10] 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]
[11] Zheng Y J, Xuan W T, Lu D Q, OuYang S G, Hu W, Guo Q 2010 Acta Phys. Sin. 59 1075 (in Chinese) [郑亚建、 宣文涛、 陆大全、 欧阳世根、 胡 巍、 郭 旗 2010 59 1075]
[12] Chen L X, Lu D Q, Hu W, Yang Z J, Cao W W, Zheng R, Guo Q 2010 Acta Phys. Sin. 59 327 (in Chinese) [陈利霞、 陆大全、 胡 巍、 杨振军、 曹伟文、 郑 睿、 郭 旗 2010 59 327]
[13] Rotschild C, Segev M, Xu Z, Kartashov Y V, Torner L, Cohen O 2006 Opt. Lett. 31 3312
[14] Rotschild C, Alfassi B, Cohen O, Segev M 2006 Nature Physics 2 769
[15] Dreischuh A, Neshev D N, Petersen D E, Bang O, Krolikowski W 2006 Phys. Rev. Lett. 96 043901
[16] Rotschild C, Cohen O, Manela O, Segev M, Carmon T 2005 Phys. Rev. Lett. 95 213904
[17] Liang Y B, Zheng Y J, Yang P B, Cao L G, Lu D Q, Hu W, Guo Q 2008 Acta Phys. Sin. 57 5690 (in Chinese) [梁炎斌、 郑亚建、 杨平保、 曹龙贵、 陆大全、 胡 巍、 郭 旗 2008 57 5690]
[18] Iturbe-Castillo M D, Stepanov S, Sanchz-Mondragon J J 1996 Opt. Lett. 21 1622
[19] Agrawal G P Translated by Jia D F, Yu Z H, Tan B, Hu Z Y 2002 Nonlinear Fiber Optics and Application of Nonlinear Fiber Optic (Beijing: Electronic Industry Press) pp34, 35 (in Chinese)
[20] Teukolsky S A, Vetterling W T, Flannery B P Translated by Fu Z Y, Zhao M N, Ding Y 1995 Numerical Recips in C: The Art of Scientific Computing (Beijing: Electronic Industry Press) pp734—749 (in Chinese )
[21] Strinic A I, Petrovic M, Timotijevic D V, Aleksic N B, Belic M R 2009 Opt. Express 17 11698
[22] Lu D Q, Hu W, Zheng Y J, Liang Y B, Cao L G, Lan S, Guo Q 2008 Phys. Rev. A 78 043815
[23] Garcia-Ripoll J J, Perez-Garcia V M, Ostrovskaya E A, Kivshar Y S 2000 Phys. Rev. Lett. 85 82
[24] Garcia-Reimbert C, Minzoni A A, Marchant T R, Smyth N F, Worthy A L 2008 Physica D 237 1088
[25] Ye F W, Kartashov Y V, Torner L 2008 Phys. Rev. A 77 043821
[26] Deng D M, Zhao X, Guo Q, Lan S 2007 J. Opt. Soc. Am. B 24 2537
[27] Buccoliero D, Desyatnikov A S, Krolikowski W, Kivshar Y S 2007 Phys. Rev. Lett. 98 053901
[28] Buccoliero D, Desyatnikov A S 2009 Opt. Express 17 9609
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