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得到了强非局域非线性介质中的形变像散椭圆呼吸子的解析解, 并基于解析解讨论了这类呼吸子的演化性质. 在传输过程中光束在两个维度上仍保持高斯的形状, 但束宽与等相位面曲率均做两个维度上不同步的等周期演化. 当光束在两个维度上均为非束腰入射时, 不管功率如何, 光束的汇聚或发散惯性将继续保持一段距离, 继而形成二维异步同周期呼吸效应. 当光束在某方向上为束腰入射时则既可能形成二维异步呼吸, 也可能只有一维呼吸. 束宽的二维异步呼吸还导致了椭球等相位面曲率以及光斑椭圆率的周期性变化. 在二维束腰重合情况下, 椭圆率的最大值和最小值总是固定的且二者之积为1; 入射位置的变化不影响椭圆率最值, 但会影响椭圆率变化速度在一个周期内的分布均匀性和最大椭圆率出现的位置.The analytical solution for the shape-variant astigmatic elliptical breathers in strongly nonlocal nonlinear medium is obtained, and the propagation properties of this type of breather is investigated according to the solution. During propagation, the beam in x- and y-direction keeps Gaussian, the beam width and the curvature of the cophasal line vary periodically but asynchronously. For the two-dimensional off-waist input case, the initial convergence (divergence) makes the width narrowed (broaden) first near the entrance plane, no matter what the input power is; then varies periodically but asynchronously in x- and y-direction. For the one-dimensional on-waist input case, the beam might breathe only in one direction. The breather of the beam width induces the periodical variation of the curvature for the elliptically cophasal surface and the ellipticity of the pattern. If the location of the waist in x-direction and that in y-direction are identical with each other, the product of the maximum and the minimum of the ellipticity keeps equal to unify. In this case, the position of the entrance plane does not affects the maxima and the minima of the ellipticity, but affects the uniformity for the variation velocity of the ellipticity in a period.
[1] Peccianti M, Conti C, Assanto G, Luca A D, Umeton C 2002 Appl. Phys. Lett. 81 3335
[2] Snyder A W, Mitchell D J 1997 Science 276 1538
[3] Pecseli H L, Rasmussen J J 1980 Plasma Phys. 22 421
[4] Dalfovo F, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys. 71 463
[5] Peccianti M, Brzdakiewicz K A, Assanto G 2002 Opt. Lett. 27 1460
[6] Rotschild C, Cohen O, Manela O Segev M, Carmon T 2005 Phys. Rev. Lett. 95 213904
[7] Nikolov N I, Neshev D, Bang O 2003 Phys. Rev. E 68 036614
[8] Larsen P V, Siensen M P, Bang O, Królikowski W Z, Trillo S 2006 Phys. Rev. E 73 036614
[9] Buccoliero D, Desyatnikov A S, Królikowski W, Kivshar Y S 2007 Phys. Rev. Lett. 98 053901
[10] Deng D M, Zhao X, Guo Q, Lan S 2007 J. Opt. Soc. Am. B 24 2537
[11] Briedis D, Petersen D E, Edmundson D, Królikowski W Z, Bang O 2005 Opt. Express 13 435
[12] Dai J H, Guo Q 2009 Acta Phys. Sin. 58 1752 (in Chinese) [戴继慧, 郭旗 2009 58 1752]
[13] Lopez-Aguayo S, Desyatnikov A S, Kivshar Y S, Skupin S, Krolikowski W, Bang O 2006 Opt. Lett. 31 1100
[14] Lu D Q, Hu W 2009 Phys. Rev. A 79 043833
[15] L B D 2003 Laser Optics (3rd Ed.) (Beijing: Higher Education Press) p163 (in Chinese) [吕百达 2003 激光光学 (第三版) (北京: 高等教育出版社) 第163页]
[16] Lu D Q, Hu W, Guo Q 2009 Europhys. Lett. 86 44004
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[1] Peccianti M, Conti C, Assanto G, Luca A D, Umeton C 2002 Appl. Phys. Lett. 81 3335
[2] Snyder A W, Mitchell D J 1997 Science 276 1538
[3] Pecseli H L, Rasmussen J J 1980 Plasma Phys. 22 421
[4] Dalfovo F, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys. 71 463
[5] Peccianti M, Brzdakiewicz K A, Assanto G 2002 Opt. Lett. 27 1460
[6] Rotschild C, Cohen O, Manela O Segev M, Carmon T 2005 Phys. Rev. Lett. 95 213904
[7] Nikolov N I, Neshev D, Bang O 2003 Phys. Rev. E 68 036614
[8] Larsen P V, Siensen M P, Bang O, Królikowski W Z, Trillo S 2006 Phys. Rev. E 73 036614
[9] Buccoliero D, Desyatnikov A S, Królikowski W, Kivshar Y S 2007 Phys. Rev. Lett. 98 053901
[10] Deng D M, Zhao X, Guo Q, Lan S 2007 J. Opt. Soc. Am. B 24 2537
[11] Briedis D, Petersen D E, Edmundson D, Królikowski W Z, Bang O 2005 Opt. Express 13 435
[12] Dai J H, Guo Q 2009 Acta Phys. Sin. 58 1752 (in Chinese) [戴继慧, 郭旗 2009 58 1752]
[13] Lopez-Aguayo S, Desyatnikov A S, Kivshar Y S, Skupin S, Krolikowski W, Bang O 2006 Opt. Lett. 31 1100
[14] Lu D Q, Hu W 2009 Phys. Rev. A 79 043833
[15] L B D 2003 Laser Optics (3rd Ed.) (Beijing: Higher Education Press) p163 (in Chinese) [吕百达 2003 激光光学 (第三版) (北京: 高等教育出版社) 第163页]
[16] Lu D Q, Hu W, Guo Q 2009 Europhys. Lett. 86 44004
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