光子学报, 2016, 45 (10): 1006003, 网络出版: 2016-11-14
Hirota方程的二阶怪波解及其传输特点
2-order Rogue Solution of Hirota Equation and Its Transmision
非线性光学 Hirota方程 数值模拟 二阶怪波 自频移 Nonlinear optics Hirota equation Numerical simulation 2-order rogue Self-steepening
摘要
为了研究Hirota方程的二阶怪波解和它在光纤中的传输特性,数值分析了二阶怪波的形成机理,并采用分步傅里叶方法数值模拟了二阶怪波在光纤中的传输特点.结果表明:二阶怪波可以看作两个怪波逐渐靠近的结果;在光纤中传输时,随着距离的增加,二阶怪波最终分裂成两组次波,每组次波的能量值降为初值的一半,它们之间的距离越来越大且互不干扰,并随着距离的增加能量逐渐降低.数值分析了自陡峭和自频移对二阶怪波传输的影响,发现自陡峭引起二阶怪波在传播过程中左波峰能量大于右波峰能量,自频移使怪波的中心发生了非线性偏离,且参数的正负决定偏离的方向.
Abstract
In order to study the 2-order rogue solution of Hirota equation and its transmision, the formation mehanism of the 2-order rogue was numerical analyzed and the characteristic of the 2-order rogue wave propagation in the fiber was simulated by the fast Fourier transform. It is found that the 2-order rogue wave can be regarded as the two 1-order waves superposition. In the transmission process, the 2-order rogue wave is firstly split into two rogue waves, and the energy of the 2-order wave is reduced by half,and the distance between them is bigger but there is no mutual interference. Finally, the effects of self-steepening and self-frequency shift for 2-order rogue were numerical analyzed. The results show that self-steepening causes the energy of left wave bigger than right wave, and self-frequency shift makes the center of rogue wave nonlinear deviated, and the parameters decide the direction of deviate.
李淑青, 常锋, 郭尊光, 刘阳. Hirota方程的二阶怪波解及其传输特点[J]. 光子学报, 2016, 45(10): 1006003. LI Shu-qing, CHANG Feng, GUO Zun-guang, LIU Yang. 2-order Rogue Solution of Hirota Equation and Its Transmision[J]. ACTA PHOTONICA SINICA, 2016, 45(10): 1006003.