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利用包含拉曼增益和自陡峭效应的非线性薛定谔方程, 忽略光纤损耗的情况下, 模拟和分析了艾里脉冲在单模光纤中的传输特性. 发现艾里脉冲在光纤中传输时由于受到拉曼增益和自陡峭效应的影响, 在一定条件下会转变为孤子, 并且, 转变后形成的孤子传播方向发生了偏移. 在时域方面, 艾里脉冲的小峰个数迅速减少, 变成含有一个主峰和次峰能量可以忽略的峰值结构, 此时, 可以把这个峰值结构近似为孤子的结构. 同时发现, 不管截止系数a和艾里函数振幅b 取什么值, 拉曼增益和自陡峭效应都会减小艾里脉冲的时移. 研究了艾里脉冲的加速度特性, 发现一定的传输距离下, 艾里脉冲的横向加速度在初始时并不是一个稳定的值, 但随着传输距离的增大, 加速度慢慢趋于稳定.By using nonlinear Schrdinger equation including Raman gain and self-steepening but ignoring fiber loss situation, the propagation characteristics of Airy pulse are simulated and analyzed in the single-mode fiber. Simulations show that Airy pulse can be converted into soliton and its propagation direction is skewed due to the effects of Raman gain and self-steepening under a certain condition. In time domain, the number of small peaks of Airy pulse reduces rapidly. Airy pulse becomes a peak structure containing a main peak and sub-peaks where the energies can be ignored by changing the coefficient a reasonablely, which is approximated as the soliton structure. Therefore, Airy pulse is regarded as transforming into soliton. Meanwhile, in the case of small values b, there exists a significant difference in shape between Airy pulse and soliton. With the value of parameter b increasing slowly, the shape of Airy pulse is very close to soliton's, therefore Airy pulse can transform into soliton by changing value b reasonablely. Compared with by changing b value, Airy pulse convered into the soliton is stable by changing the a value reasonablely. Simultaneously, with the increases of values of coefficient a and amplitude b, the time-shift of Airy pulse increases. However, the time-shift of Airy pulse would decrease when Raman gain and Self-steepening become strong, no matter what the values of a and b are. Further, the acceleration properties of Airy pulse are investigated. It is found that Airy pulse autoacceleration is not a stable value at the beginning but it gradually stabilizes with the increase of transmission distance. The reason is that the energies of secondary peaks exert a tremendous influence on the main lobe of Airy pulse at the beginning, however, secondary peaks diffuse fast with the increase of transmission and then the influence can be ignored to a certain extent. So, the main peak gradually stabilizes with the increase of transmission distance.
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Keywords:
- Airy pulse /
- Raman gain /
- self-steepening /
- self-acceleration characteristics
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[3] Siviloglou G A, Brokly J, Dogariu A, Christodoulides D 2007 Phys. Rev. Lett. 99 213901
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[12] Zhang P, Wang S, Liu X, Lu C, Chen Z G, Zhang X 2011 Opt. Lett. 36 3191
[13] Siviloglou G A, Broky J, Dogaru A, Christodoulides D N 2008 Opt. Lett. 33 207
[14] Yu Y, Jia W G, Yan Q, Menke N M L, Zhang J P 2015 Acta Phys. Sin. 64 054207 (in Chinese) [于宇, 贾维国, 闫青, 门克内木乐, 张俊平 2015 64 054207]
[15] Yu Y, Jia W G, Yan Q, Menke N M L, Zhang J P 2015 Chin. Phys. B 24 084210
[16] Yan Q, Jia W G, Yu Y, Zhang J P, Menke N M L 2015 Acta Phys. Sin. 64 184211 (in Chinese) [闫青, 贾维国, 于宇, 张俊萍, 门克内木乐 2015 64 184211]
[17] Zhu K Z, Jia W G, Zhang K, Yu Y, Zhang J P, Menke N M L 2016 Acta Phys. Sin. 65 024208 (in Chinese) [朱坤占, 贾维国, 张魁, 于宇, 张俊平, 门克内木乐 2016 65 024208]
[18] Polyn K P, Kolesik M, Moloney J V, Sivilogou G A, Christodoulides D N 2009 Science 324 229
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[1] Berry M V, Balazs N L 1979 Am. J. Phys. 47 264
[2] Siviloglou G A, Christodoulides D N 2007 Opt. Lett. 32 979
[3] Siviloglou G A, Brokly J, Dogariu A, Christodoulides D 2007 Phys. Rev. Lett. 99 213901
[4] Zhang L F, Liu K, Zhang H Z, Zhang J G, Li Y, Fan D Y 2015 Opt. Express 23 2566
[5] Cai W Y, Matthew S M, Christodoulides D N, Wen S C 2014 Opt. Commun. 316 127
[6] Yiska F, Amitay R, Marom D M 2011 Opt. Express 19 17299
[7] Baldeck P L, Alfano R R, Agrawal G P 1988 Appl. Phys. Lett. 52 1939
[8] Xu J, Liu J, Jia J, Wang Y T, Xie J H, Liang X Y 2010 J. Opt. 12 5705
[9] Cottrell D M, Davis J A, Hazard T M 2009 Opt. Lett. 34 2634
[10] Bandres M A, Gutierrez G C 2007 Opt. Express 15 16719
[11] Broky J, Siviloglou G A, Christodoulides D N 2008 Opt. Express 16 12880
[12] Zhang P, Wang S, Liu X, Lu C, Chen Z G, Zhang X 2011 Opt. Lett. 36 3191
[13] Siviloglou G A, Broky J, Dogaru A, Christodoulides D N 2008 Opt. Lett. 33 207
[14] Yu Y, Jia W G, Yan Q, Menke N M L, Zhang J P 2015 Acta Phys. Sin. 64 054207 (in Chinese) [于宇, 贾维国, 闫青, 门克内木乐, 张俊平 2015 64 054207]
[15] Yu Y, Jia W G, Yan Q, Menke N M L, Zhang J P 2015 Chin. Phys. B 24 084210
[16] Yan Q, Jia W G, Yu Y, Zhang J P, Menke N M L 2015 Acta Phys. Sin. 64 184211 (in Chinese) [闫青, 贾维国, 于宇, 张俊萍, 门克内木乐 2015 64 184211]
[17] Zhu K Z, Jia W G, Zhang K, Yu Y, Zhang J P, Menke N M L 2016 Acta Phys. Sin. 65 024208 (in Chinese) [朱坤占, 贾维国, 张魁, 于宇, 张俊平, 门克内木乐 2016 65 024208]
[18] Polyn K P, Kolesik M, Moloney J V, Sivilogou G A, Christodoulides D N 2009 Science 324 229
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