五阶非线性克尔效应影响下光脉冲的传输

发布时间：2018-09-17 19:11

【摘要】：本文研究的理论模型是变系数的五次金兹堡-朗道(Ginzburg-Landau)方程,首先,研究理论模型的精确解,根据计算结果理论分析了精确解在非均匀光纤系统中的传输情况,并对理论分析进行数值验证。然后,在考虑非均匀光纤系统中的五阶非线性克尔效应时,研究了精确孤子解形式的超短脉冲的传输特性,并讨论两个这种超短光脉冲在传输过程中的相互作用。最后,在考虑五阶非线性克尔效应时,研究光纤放大器中光孤子的传输特性,并讨论了五阶非线性克尔效应对光孤子的具体影响。在实际应用中,这些研究对于超短脉冲在非均匀光纤系统中的传输提供了一定的理论依据,还有助于控制光纤放大器和非均匀光纤系统中五阶非线性克尔效应的影响。本文研究的主要内容包含以下几个方面:(1)介绍在光纤通信发展中非线性光纤光学的研究背景,简述国内外光孤子在非均匀光纤系统中的研究现状,并简要分析五阶非线性克尔效应的研究意义。(2)研究理论模型的精确解。在考虑光纤传输介质中五阶非线性克尔效应时,利用拟解法计算出满足特殊条件下的精确孤子解,在理论的层面上分析精确解的传输情况。当忽略五阶非线性克尔效应,计算出光纤传输系统中存在的精确耗散孤子解,同样分析耗散孤子解的传输情况。最后,对精确的孤子解和耗散孤子解进行数值分析,验证理论研究的结果。(3)在考虑五阶非线性克尔效应的非均匀光纤传输系统中,用分步傅里叶法研究精确孤子解超短脉冲的传输稳定性和相互作用。在入射脉冲中分别加入振幅微扰和随机噪声,数值模拟其传输稳定性;并通过改变两个相邻入射脉冲之间的距离,数值模拟在此系统中的传输情况,分析两个光孤子之间的相互作用。(4)在光纤放大器中考虑五阶非线性克尔效应时,用分步傅里叶法研究光孤子的传输特性。首先,以双曲正割脉冲作为入射脉冲,研究亮孤子中的演化过程和其传输的稳定性,并分析多个亮孤子的传输情况;其次,以双曲正切脉冲作为入射脉冲,研究暗孤子的传输情况;最后,讨论五阶非线性克尔效应对光孤子的具体影响。
[Abstract]:The theoretical model studied in this paper is the quintic Kingsbauer-Landau (Ginzburg-Landau) equation with variable coefficients. Firstly, the exact solution of the theoretical model is studied, and the transmission of the exact solution in non-uniform optical fiber system is analyzed according to the theory of calculation results. The theoretical analysis is verified numerically. Then, considering the fifth-order nonlinear Kerr effect in non-uniform optical fiber systems, the propagation characteristics of ultrashort pulses in the form of exact soliton solutions are studied, and the interaction of two ultrashort optical pulses in the transmission process is discussed. Finally, the propagation characteristics of optical solitons in fiber amplifiers are studied when the fifth-order nonlinear Kerr effect is considered, and the influence of the fifth-order nonlinear Kerr effect on the optical solitons is discussed. In practical applications, these studies provide a theoretical basis for the transmission of ultrashort pulses in non-uniform optical fiber systems, and help to control the influence of the fifth-order nonlinear Kerr effect in fiber amplifiers and non-uniform optical fiber systems. The main contents of this paper include the following aspects: (1) the research background of nonlinear optical fiber optics in the development of optical fiber communication is introduced, and the research status of optical solitons in non-uniform optical fiber systems at home and abroad is briefly described. The significance of the fifth order nonlinear Kerr effect is briefly analyzed. (2) the exact solution of the theoretical model is studied. Considering the fifth-order nonlinear Kerr effect in the optical fiber transmission medium, the exact soliton solution satisfying the special conditions is calculated by using the quasi method, and the transmission of the exact solution is analyzed on the theoretical level. When the fifth-order nonlinear Kerr effect is ignored, the exact dissipative soliton solutions in the optical fiber transmission system are calculated, and the transmission of the dissipative soliton solutions is also analyzed. Finally, numerical analysis of exact soliton solution and dissipative soliton solution is carried out to verify the results of theoretical research. (3) in a non-uniform optical fiber transmission system considering the fifth-order nonlinear Kerr effect, The propagation stability and interaction of ultrashort pulses for accurate soliton solutions are studied by using the split-step Fourier method. The transmission stability is numerically simulated by adding amplitude perturbation and random noise to the incident pulse, and the transmission in this system is simulated by changing the distance between two adjacent incident pulses. The interaction between the two solitons is analyzed. (4) the propagation characteristics of the optical solitons are studied by using the split-step Fourier method when the fifth-order nonlinear Kerr effect is considered in the fiber amplifier. Firstly, the evolution process and the transmission stability of bright solitons are studied by using hyperbolic tangent pulse as incident pulse, and the transmission of several bright solitons is analyzed, secondly, the hyperbolic tangent pulse is used as incident pulse. The propagation of dark solitons is studied. Finally, the influence of fifth-order nonlinear Kerr effect on optical solitons is discussed.
【学位授予单位】：山西大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TN929.11

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