In this work, we study the propagation of solitons in lossy optical fibers. The main objective of this work is to study the loss of energy of the soliton wave during propagation and then to evaluate the impact of this loss on the transmission of the soliton signal. In this context, a numerical scheme was developed to solve a system of complex partial differential equations (CPDE) that describes the propagation of solitons in optical fibers with loss and nonlinear amplification mechanisms. The numerical procedure is based on the mathematical theory of Taylor series of complex functions. We adapted the Finite Difference Method (FDM) to approximate derivatives of complex functions. Then, we solve the algebraic system resulting from the discretization, implicitly, through the relaxation Gauss-Seidel method (RGSM). The numerical study of CPDE system with linear and cubic attenuation showed that soliton waves undergo attenuation, dispersion, and oscillation effects. On the other hand, we find that by considering the nonlinear term (cubic term) as an optical amplification, it is possible to partially compensate for the attenuation of the optical signal. Finally, we show that a gain of 9% triples the propagation distance of the fundamental soliton wave, when the dissipation rate is 1%.
翻译:在这项工作中,我们研究了光纤损失中的单线体的传播。这项工作的主要目的是研究隔热波在传播过程中的能量损失,然后评估隔热波的能量损失对隔热信号传输的影响。在这方面,我们开发了一个数字方案,以解决复杂的局部偏差方程系统(CPDE),该系统描述光纤中单线体与损耗和非线性放大机制的传播。数字程序以泰勒一系列复杂功能的数学理论为基础。我们调整了非线性差异法(FDM)以适应复杂函数的近似衍生物。然后,我们通过松散式高升降法(RGSM),间接地解决了因离散而导致的升温系统。对带有线性和立子增强作用的CPDE系统(CPDE)的数值研究显示,索利特波的传播以降低、分散和振荡效应的方式进行。另一方面,我们发现,通过将非线性术语(Ubic用术语)作为光学振荡作用的近似的衍生物。然后,我们通过松动的松动方法,通过松动方法解决了离分化,通过松动法法方法,从而在最后显示了离差率后,使我们获得了离差率的升升幅率。