掺杂光纤中Peregrine孤子传输特性的研究
发布时间：2019-06-04 16:06
【摘要】：怪波是源于海洋中的一种巨型波,它的峰值通常要比周围的水波高两到三倍,并且瞬时出现瞬时消失,没有任何征兆,在海洋中具有巨大的破坏力,因此引起了人们的广泛关注。由于海洋中的怪波难以监测,所以人们开始探索其它领域中的怪波现象。光学中,Solli等人首次实验上在产生超连续光谱的光纤中观察到怪波的存在。光学平台上怪波现象的发现,为我们研究怪波的产生机理提供了便利。目前,关于怪波的形成原因,有多种解释。其中最重要的一个原因是调制不稳定性,在反常色散区,色散和非线性的相互作用,可以导致对稳态的调制,从而使准连续波分裂成一系列高峰值脉冲串。数学上调制不稳定性的增长和衰减进程可以用非线性薛定谔方程的一组精确的平面波背景上的孤子解来描述。平面波背景上的孤子解可以分为Akhmediev呼吸子(Akhmediev breathers,简称ABs)解,Kuznetsov-Ma(Kuznetsov-Ma,简称KM)孤子解和Peregrine孤子(Peregrine soliton,简称PS)解。Peregrine孤子解是一个在时间和空间上都局域化的单脉冲。目前Peregrine孤子已普遍被用来描述光学怪波。本文主要研究Peregrine孤子在掺杂光纤中的传输。具体内容包括以下五个方面:(1)介绍怪波的基本概念,产生原因及研究进展和应用领域。(2)由Maxwell方程出发,推导出光脉冲在光纤中传输的非线性薛定谔方程,并讨论该方程在平面波背景上孤子解,Akhmediev呼吸子(AB)、Kuznetsov-Ma孤子(KM)、Peregrine孤子(PS)。由掺杂光纤中光脉冲传输的非线性型薛定谔方程数值模型,介绍数值模拟方法—分步傅立叶方法。(3)将Peregrine孤子解的初始波形作为初始输入脉冲,在掺杂光纤中传输,研究其传输特性。研究发现Peregrine孤子在掺杂光纤中传输时,会受到小信号增益、饱和能量等参数的影响。小信号增益越大,饱和能量越高,脉冲峰值强度相继逐渐增强,脉宽变窄,激发产生的脉冲空间间隔逐渐减小。另外研究三种不同的初始输入即Peregrine孤子,平面波背景上的高斯型脉冲和双曲正割型脉冲在掺杂光纤中的传输,由于调制不稳定性都可以产生类Peregrine孤子。(4)Peregrine孤子在掺杂光纤中传输时,产生高峰值单脉冲后会迅速分裂产生多个子脉冲,因此不能稳定传输。为了获得稳定传输的高峰值脉冲,分别利用相干叠加和滤波的方法消去背景波,作为初始波形输入到掺杂光纤中。研究结果表明,两种方法得到的高峰值脉冲在掺杂光纤中可以稳定传输,并且在传输过程中脉宽呈呼吸式的周期变化,强度呈周期性的振荡,脉冲强度的平均值不断的增加。
[Abstract]:A strange wave is a giant wave derived from the ocean. Its peak value is usually two to three times higher than that of the surrounding water wave, and it suddenly disappears, without warning, and has great destructive power in the ocean. Therefore, it has aroused widespread concern. Because the strange wave in the ocean is difficult to monitor, people begin to explore the strange wave phenomenon in other fields. In optics, Solli et al observed the existence of strange waves in the fiber which produces supercontinuum spectrum for the first time. The discovery of strange wave phenomenon on optical platform provides us with convenience for us to study the mechanism of strange wave generation. At present, there are many explanations for the causes of strange waves. One of the most important reasons is modulation instability. In the abnormal dispersion region, dispersion and nonlinear interaction can lead to steady-state modulation, thus dividing the quasi-continuous wave into a series of high peak pulse strings. The growth and decay process of modulation instability can be described by a set of exact soliton solutions on the background of plane waves of nonlinear Schrodinger equation. The soliton solutions on the background of plane waves can be divided into Akhmediev respirator (Akhmediev breathers, (ABs) solution, Kuznetsov-Ma (Kuznetsov-Ma, short KM) soliton solution and Peregrine soliton (Peregrine soliton,. Peregrine soliton solution is a monopulse localized in time and space. At present, Peregrine solitons have been widely used to describe optical strange waves. In this paper, the propagation of Peregrine solitons in doped fibers is studied. The specific contents include the following five aspects: (1) the basic concept, causes, research progress and application fields of strange waves are introduced. (2) based on the Maxwell equation, the nonlinear Schrodinger equation of optical pulse propagation in optical fiber is derived. The soliton solution of the equation in the background of plane wave, Akhmediev respirator (AB), Kuznetsov-Ma soliton (KM), Peregrine soliton (PS)., is also discussed. Based on the nonlinear Schrodinger equation numerical model of optical pulse transmission in doped optical fiber, the numerical simulation method, split-step Fourier method, is introduced. (3) the initial waveform of Peregrine soliton solution is used as the initial input pulse to transmit in the doped optical fiber. Its transmission characteristics are studied. It is found that Peregrine solitons are affected by small signal gain, saturation energy and other parameters when they are propagated in doped fibers. The larger the small signal gain is, the higher the saturation energy is, the higher the peak intensity of the pulse is, the narrower the pulse width is, and the space interval of the pulse produced by the excitation is gradually reduced. In addition, the propagation of three different initial inputs, namely, Peregrine soliton, Gaussian pulse and hyperbolic Secant pulse in the background of plane wave, is studied. Due to modulation instability, Peregrine-like solitons can be generated. (4) when Peregrine solitons propagate in doped fibers, the peak monopulse will split rapidly to produce multiple sub-pulse, so it can not transmit stably. In order to obtain the high peak pulse of stable transmission, the background wave is eliminated by coherent superposition and filtering respectively, and the background wave is input into the doped fiber as the initial waveform. The results show that the high peak pulse obtained by the two methods can be transmitted stably in the doped fiber, and the pulse width changes periodically, the intensity oscillates periodically, and the average pulse intensity increases continuously in the process of transmission.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN253
本文编号：2492833
[Abstract]:A strange wave is a giant wave derived from the ocean. Its peak value is usually two to three times higher than that of the surrounding water wave, and it suddenly disappears, without warning, and has great destructive power in the ocean. Therefore, it has aroused widespread concern. Because the strange wave in the ocean is difficult to monitor, people begin to explore the strange wave phenomenon in other fields. In optics, Solli et al observed the existence of strange waves in the fiber which produces supercontinuum spectrum for the first time. The discovery of strange wave phenomenon on optical platform provides us with convenience for us to study the mechanism of strange wave generation. At present, there are many explanations for the causes of strange waves. One of the most important reasons is modulation instability. In the abnormal dispersion region, dispersion and nonlinear interaction can lead to steady-state modulation, thus dividing the quasi-continuous wave into a series of high peak pulse strings. The growth and decay process of modulation instability can be described by a set of exact soliton solutions on the background of plane waves of nonlinear Schrodinger equation. The soliton solutions on the background of plane waves can be divided into Akhmediev respirator (Akhmediev breathers, (ABs) solution, Kuznetsov-Ma (Kuznetsov-Ma, short KM) soliton solution and Peregrine soliton (Peregrine soliton,. Peregrine soliton solution is a monopulse localized in time and space. At present, Peregrine solitons have been widely used to describe optical strange waves. In this paper, the propagation of Peregrine solitons in doped fibers is studied. The specific contents include the following five aspects: (1) the basic concept, causes, research progress and application fields of strange waves are introduced. (2) based on the Maxwell equation, the nonlinear Schrodinger equation of optical pulse propagation in optical fiber is derived. The soliton solution of the equation in the background of plane wave, Akhmediev respirator (AB), Kuznetsov-Ma soliton (KM), Peregrine soliton (PS)., is also discussed. Based on the nonlinear Schrodinger equation numerical model of optical pulse transmission in doped optical fiber, the numerical simulation method, split-step Fourier method, is introduced. (3) the initial waveform of Peregrine soliton solution is used as the initial input pulse to transmit in the doped optical fiber. Its transmission characteristics are studied. It is found that Peregrine solitons are affected by small signal gain, saturation energy and other parameters when they are propagated in doped fibers. The larger the small signal gain is, the higher the saturation energy is, the higher the peak intensity of the pulse is, the narrower the pulse width is, and the space interval of the pulse produced by the excitation is gradually reduced. In addition, the propagation of three different initial inputs, namely, Peregrine soliton, Gaussian pulse and hyperbolic Secant pulse in the background of plane wave, is studied. Due to modulation instability, Peregrine-like solitons can be generated. (4) when Peregrine solitons propagate in doped fibers, the peak monopulse will split rapidly to produce multiple sub-pulse, so it can not transmit stably. In order to obtain the high peak pulse of stable transmission, the background wave is eliminated by coherent superposition and filtering respectively, and the background wave is input into the doped fiber as the initial waveform. The results show that the high peak pulse obtained by the two methods can be transmitted stably in the doped fiber, and the pulse width changes periodically, the intensity oscillates periodically, and the average pulse intensity increases continuously in the process of transmission.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN253
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相关期刊论文 前2条
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2 张解放;楼吉辉;;非均匀非线性波导中线光学畸形波及其传播控制[J];光学学报;2013年09期
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