摻雜光纖中Peregrine孤子傳輸特性的研究
發(fā)布時間：2019-06-04 16:06
【摘要】：怪波是源于海洋中的一種巨型波,它的峰值通常要比周圍的水波高兩到三倍,并且瞬時出現(xiàn)瞬時消失,沒有任何征兆,在海洋中具有巨大的破壞力,因此引起了人們的廣泛關(guān)注。由于海洋中的怪波難以監(jiān)測,所以人們開始探索其它領(lǐng)域中的怪波現(xiàn)象。光學中,Solli等人首次實驗上在產(chǎn)生超連續(xù)光譜的光纖中觀察到怪波的存在。光學平臺上怪波現(xiàn)象的發(fā)現(xiàn),為我們研究怪波的產(chǎn)生機理提供了便利。目前,關(guān)于怪波的形成原因,有多種解釋。其中最重要的一個原因是調(diào)制不穩(wěn)定性,在反常色散區(qū),色散和非線性的相互作用,可以導致對穩(wěn)態(tài)的調(diào)制,從而使準連續(xù)波分裂成一系列高峰值脈沖串。數(shù)學上調(diào)制不穩(wěn)定性的增長和衰減進程可以用非線性薛定諤方程的一組精確的平面波背景上的孤子解來描述。平面波背景上的孤子解可以分為Akhmediev呼吸子(Akhmediev breathers,簡稱ABs)解,Kuznetsov-Ma(Kuznetsov-Ma,簡稱KM)孤子解和Peregrine孤子(Peregrine soliton,簡稱PS)解。Peregrine孤子解是一個在時間和空間上都局域化的單脈沖。目前Peregrine孤子已普遍被用來描述光學怪波。本文主要研究Peregrine孤子在摻雜光纖中的傳輸。具體內(nèi)容包括以下五個方面:(1)介紹怪波的基本概念,產(chǎn)生原因及研究進展和應用領(lǐng)域。(2)由Maxwell方程出發(fā),推導出光脈沖在光纖中傳輸?shù)姆蔷�性薛定諤方程,并討論該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)。由摻雜光纖中光脈沖傳輸?shù)姆蔷�性型薛定諤方程數(shù)值模型,介紹數(shù)值模擬方法—分步傅立葉方法。(3)將Peregrine孤子解的初始波形作為初始輸入脈沖,在摻雜光纖中傳輸,研究其傳輸特性。研究發(fā)現(xiàn)Peregrine孤子在摻雜光纖中傳輸時,會受到小信號增益、飽和能量等參數(shù)的影響。小信號增益越大,飽和能量越高,脈沖峰值強度相繼逐漸增強,脈寬變窄,激發(fā)產(chǎn)生的脈沖空間間隔逐漸減小。另外研究三種不同的初始輸入即Peregrine孤子,平面波背景上的高斯型脈沖和雙曲正割型脈沖在摻雜光纖中的傳輸,由于調(diào)制不穩(wěn)定性都可以產(chǎn)生類Peregrine孤子。(4)Peregrine孤子在摻雜光纖中傳輸時,產(chǎn)生高峰值單脈沖后會迅速分裂產(chǎn)生多個子脈沖,因此不能穩(wěn)定傳輸。為了獲得穩(wěn)定傳輸?shù)母叻逯得}沖,分別利用相干疊加和濾波的方法消去背景波,作為初始波形輸入到摻雜光纖中。研究結(jié)果表明,兩種方法得到的高峰值脈沖在摻雜光纖中可以穩(wěn)定傳輸,并且在傳輸過程中脈寬呈呼吸式的周期變化,強度呈周期性的振蕩,脈沖強度的平均值不斷的增加。
[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.
【學位授予單位】：太原理工大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN253
本文編號：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.
【學位授予單位】：太原理工大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN253
【參考文獻】
相關(guān)期刊論文 前2條
1 楊光曄;李祿;田晉平;;基于譜過濾方法的Kuznetsov-Ma孤子向準基態(tài)孤子轉(zhuǎn)化研究[J];光學學報;2016年06期
2 張解放;樓吉輝;;非均勻非線性波導中線光學畸形波及其傳播控制[J];光學學報;2013年09期
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