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五階非線性克爾效應影響下光脈沖的傳輸

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【摘要】:本文研究的理論模型是變系數的五次金茲堡-朗道(Ginzburg-Landau)方程,首先,研究理論模型的精確解,根據計算結果理論分析了精確解在非均勻光纖系統(tǒng)中的傳輸情況,并對理論分析進行數值驗證。然后,在考慮非均勻光纖系統(tǒng)中的五階非線性克爾效應時,研究了精確孤子解形式的超短脈沖的傳輸特性,并討論兩個這種超短光脈沖在傳輸過程中的相互作用。最后,在考慮五階非線性克爾效應時,研究光纖放大器中光孤子的傳輸特性,并討論了五階非線性克爾效應對光孤子的具體影響。在實際應用中,這些研究對于超短脈沖在非均勻光纖系統(tǒng)中的傳輸提供了一定的理論依據,還有助于控制光纖放大器和非均勻光纖系統(tǒng)中五階非線性克爾效應的影響。本文研究的主要內容包含以下幾個方面:(1)介紹在光纖通信發(fā)展中非線性光纖光學的研究背景,簡述國內外光孤子在非均勻光纖系統(tǒng)中的研究現狀,并簡要分析五階非線性克爾效應的研究意義。(2)研究理論模型的精確解。在考慮光纖傳輸介質中五階非線性克爾效應時,利用擬解法計算出滿足特殊條件下的精確孤子解,在理論的層面上分析精確解的傳輸情況。當忽略五階非線性克爾效應,計算出光纖傳輸系統(tǒng)中存在的精確耗散孤子解,同樣分析耗散孤子解的傳輸情況。最后,對精確的孤子解和耗散孤子解進行數值分析,驗證理論研究的結果。(3)在考慮五階非線性克爾效應的非均勻光纖傳輸系統(tǒng)中,用分步傅里葉法研究精確孤子解超短脈沖的傳輸穩(wěn)定性和相互作用。在入射脈沖中分別加入振幅微擾和隨機噪聲,數值模擬其傳輸穩(wěn)定性;并通過改變兩個相鄰入射脈沖之間的距離,數值模擬在此系統(tǒng)中的傳輸情況,分析兩個光孤子之間的相互作用。(4)在光纖放大器中考慮五階非線性克爾效應時,用分步傅里葉法研究光孤子的傳輸特性。首先,以雙曲正割脈沖作為入射脈沖,研究亮孤子中的演化過程和其傳輸的穩(wěn)定性,并分析多個亮孤子的傳輸情況;其次,以雙曲正切脈沖作為入射脈沖,研究暗孤子的傳輸情況;最后,討論五階非線性克爾效應對光孤子的具體影響。
[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.
【學位授予單位】:山西大學
【學位級別】:碩士
【學位授予年份】:2016
【分類號】:TN929.11

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