飞秒光脉冲在光子晶体光纤中的非线性传输特性研究
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摘要
与传统光纤相比,光子晶体光纤(photonic crystal fiber, PCF)灵活设计的结构和特殊的导光机制,使其具有许多引人注目的特性,如无截止单模特性、可控的色散特性、极强的非线性效应及高双折射特性等。因此,PCF在非线性光学、光纤通信和光纤传感等领域都有着广泛的应用前景,是目前国内外的研究热点之一。
本论文的工作集中在飞秒光脉冲在PCF中的非线性传输特性方面,研究了利用PCF实现飞秒脉冲的光谱压缩以及超连续谱的产生,主要内容如下：
1.介绍了PCF的概念、导光原理以及制作方法,阐述了PCF的优良光学特性,并讨论了PCF光学非线性的应用领域。
2.根据麦克斯韦方程组推导了超短光脉冲在PCF中传输的广义非线性薛定谔方程,并分析了数值求解该方程的预测校正的对称分布傅立叶算法。基于该算法,运用Matlab语言编写了模拟光脉冲在PCF中传输的相关程序。另外,对超短光脉冲在PCF中传输过程中所涉及到的几种非线性效应进行了简单的分析。
3.基于广义非线性薛定谔方程,利用预测校正傅立叶方法数值模拟了波长为1550 nm的无初始啁啾飞秒光脉冲在PCF反常色散区中的非线性传输特性,提出了一种飞秒光脉冲谱宽压缩的新方法,数值分析了初始超短光脉冲的峰值功率、中心波长以及光纤长度等参数对谱宽压缩的影响,并讨论了产生谱宽压缩的机制。
4.利用广义非线性薛定谔方程,数值模拟了飞秒光脉冲在高非线性PCF中超连续谱的产生,系统地讨论了脉冲初始参数,具体包括中心波长、峰值功率、和初始啁啾,以及光纤长度对超连续谱形状和带宽的影响。
5.采用矢量耦合非线性薛定谔方程,数值模拟了中心波长为1550 nm的超短光脉冲在双折射PCF中超连续谱的产生及其偏振特性,讨论了超短光脉冲在三种不同色散特性的双折射PCF中传输时,高阶色散和非线性效应对脉冲的波形、光谱展宽以及光谱偏振特性的影响。
Since the photonic crystal fiber was firstly demonstrated by J. C. Knight in 1996s, its great flexibility in design and unique optical properties have attracted considerable attention. Compared to conventional fiber, PCFs have many unusual characteristics, such as endless single mode propagation, controllable dispersion properties, strong nonlinear effects and high birefringence, which make PCFs have wide application in the field of nonlinearity optics, optical communication, fiber sense and many other fields. Therefore, PCFs have become one of research interests in the past years.
This thesis is mainly focused on research of nonlinear propagation of ultra-short femtosecond pulses in PCFs; the main contents are listed below:
First, contents of the concept, optical properties and preparation of PCFs are introduced detaily. Applications of nonlinear effects of PCFs, as well as theories of fine feather of PCFs, are analyzed.
Second, generalized nonlinear Schrodinger equation(GNLSE) as model of nonlinear propagation of ultra-short laser pulses in PCFs is found from Maxwell's equation. The predictor-corrector symmetrized split-step Fourier method is proposed for solving the GNLSE, and based on the arithmetic, Matlab is aided for design of computer program, which is used to investigate nonlinear propagation of ultra-short laser pulses in PCFs numerically.
Third, based on GNLSE, the numerical investigation of nonlinear propagation of chirp-free femtosecond pulses in PCFs with anomalous dispersion is presented. It is found that the compressed spectral width is strongly dependent on the initial peak power, central wavelength and propagation length of the incident pulse. The mechanisms responsible for the spectral compression are discussed.
Fourth, femtosecond laser pulse propagation and supercontinuum (SC) generation in PCFs are investigated numerically based on GNLSE. The effects of the parameters of the initial laser pulse, peak power, initial chirp and fiber length on spectral properties of SC are analyzed systematically for optimizing SC.
Fifth, the coupled nonlinear Schrodinger equations (CNLSE) are adopted to describe the evolution of ultra-short laser pulse propagation in bierfringent photonic crystal fibers, and solved with the symmetrized split-step Fourier method. It has been investigated of generation and polarization properties of the supercontinuum by ultra-short pulse in bierfringent photonic crystal fibers with different dispersion profiles in the 1550-nm window by numerical stimulation. The impact of high-order dispersion and nonlinear effects is analyzed with different dispersion profiles.
本论文的工作集中在飞秒光脉冲在PCF中的非线性传输特性方面,研究了利用PCF实现飞秒脉冲的光谱压缩以及超连续谱的产生,主要内容如下：
1.介绍了PCF的概念、导光原理以及制作方法,阐述了PCF的优良光学特性,并讨论了PCF光学非线性的应用领域。
2.根据麦克斯韦方程组推导了超短光脉冲在PCF中传输的广义非线性薛定谔方程,并分析了数值求解该方程的预测校正的对称分布傅立叶算法。基于该算法,运用Matlab语言编写了模拟光脉冲在PCF中传输的相关程序。另外,对超短光脉冲在PCF中传输过程中所涉及到的几种非线性效应进行了简单的分析。
3.基于广义非线性薛定谔方程,利用预测校正傅立叶方法数值模拟了波长为1550 nm的无初始啁啾飞秒光脉冲在PCF反常色散区中的非线性传输特性,提出了一种飞秒光脉冲谱宽压缩的新方法,数值分析了初始超短光脉冲的峰值功率、中心波长以及光纤长度等参数对谱宽压缩的影响,并讨论了产生谱宽压缩的机制。
4.利用广义非线性薛定谔方程,数值模拟了飞秒光脉冲在高非线性PCF中超连续谱的产生,系统地讨论了脉冲初始参数,具体包括中心波长、峰值功率、和初始啁啾,以及光纤长度对超连续谱形状和带宽的影响。
5.采用矢量耦合非线性薛定谔方程,数值模拟了中心波长为1550 nm的超短光脉冲在双折射PCF中超连续谱的产生及其偏振特性,讨论了超短光脉冲在三种不同色散特性的双折射PCF中传输时,高阶色散和非线性效应对脉冲的波形、光谱展宽以及光谱偏振特性的影响。
Since the photonic crystal fiber was firstly demonstrated by J. C. Knight in 1996s, its great flexibility in design and unique optical properties have attracted considerable attention. Compared to conventional fiber, PCFs have many unusual characteristics, such as endless single mode propagation, controllable dispersion properties, strong nonlinear effects and high birefringence, which make PCFs have wide application in the field of nonlinearity optics, optical communication, fiber sense and many other fields. Therefore, PCFs have become one of research interests in the past years.
This thesis is mainly focused on research of nonlinear propagation of ultra-short femtosecond pulses in PCFs; the main contents are listed below:
First, contents of the concept, optical properties and preparation of PCFs are introduced detaily. Applications of nonlinear effects of PCFs, as well as theories of fine feather of PCFs, are analyzed.
Second, generalized nonlinear Schrodinger equation(GNLSE) as model of nonlinear propagation of ultra-short laser pulses in PCFs is found from Maxwell's equation. The predictor-corrector symmetrized split-step Fourier method is proposed for solving the GNLSE, and based on the arithmetic, Matlab is aided for design of computer program, which is used to investigate nonlinear propagation of ultra-short laser pulses in PCFs numerically.
Third, based on GNLSE, the numerical investigation of nonlinear propagation of chirp-free femtosecond pulses in PCFs with anomalous dispersion is presented. It is found that the compressed spectral width is strongly dependent on the initial peak power, central wavelength and propagation length of the incident pulse. The mechanisms responsible for the spectral compression are discussed.
Fourth, femtosecond laser pulse propagation and supercontinuum (SC) generation in PCFs are investigated numerically based on GNLSE. The effects of the parameters of the initial laser pulse, peak power, initial chirp and fiber length on spectral properties of SC are analyzed systematically for optimizing SC.
Fifth, the coupled nonlinear Schrodinger equations (CNLSE) are adopted to describe the evolution of ultra-short laser pulse propagation in bierfringent photonic crystal fibers, and solved with the symmetrized split-step Fourier method. It has been investigated of generation and polarization properties of the supercontinuum by ultra-short pulse in bierfringent photonic crystal fibers with different dispersion profiles in the 1550-nm window by numerical stimulation. The impact of high-order dispersion and nonlinear effects is analyzed with different dispersion profiles.
引文
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