色散平坦微结构光纤理论设计及四波混频特性的研究
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摘要
微结构光纤,也叫光子晶体光纤或多孔光纤,具有许多传统光纤难以实现的优良特性,是目前光纤光学领域的一个研究热点。特别是具有色散平坦特性的微结构光纤,在密集波分复用系统、超连续谱产生和波长转换等方面有着重要的应用,是微结构光纤研究的重点方向之一。本文针对色散平坦微结构光纤设计参数多,设计步骤复杂;色散特性对结构参数依赖性强,对制备工艺要求高;特定应用中需要将色散平坦特性和其它特性相结合等问题进行了理论研究,并设计了多种性能优良、易于制备的色散平坦微结构光纤。本文主要研究内容如下:
第一,研究了使用无量纲化方法计算微结构光纤的色散,即将总色散看作波导色散与材料色散之和时,产生的误差随光纤结构参数变化的规律。以5%和5 ps/km/nm分别作为相对误差界限和绝对误差界限,探索了用无量纲化方法计算色散时所适用的微结构光纤的参数边界。并以麦克斯韦方程组为基础,推导了微结构光纤无量纲化模式面积计算的表达式。
第二,针对包层大空气孔在拉制过程中容易产生形变的问题,提出了色散特性随外包层空气孔形变不敏感的色散平坦双包层微结构光纤。采用多极法,对内包层空气孔层数不同时,微结构光纤色散特性对外包层空气孔形变的依赖程度;光纤二阶模与基模损耗的比值随外包层空气孔间距改变而变化的规律等进行了研究。通过优化结构参数,设计了色散特性对外包层空气孔形变依赖性低的色散平坦双包层微结构光纤。适当调整外包层空气孔间距,还可以得到同时支持单模传输的色散平坦双包层微结构光纤。
第三,采用无量纲化模场面积方法,研究了纤芯分别忽略1个空气孔和7个空气孔的微结构光纤,其有效模场面积大小随包层空气填充率和波长变化而变化的规律,比较了两种结构的微结构光纤在降低有效模场面积方面的优劣。根据所得规律,分别忽略7个和19个空气孔而形成光纤纤芯,设计了在通信波段集高非线性特性和色散平坦特性于一身的微结构光纤。
第四,提出了800 nm波段的色散平坦高非线性微结构光纤的设计方案。石英的材料色散在该波段绝对值大,色散曲线随波长变化呈非线性关系,为了使波导色散平衡材料色散的影响,必须在包层中引入多种大小不同的空气孔,以增加光纤的设计自由度。通过增大第一层空气孔孔径或者减小空气孔间距等方法,设计了在800 nm波段集单模传输、色散平坦特性和高非线性特性于一身的微结构光纤。
第五,利用钛-蓝宝石飞秒激光器产生的飞秒脉冲作为泵浦源,对具有双零色散点的微结构光纤和色散位移微结构光纤的四波混频现象进行了实验研究。通过理论模拟,对实验现象进行了解释,理论分析与实验结果相吻合。
Microstructure fiber, also called photonic cystal fiber or holey fiber, possesses many intriguing properties that are hardly achievable in traditional fiber. It is a research hotspot in the area of fiber optics. Microstructure fiber with flattened dispersion shows lots of application potentials in dense wavelength division multiplexing, supercontinuum generation and wavelength conversion, etc. Thus, dispersion falttened microstructure fiber is one of the most important research directions in microstructure fiber optics. However, due to a large number of design parameters and the dispersion's strong dependence on precision of the fiber structure, it is a difficult task to design and fabricate dispersion flattened microstucture fiber. In addition, other properties are usually needed to incorporate with the flattened dispersion property to enhance the system performance. In view of this situation, in this thesis, structural parameters' influrences on the optical properties of microstructure fiber are analyzed. Fabrication fridenly dispersion flattened microstructure fibers incorporated with other intriguing properties are designd. The main contents are described as follows:
First, the error of treating group velocity dispersion of microstructure fiber as sum of material and waveguide component is computed, its relation with structural parameters is analyzed. Taken 5% and 5 ps/km/nm as relative and absolute error limit, the valid micorstrcture fiber structural boundries of employing the normalized method in dispersion calculation are proposed. Based on Maxwell equation, normalized effective mode area expression of microstructure fiber is also deduced. By employing the expression, simulation complexity of mode area is reduced.
Second, large cladding air holes are prone to deformation in fiber fabrication and the dispersion of the realized fiber would be influrenced. To deal with this problem, double cladding microstructure fibers, whose dispersions are insensitive to the deformation of large outer cladding air holes, are proposed. By employing multipole method, the diseprsioon and loss property of double cladding microstucture fiber is analyzed with an emphasis on two issues listed below: first, disperison's dependence on deformation of outer cladding air holes with different number of inner air-hole layers; second, the ratio of the loss of fundamental mode to that of second order mode with different outer cladding air-hole pitch. Several dispersion flattened double cladding microstructure fibers are designed. By further adjusting the outer air-hole pitch, the fibers can also support sinlge mode transmission.
Third, effective mode areas of two different kinds of microstructure fibers, whose core are formed by omitting one or seven air holes, respectively, are computed by normalized mode area expression. Their relations to the cladding air filling fraction and wavelength are analyzed. It is found that efefective mode area can be reduced tremendously if the air-hole number in the first inner ring is increased and the channel between two air holes is narrowed. According to the analysis, dispersion flattended highly nonlinear microstructure fibers in telecommunication band are designed. Their cores are either formed by omitting seven or by nineteen air holes.
Fourth, dispersion flattended highly nonlinear microstructure fiber in 800 nm band is proposed. Due to large absolute value of silica's dispersion and its nonlinear relation to wavelength around 800 nm, it is difficult to counterbalance the material dispersion of silica by waveguide dispersion. More air-hole diameters have to be employed to enhance the design freedom. Highly nonlinear microstructure fiber with flattened dispersion and single-mode transmission in 800 nm band can be achieved by enlarging the air holes in first inner ring, decreasing the cladding air-hole pitch, etc.
Fifth, four-wave mixing is observed both in microstructure fiber with two zero dispersion wavelengths and in dispersion shifted microstructure fiber by using Ti: sapphire fs pulse as pump. The experimental results are explained by theoretical analyses and the theoretical analyses agree well with experimental results.
第一,研究了使用无量纲化方法计算微结构光纤的色散,即将总色散看作波导色散与材料色散之和时,产生的误差随光纤结构参数变化的规律。以5%和5 ps/km/nm分别作为相对误差界限和绝对误差界限,探索了用无量纲化方法计算色散时所适用的微结构光纤的参数边界。并以麦克斯韦方程组为基础,推导了微结构光纤无量纲化模式面积计算的表达式。
第二,针对包层大空气孔在拉制过程中容易产生形变的问题,提出了色散特性随外包层空气孔形变不敏感的色散平坦双包层微结构光纤。采用多极法,对内包层空气孔层数不同时,微结构光纤色散特性对外包层空气孔形变的依赖程度;光纤二阶模与基模损耗的比值随外包层空气孔间距改变而变化的规律等进行了研究。通过优化结构参数,设计了色散特性对外包层空气孔形变依赖性低的色散平坦双包层微结构光纤。适当调整外包层空气孔间距,还可以得到同时支持单模传输的色散平坦双包层微结构光纤。
第三,采用无量纲化模场面积方法,研究了纤芯分别忽略1个空气孔和7个空气孔的微结构光纤,其有效模场面积大小随包层空气填充率和波长变化而变化的规律,比较了两种结构的微结构光纤在降低有效模场面积方面的优劣。根据所得规律,分别忽略7个和19个空气孔而形成光纤纤芯,设计了在通信波段集高非线性特性和色散平坦特性于一身的微结构光纤。
第四,提出了800 nm波段的色散平坦高非线性微结构光纤的设计方案。石英的材料色散在该波段绝对值大,色散曲线随波长变化呈非线性关系,为了使波导色散平衡材料色散的影响,必须在包层中引入多种大小不同的空气孔,以增加光纤的设计自由度。通过增大第一层空气孔孔径或者减小空气孔间距等方法,设计了在800 nm波段集单模传输、色散平坦特性和高非线性特性于一身的微结构光纤。
第五,利用钛-蓝宝石飞秒激光器产生的飞秒脉冲作为泵浦源,对具有双零色散点的微结构光纤和色散位移微结构光纤的四波混频现象进行了实验研究。通过理论模拟,对实验现象进行了解释,理论分析与实验结果相吻合。
Microstructure fiber, also called photonic cystal fiber or holey fiber, possesses many intriguing properties that are hardly achievable in traditional fiber. It is a research hotspot in the area of fiber optics. Microstructure fiber with flattened dispersion shows lots of application potentials in dense wavelength division multiplexing, supercontinuum generation and wavelength conversion, etc. Thus, dispersion falttened microstructure fiber is one of the most important research directions in microstructure fiber optics. However, due to a large number of design parameters and the dispersion's strong dependence on precision of the fiber structure, it is a difficult task to design and fabricate dispersion flattened microstucture fiber. In addition, other properties are usually needed to incorporate with the flattened dispersion property to enhance the system performance. In view of this situation, in this thesis, structural parameters' influrences on the optical properties of microstructure fiber are analyzed. Fabrication fridenly dispersion flattened microstructure fibers incorporated with other intriguing properties are designd. The main contents are described as follows:
First, the error of treating group velocity dispersion of microstructure fiber as sum of material and waveguide component is computed, its relation with structural parameters is analyzed. Taken 5% and 5 ps/km/nm as relative and absolute error limit, the valid micorstrcture fiber structural boundries of employing the normalized method in dispersion calculation are proposed. Based on Maxwell equation, normalized effective mode area expression of microstructure fiber is also deduced. By employing the expression, simulation complexity of mode area is reduced.
Second, large cladding air holes are prone to deformation in fiber fabrication and the dispersion of the realized fiber would be influrenced. To deal with this problem, double cladding microstructure fibers, whose dispersions are insensitive to the deformation of large outer cladding air holes, are proposed. By employing multipole method, the diseprsioon and loss property of double cladding microstucture fiber is analyzed with an emphasis on two issues listed below: first, disperison's dependence on deformation of outer cladding air holes with different number of inner air-hole layers; second, the ratio of the loss of fundamental mode to that of second order mode with different outer cladding air-hole pitch. Several dispersion flattened double cladding microstructure fibers are designed. By further adjusting the outer air-hole pitch, the fibers can also support sinlge mode transmission.
Third, effective mode areas of two different kinds of microstructure fibers, whose core are formed by omitting one or seven air holes, respectively, are computed by normalized mode area expression. Their relations to the cladding air filling fraction and wavelength are analyzed. It is found that efefective mode area can be reduced tremendously if the air-hole number in the first inner ring is increased and the channel between two air holes is narrowed. According to the analysis, dispersion flattended highly nonlinear microstructure fibers in telecommunication band are designed. Their cores are either formed by omitting seven or by nineteen air holes.
Fourth, dispersion flattended highly nonlinear microstructure fiber in 800 nm band is proposed. Due to large absolute value of silica's dispersion and its nonlinear relation to wavelength around 800 nm, it is difficult to counterbalance the material dispersion of silica by waveguide dispersion. More air-hole diameters have to be employed to enhance the design freedom. Highly nonlinear microstructure fiber with flattened dispersion and single-mode transmission in 800 nm band can be achieved by enlarging the air holes in first inner ring, decreasing the cladding air-hole pitch, etc.
Fifth, four-wave mixing is observed both in microstructure fiber with two zero dispersion wavelengths and in dispersion shifted microstructure fiber by using Ti: sapphire fs pulse as pump. The experimental results are explained by theoretical analyses and the theoretical analyses agree well with experimental results.
引文
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