摘要
纳米技术与光子技术的结合促进了光子晶体概念的提出。作为光子晶体一个重要应用,光子晶体光纤的出现标志着新一代光纤的诞生。与传统光纤相比,光子晶体光纤具有许多无法比拟的奇异特性,如无尽单模传输、可控的色散、非线性特性以及高双折射特性等。近年来,光子晶体光纤的研究与发展更是引起了世界范围的广泛关注,呈现出“新结构、新应用”两大特点。
本论文旨在运用数值方法,围绕新型光子晶体光纤的设计、特性及应用进行前瞻性、探索性的理论分析研究,内容包括光波导的有限元模型以及光子晶体光纤的模式特性、偏振特性、色散特性及损耗特性等几个方面。主要研究内容如下:
第一部分:有限元法及其在光波导中的应用研究
建立了基于线性三角形单元的三分量有限元分析模型,分析了正三角形格子光子晶体光纤的模场特性,总结了三分量有限元法的优缺点。
建立了基于混合棱边/节点元带有完全匹配层吸收边界条件的全矢量有限元分析模型,验证了该模型的正确性与有效性。深入研究了有限元方法中的对称边界条件。
第二部分:光子晶体光纤的瑞利散射特性数值研究
建立了基于全矢量有限元方法的光纤瑞利散射损耗数值分析模型。分析了F掺杂以及GeO_2掺杂高折射率芯Bragg光纤的瑞利散射特性,深入研究了结构参量对瑞利散射损耗的影响;分析了正三角形格子光子晶体光纤的瑞利散射特性,深入研究了瑞利散射系数、光纤结构参数等参量对瑞利散射损耗的影响。
第三部分:宽带色散平坦光子晶体光纤的设计
提出了一种用于实现宽带平坦色散的光子晶体光纤结构,分析了该结构光纤的模场特性以及波导色散特性,通过优化在理论上实现了1130～1710nm波长范围内色散值为0.3±0.3 ps/(km·nm)的近零色散平坦光纤,研究了结构偏差对色散平坦特性的影响。
第四部分:高双折射低限制损耗光子晶体光纤的设计
提出了一种高双折射低限制损耗光子晶体光纤结构,深入研究了光纤结构参数与模式双折射、限制损耗之间的关系,发现该结构光纤不仅可以获得高达10~(-3)量级的模式双折射,而且可以在包层空气孔环数仅为4的情况下实现不超过0.1dB/km的极低限制损耗。
第五部分:宽带单模单偏振光子晶体光纤的设计
提出了一种基于长方形格子的单模单偏振光子晶体光纤结构,深入研究了该结构光纤的单偏振特性,理论上实现了1.20～1.66μm波长范围内仅有慢轴模且限制损耗低于0.1dB/km的超宽带单模单偏振光子晶体光纤,研究了结构偏差对光纤单偏振传输特性的影响,最后分析了单模单偏振光子晶体光纤与传统单模光纤的耦合特性。
Photonic crystal fibers (PCFs), one of the most important applications of photonic crystal (PC) technology, have attracted significant attention all over the world. Compared with traditional fibers, PCFs posses many unique properties, such as light guidance in air, endlessly single-mode transmission, controllable dispersion, and high nonlinearity and birefringence, which are expected to bring a huge impact to future optical communications. Worldwide efforts have been taken to the research and development (R&D) of PCFs in "novel structures, new applications".
This dissertation focuses on the analysis and design of novel index-guiding PCFs aiming at some potential applications in future optical communications.
It first presents an overall survey of the current state of the art in PCFs.
In chapter 2, a versatile simulation platform based a full-vector finite element method (FEM) for the analysis of PCFs is established. In order to avoid spurious solutions, a hybrid edge/nodal element is applied and, to investigate the behavior of not only bound modes but leaky modes in optical waveguides, an anisotropic perfectly matched layer (PML) is employed as boundary condition at the edges of the computational window. The validity and usefulness of the FEM is verified when a rib anti-resonant reflecting optical waveguide (ARROW) and the hexagonal-lattice PCFs are taken into consideration. Perfect magnetic conductor (PMC) and perfect electric conductor (PEC) boundaries are discussed in detail in the analysis of a step-index fiber.
In the third chapter, an analytical model for Rayleigh scattering in fibers is presented based on the full-vector finite element method. By using this model, the Rayleigh scattering losses in F-doped and GeO_2-doped High-index-core Bragg fibers, as well as PCFs with air holes arranged in hexagonal lattice are numerically investigated.
Chapter 4 presents a novel design for realizing flattened dispersion in PCFs, using a square-lattice PCF with a central air-hole defect in the core region. The influences of the central air-hole defect on the mode field and dispersion are discussed in detail. Based on the mutual cancellation between the waveguide and the material dispersions, a nearly-zero dispersion-flattened PCF with dispersion within 0.3±0.3 ps/(km·nm) and confinement loss less than 0.1dB/km at wavelengths ranging from 1130nm to 1710nm is numerical demonstrated. Influence of varying PCF parameters on the dispersion properties of the dispersion-flattened PCF is analyzed. Owing to its ultra-fattened dispersion features, as well as low confinement losses and small effective mode area, the proposed PCF may be used for some nonlinear optical applications.
Described in chapter 5 is a novel systematic scheme to achieve both high birefringence and low confinement loss in PCFs with finite number of air holes (i.e. 4 rings) in the cladding region, based on the fact that the modal birefringence of PCFs is dominated by the inner-ring air holes in PCFs. The relationships between fiber parameters and birefringence in the proposed PCFs are investigated. Numerical results show that fibers with modal birefringence in the order of 10~(-3) and confinement loss less than 0.1dB/km can be easily realized in PCFs with only four rings of air holes in the cladding region.
In the last chapter we propose a novel design for achieving wide-band single-polarization single-mode (SPSM) operation in photonic crystal fiber, using a rectangular-lattice PCF with two lines of three central air holes enlarged. The proposed PCF composed entirely of silica material is modeled by a full-vector finite element method with anisotropic perfectly matched layers. The polarization-dependent cutoff properties and confinement losses of the proposed structure are numerically analyzed as functions of PCF parameters and wavelengths. By adjusting the size of the central enlarged air holes, the position of the regime of single polarization can be tuned freely as required. The wide-band SPSM operation feature, low confinement losses and the small effective mode area are the main properties of the proposed PCF structure. Using this structure an ultra-wide-band SPSM-PCF with confinement loss less than 0.1dB/km within wavelength range from 1.20 to 1.66μm and effective mode area about 5.9μm~2 at 1.55μm is successfully designed. The proposed fiber is a nonlinear one that might be suitable for some nonlinear optical applications, or it can be used as polarizing elements in optical devices with wide SPSM operating bandwidths requirement such as an all fiber polarizer within the whole telecommunication window.
引文
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