利用最小二乘拟合法分析了光子晶体的能带结构，定量分析了二维光子晶体的色散参量.为了考虑脉冲各频率的作用，通过引入与频率分量相关的权重因子，从而解析了群速度和平均群速度色散，进而解析出脉冲波络渐变的理论结果.通过FDTD数值模拟后，发现数值模拟结果与理论解析结果完全相吻合.本文处理光子晶体的色散参量的方法，为制作光子晶体色散器件如光子晶体色散补偿器、脉冲展宽和压缩器有一定的借鉴作用.

运用光学传输矩阵理论, 研究了含负折射率材料1维光子晶体缺陷模的偏振特性。结果显示, 零均折射率带隙中缺陷模对入射角和偏振有较强的依赖。通过对缺陷层参数的优化设计, 得到了一系列的偏振无关非全向缺陷模, 这是传统1维光子晶体中不能出现的。应用这些缺陷模, 设计了低通、高通、带通空间滤波器。与传统光子晶体空间滤波器相比, 这些空间滤波器具有偏振无关的优点。

We propose a new type of wavelength division demultiplexer composed of a photonic crystal waveguide with asymmetric corrugated exit surface. The focus displacement for different symmetric corrugated surfaces is relative to the intensity of the excited surface mode. By systematically investigating the effects of the parameters of the corrugated surface on the focus shift, we demonstrate an on-axis focus by a photonic crystal waveguide with an asymmetric corrugated exit surface at a specific wavelength. The precise equivalences of surface modes at each side of the exit surface are broken. Thus, for the light source with other wavelengths, the emerging beams are off-axis focused at different directions, similar to the function of a wavelength division demultiplexer.

采用传输矩阵法和时域有限差分(FDTD)法, 对基于人工介质的低通空间滤波器的传输特性进行了数值模拟和分析, 提出了两种具体的设计方案,得到了控制空间滤波器截止波矢的方法。数值计算结果表明,利用不确定介质或低有效折射率光子晶体都可实现高性能的低通空间滤波。两种滤波器都由薄平板构成,所占的空间体积只有几个波长量级,可大大减少传统空间滤波器所占的空间体积。

增益或损耗对光纤的传输特性影响很大。使用Davidenko方法对复折射率光纤的传输特性进行了分析。研究了复折射率纤芯或复折射率包层阶跃光纤,通过比较发现,使用Davidenko方法得到的解与精确解符合得很好。对于芯区为复折射介质的光纤,HE11模与LP01模增益值偏差约为0.6％;对于包层区为复折射率介质的光纤,HE11模与LP01模增益值偏差约为2％。实际研究工作中,为了得到更精确的结果,应该求解全矢量的复本征方程,尤其是包层具有增益或损耗的光纤。

Different from previous focusing on subwavelength imaging in the near field, we outline another potentially useful application of the self-collimating photonic crystal -- low-pass spatial filtering. A two-dimensional square-lattice photonic crystal is taken as an example and the low-pass spatial filtering is demonstrated by the dispersion analysis and numerical simulations. The high-spatial-frequency components, whose incident angles exceed a critical value, are reflected totally because no Bloch modes of the photonic crystal can be excited. However, the low-spatial-frequency components are coupled to the self-collimating modes and permeate the photonic crystal with high transmissivity.

A theoretical method to analyze four-layer large flattened mode (LFM) fibers is presented. The influence of the second cladding on the properties of four-layer LFM fiber, including the fundamental and higher-order modal fields, effective area, bending loss, and dispersion, are studied by comparison. At the same time, the reasons for the different characteristics are considered. The obtained results indicate that the effective area of the four-layer LFM fiber is about 1.6 times larger than that of the conventional standard step-index fiber and the fibers have better bend-induced filtering ability than three-layer LFM fibers.

We have investigated the basic properties of subwavelengthdiameter hollow optical fiber with exact solutions of Maxwell’s equations. The characteristics of modal field and waveguide dispersion have been studied. It shows that the subwavelength-diameter hollow optical fibers have interesting properties, such as enhanced evanescent field, local enhanced intensity in the hollow core and large waveguide dispersion that are very promising for many miniaturized high performance and novel photonic devices.

Optical properties of a two-dimensional square-lattice photonic crystal are systematically investigated within the partial bandgap through anisotropic characteristics analysis and numerical simulation of field pattern. Using the plane-wave expansion method and Hellmann–Feynman theorem, the relationships between the incident and refracted angles for both phase and group velocities are calculated to analyze light propagation from air to photonic crystals. Three kinds of flat slab focusing are summarized and demonstrated by numerical simulations using the multiple scattering method.