Analytical solution of the scalar wave equation for slightly deformed optical Bragg waveguide

Using a simple analytical method, we study the electromagnetic-wave propagation in an optical Bragg waveguide which is slightly deformed at one side. We show the results of computations in the form of dispersion curves and provide a comparison with standard circular Bragg waveguides and step-index circular waveguides. We show that the correspondence between the cutoff V values for the standard step-index fiber and the new Bragg waveguide, which is slightly flattened on one side, is quite close for the lowest mode under the weak guidance condition.     

光纤波导色散的比例性质研究

基于麦克斯韦方程组的比例性质,讨论了光纤波导色散的比例性质,并对普通光纤、Bragg光纤和光子晶体光纤的波导色散进行了理论研究。以Bragg光纤为例,提出了一种根据波导色散的比例性质灵活设计光纤色散特性的方法。     

Directional coupler wavelength selective filter based on dispersive Bragg reflection waveguide

A new type of wavelength selective filter, based on high differential dispersion between two coupled waveguides, is presented. The Bragg Reflection Waveguide displays high effective refractive index dispersion, due to the interaction of the guided mode with the two confining Bragg reflectors. When coupled with a weakly guided buried channel silica waveguide, a very narrow bandwidth filter (<1 nm) can be easily produced, in a shorter length, with respect to directional couplers made with standard step index channel waveguides. The complete design methodology, fabrication and characterization are presented.     

Computing Eigen value equation and modal dispersion characteristics of an elliptical Bragg waveguide

Using the method of separation of variables in the elliptical coordinate system, a recursive formula for the electromagnetic fields in a new type of Bragg waveguide having elliptical core cross section with multilayered cladding is derived. The eigen equation is written in the form of Mathieu and the modified Mathieu functions and a dispersion relation is obtained for various modes supported by the proposed Bragg waveguide. The cutoff frequencies for several lower order even-odd modes have been calculated and their propagation characteristics are plotted. The results show that the dispersion curves are discontinuous and modes can exist only in particular wavelength bands. The effects of elliptical eccentricity on the mode cutoff values and mode transmission are addressed. Finally, the modal birefringence in the said waveguide is also estimated.     

高折射率芯Bragg光纤的色散特性研究

应用超格子模型分析了高折射率芯Bragg光纤的色散特性，讨论了Bragg光纤的色散的比例性质以及光纤的芯径、包层周期、填充率与波导色散的关系，并利用这些关系举例实现了Bragg光纤在1.55μm附近的宽带色散平坦. 关键词： Bragg光纤 模式 色散 波导色散     

Bragg光纤包层制作误差对导模特性的影响

对Bragg光纤中包层制造误差对导模特性的影响进行了深入的分析和研究,给出了一般N层波导中模式场标量波动方程求解的传输矩阵方法,并将其应用在Bragg光纤模式场的分析当中。分别研究了Bragg包层存在折射率误差和厚度误差时对光纤基模模式场的有效折射率、模场半径和芯区功率占比的影响,并利用统计的方法分析了不同制作误差时导模特性的相对变化。折射率误差在1‰的水平时,基模有效折射率、模场半径和芯区功率占比的方差水平为1.55×10~(-4)、1.04×10~(-1)和1.79×10~(-2);厚度误差在2%的水平时模式场参量的方差水平分别为3.61×10~(-5)、1.84×10~(-2)和2.35×10~(-3)。     

K-Na离子交换单模平面波导的制备及其表征

通过K-Na离子交换技术制备了多模玻璃平面波导.采用棱镜耦合技术测量了波导的有效折射率,用IWKB方法拟合得到K-Na离子交换波导的折射率分布符合高斯分布,由色散曲线得到单模波导的制备条件(即扩散深度范围),从而得出单模波导的离子交换时间范围,制备出单模波导,并通过求解WKB色散方程得出单模波导的表面折射率.用普通数码相机,通过对离子交换平面玻璃光波导传输线进行数字成像,根据传输线上的光强分布拟合出光强传输衰减曲线,计算出单模波导的传输损耗大约为0.4 dB/cm.     

取样布拉格光纤光栅的传输矩阵

根据在一般坐标系下均匀布拉格光纤光栅的传输矩阵,得到了取样布拉格光纤光栅的传输矩阵。利用傅里叶变换得到了取样布拉格光纤光栅的谐振方程。结果表明,在不考虑平均折射率变化的情况下,谐振峰的位置是由光栅的周期和取样周期共同确定的,与取样时的占空比、光栅长度和耦合系数没有关系。类似于物理光栅,取样布拉格光纤光栅也存在缺级现象,给出了出现缺级的条件。     

Performance study of a liquid-core Bragg fiber sensor in presence of a defect layer

Performance parameter of a Bragg fiber waveguide based resonant sensor in presence of a defect layer in cladding regions is theoretically studied. The Bragg fiber waveguide consists of a liquid-core surrounded by alternate high and low refractive indices materials in cladding regions. Reflectivity of the proposed waveguide based resonant sensor is formulated using transfer matrix method for a non-homogeneous multilayer cylindrical system. The waveguide shows a band gap region with a narrow defect mode in the band gap region under the considered wavelength range. Instead of taking a whole band gap as a sensing signal, here the defect peak is taken as the sensing signal. It is observed that the intensity of defect mode is more sensitive for core refractive index than the intensity of traditional band gap region (lobe). This study shows that the higher sensitivity can be achieved by creating the defect at a position in cladding region where the intensity of transmitted light lies between 40% and 90%. Presence of a defect layer is able to increase the detection accuracy of the sensor and, hence increase the overall performance of this sensor.     

Analysis of circular fibers with an arbitrary index profile by the Galerkin method

We propose a full-vectorial Galerkin method for the analysis of circular symmetric fibers with arbitrary index profiles. A set of orthogonal Laguerre-Gauss functions is used to calculate the dispersion relation and mode fields of TE and TM modes. Examples are given for both standard step-index fibers and Bragg fibers. For standard step-index fiber with low or high index contrast, the Galerkin method agrees well with the analytical results. In the case of the TE mode of a Bragg fiber it agrees well with the asymptotic results.     

Loss and dispersion tailoring in 1D photonics band gap Bragg reflection waveguides: finite chirped claddings as a design tool

We exploit a simple and accurate matrix method to analyze the effects of introducing a linear chirp either in thickness or in refractive index of the cladding layers on the propagation characteristics (loss and dispersion) of 1D photonic band gap planar Bragg reflection waveguides (BRWs). We show that an appropriate chirp in the otherwise periodic claddings of finite extent BRWs could be gainfully exploited to tailor its leakage loss and waveguide dispersion features. In particular, we theoretically demonstrate that for some reported sample BRWs, leakage loss and waveguide dispersion could be significantly reduced by a factor of 30–50 and by about two orders of magnitude, respectively as compared to un-chirped BRWs. Furthermore, we also show that in contrast to un-chirped BRWs, how chirped BRWs could be designed with attractive feature like much less number of cladding layers and nearly wavelength independent losses. Our analysis and proposal should serve as a useful design tool to tailor the propagation characteristics of BRWs.     

光纤纤芯及包层模有效折射率计算及仿真

光纤结构设计、模间色散求解、光纤光栅模式耦合等问题的研究, 都需要对光纤纤芯及包层模的有效折射率进行精确计算. 本文以光纤三层结构模型为基础, 结合该模型下的模式本征方程, 使用截弦法求解了纤芯模有效折射率, 并将计算结果与COMSOL软件模拟的对应纤芯模的传输光场进行对比, 验证了计算结果正确.使用区间遍历算法对包层模有效折射率进行了求解, 与已有的传统方法相比, 该方法可以有效防止求解过程中根的遗漏、避免特征方程产生的奇点, 并能保证模式的正规性.本文采用Mathematica软件对求解过程进行仿真, 获得了纤芯模和包层模有效折射率与波长关系曲线. 关键词： 光纤传输模式 有效折射率 截弦法 区间遍历算法     

Modal analysis and cutoff frequencies of a doubly clad plasma loaded waveguide having a lemniscates of Bernoulli-type core cross-section

The modal dispersion characteristics of EM waves in a new unconventional plasma loaded doubly clad waveguide having a shape of the lemniscates of Bernoulli-type core cross-section have been studied analytically. The proposed waveguide has three parts namely the core with slighter high index, the inner cladding with plasma and the outer cladding with air. Now using the necessary orthogonal coordinates for the proposed structure and imposing the boundary conditions under the weak guidance condition, the modal characteristics equation has been obtained considering variations in plasma width and plasma frequency, the dispersion curves and cutoff frequencies have been obtained and presented in this paper. It is noted that as the width of plasma layer increases, the cutoff frequency also increases considerably in all considered cases. This shows that using plasma width as a new parameter we can control any particular mode on our wish.     

基于包层模谐振的三包层石英特种光纤温度传感特性研究

提出了一种基于包层模谐振的光纤温度传感器. 它是通过将三包层石英特种光纤(TCQSF)两端分别与普通单模光纤(SMF)电弧熔接构成的SMF-TCQSF-SMF结构. 根据耦合模理论, 首先将TCQSF等效为三个同轴波导, 按各波导模场的分布特点标量计算其传输模式的色散曲线, 并深入研究其耦合长度与传输谱线之间的关系; 其次根据光纤的热光效应及热膨胀效应, 分析计算该传感器的温度灵敏度; 最后选取耦合长度为一个拍长时的传感器进行温度传感实验. 实验结果表明, 在35-95 ℃的温度变化范围内, 其温度灵敏度为73.74 pm/℃, 与理论计算结果一致. 因此, 该传感器具有结构简单、制备容易、灵敏度高、包层模激发可控等优点, 可用于工业生产、生物医学等温度传感领域.     

在非线性条件下光纤传输特性的数值分析

采用有限差分法数值求解考虑了非线性系数后的标量波动方程，发现若令两次的ｎｗ迭代差值小于１０－９以及对光纤径向迭代做足够多的分层时，则有限差分法具有较高的精确度，并且适用于任意折射率剖面光纤。同时通过计算发现在非线性条件下，光纤的色散值比线性条件下的偏大，即零色散点向短波长方向移动，而且发现波长越短，非线性效果越明显。最后给出了普通单模光纤中在非线性条件下的模拟结果。     

光纤光栅非线性对色散特性的影响

通过在能量较高、考虑非线性时,求解光纤光栅非线性耦合模方程连续波条件下的解,得到光纤光栅失谐量δ与光脉冲传播常量q的非线性色散关系和光栅致群速度色散系数βg2与δ的关系.用MATLAB绘图,得到非线性参量γ和光脉冲能量P0的乘积γP0对色散和βg2的影响.结果表明:随着βg2的增加,非线性色散曲线的上、下两支向δ的负值区移动,当超过某一临界值时,曲线上支开始形成环,这时光纤光栅引起的群速度色散中的反常色散区消失,全部变成正常色散.     

Light guidance in a photonic bandgap slab waveguide consisting of two different Bragg reflectors

By means of a zigzag-wave model, we perform a comprehensive analysis of the guided modes of a photonic bandgap slab waveguide that consists of a low-index guiding layer placed between two different Bragg reflectors. We show that the guided modes of the waveguide operate inside the overlapped bandgaps of the two Bragg reflectors. We label each mode with three mode orders, which reflect the features of the mode-field distribution in the guiding layer and the two Bragg reflectors, respectively. We discuss in detail the transmission characteristics of the guided modes, including the dispersion curves, the cutoff conditions, and the confinement factors, and highlight the mode-selection characteristics of the waveguide. We also study the effects of truncating the Bragg reflectors by deriving an analytical expression to show the dependence of the leakage losses of the modes on the numbers of the periods in the truncated Bragg reflectors.     

Modes of Bragg fiber with delta-function walls: Scalar approximation

An analytical theory of cylindrical low-contrast Bragg optical waveguides, i.e., Bragg fibers, was developed on the basis of the representation of thin diffuse layers by delta functions. A dispersion relation for the Bragg optical waveguide with a finite number of layers was derived in the scalar approximation. Mode fields and losses were numerically calculated for a fiber with parameters close to those of actual fiber known from the literature. A comparison with the planar model was performed, which showed significant qualitative similarity. The presented model of Bragg fibers is more realistic than the model with sharp layer boundaries.     

各向异性色散左手材料平面波导的导模特性(英文)

对芯层为左手材料而内外包层都是普通材料的非对称三层平面波导TE振荡模进行了分析.在考虑左手材料色散和各向异性的情况下,从Maxwell方程组出发,得到了TE振荡模的色散方程和功率流分布,并且画出了相应的色散曲线.我们找到了8个TE振荡模,而且包括基模.随着模阶数的增加,模色散曲线右移,功率流曲线下移.但是,随着波导厚度的增加,色散曲线左移,功率流曲线上移.此外,TE振荡模有反常色散特性和负的群速,这正揭示了左手材料的本质特性.     

Anomalous behaviour in a Bragg reflection waveguide

A novel asymmetric Bragg reflection waveguide (BRW) showing anomalous dispersion characteristic is presented. The abnormal behaviour of increase of modal effective index with wavelength is primarily caused by the changes taking place in the imaginary part of the Bloch wavevector, in the periodic stratified cladding. The phase velocity and the group velocity dispersion characteristics for the waveguide have also been analyzed. Such an anomalous behaviour can find applications in the design of integrated optical devices.