A simple method for prediction of first-order modal field and cladding decay parameter in graded index fiber

Based on a series expansion method involving the Chebyshev technique, we present analytical expressions for first higher order modal field as well as cladding decay parameter in case of graded index fiber. This method utilizes the formulation of a linear relation of the ratio of first- and zero-order modified Bessel functions, with reciprocal of Cladding decay parameter. This leads to the evaluation of the Cladding decay parameter from a simple equation involving a third-order determinant and the first higher order modal field is thereafter found from two simple equations. Thus the paper presents the technique of avoiding complicated calculations of Chebyshev coefficients and therefore, the present formalism will be extremely important for practical engineering problems. Taking step and parabolic index fibers as examples, we show that our estimations of the said propagation characteristics agree excellently with the available exact results. The concerned calculations involve very little computations.     

A simple technique for evaluation of transmission coefficient at the splice with angular offset and transverse offset for first higher mode propagation in graded index fibers

We present simple and accurate analytical expressions for transmission coefficient at the splice with angular offset and transverse offset in case of first higher mode propagation in graded index fibers. We employ the simple series expression for first higher order modal field for graded index fiber. The evaluation of the concerned parameters based on our formalism requires very little computations. Here, we show that our estimations match excellently well with the exact results in case of step and parabolic index fibers. Further, splice being highly tolerant for longitudinal separation, our analysis is judiciously restricted to the case of transverse and angular mismatches only. The analysis should find application in dual mode graded index fiber in all optical technology.     

A simple but accurate technique of predicting radial variation of pump and signal intensities in erbium-doped graded index fiber amplifier for propagation of first higher order mode

An optically pumped doped fiber amplifier has emerged as an important device for providing broadband amplification in case of multi-channel optical signals in long-haul communication systems. In this context, dual mode graded index fiber is finding application in all optical technology. So it is needed to prescribe accurately the first order modal field in the doped fiber, both for the pump and the signal as well and it is also equally important to study their variations with the distance. Employing the simple but accurate power series expression of first higher order modal field for graded index fiber, we predict the variation of modal intensity with the radial distance from the axis of the fiber, both for pump and signal fields. Taking step and parabolic index fibers of some typical V values as examples, we show that our estimation matches excellently with the exact results. Our formalism involves little computations in the process of evaluation of the concerned parameters. Such simple but accurate analysis will be beneficial for the system engineers.     

非线性包层光纤中TE0模的传播特性分析

本文对具有Kerr非线性包层和线性匀芯的光纤在不同光功率下的传播特性进行了理论分析和数值计算.结果表明,在适当光功率下,当模折射率N等于芯折射率n_f时,芯场变得相当均匀,而包层场迅速衰减.对于自聚焦包层,当从N<n_f逐渐变到N>n_f时,芯场剖面越过N=n_f从凸变凹.在拐点,芯场成为均匀的.论文给出了模场分布和光功率与模折射率的关系.指出纤芯出现匀场预期会在光纤器件、光电子器件、光子器件中得到应用.     

Microbend fiber optic detection of continuously varying refractive index of chlorinated water

In this paper we report a simple microbend fiber optic sensor using a plastic fiber, LED and photodetector assembly for sensing minute variation of refractive index of chlorinated water. Chlorinated water has slightly higher refractive index and gradual release of chlorine from bleaching powder treated water causes a temporal decrease in refractive index of the solution. The evaporation of chlorine from water and the change in refractive index is found to follow a first order exponential decay function of time. Introducing microbends in an optical fiber is easier and less complex than etching of fiber cladding for traditional optical fiber sensors.     

An Efficient Dispersion Calculation Method for Axially Symmetric Optical Fibers

An efficient numerical modal calculation method for an axially symmetric optical fiber is presented using a numerical Galerkin's method. By decomposing the transverse electric field of a guided wave with Bessel functions of the first kind in cylindrical polar coordinates, we have shown that dispersion characteristics of an optical fiber can be obtained very easily. In order to illustrate the effectiveness of this suggested method, numerical examples are given for a step index fiber, a W-shape depressed inner cladding fiber, and a dispersion-flattened fiber.     

An analytical model for studying two-mode fibers: Splice loss prediction

In this paper we present a simple analytical model for the modal fields of an arbitrary graded index core two mode fiber and use it to study loss and mode conversion at a splice. The model is simple enough to obtain the modal field distributions and predict splice loss across jointed two-mode fiber links within a few percent accuracy on a pocket programable calculator.     

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     

Evaluation of dimensionless vector and scalar propagation constants for single-mode graded index fibers by a simple technique

We present simple but accurate analytical expressions for prediction of scalar and vector propagation constants for single-mode graded index fibers. Our formulation is based on the recently developed Chebyshev power series expression for the fundamental mode of graded index fibers. Taking parabolic index fiber as example, we show that our estimations agree excellently with the exact results. The concerned calculations involve very little computations.     

用耦合波理论求解渐变折射率光纤的传播常数和模式场

本文应用耦合波理论来计算任意渐变折射李光纤的传播常数和模场分布.将无限伸展的抛物型折射率分布光纤作为一个理想波导,任意径向不均匀折射率分布光纤便可以视作该理想波导的微扰,其模场可以展开成一组完备的理想波导模的叠加.然后,模场和传播常数可以通过耦合波方程求得.进一步将一阶微分方程组形式的耦合波方程变换成线性方程组,使计算过程大大简化.文中给出了数值计算结果,并将其与准确值进行了比较.     

Deposition of coatings on long-period fiber gratings: tunnel effect analogy

The sensitivity of Long-period fiber gratings (LPFGs), coated with high-refractive-index thin film overlays, to the refractive index and the thickness of the overlay, and to the ambient refractive index, can be enhanced with a design based on a two-overlay coating of an LPFG. The first overlay of lower refractive index than the cladding affects the guidance of a cladding mode in the second overlay of higher refractive index than the cladding. This causes a more abrupt cladding modal redistribution than with the deposition of a unique high-refractive-index overlay. The phenomenon is analyzed with a method based on a vectorial analysis of modes and the application of coupled mode theory.     

A simple but accurate method for prediction of splice loss in single-mode dispersion shifted trapezoidal as well as dispersion flattened graded and step W fibers

We present simple and accurate analytical expressions for transmission coefficient at the splice for both angular offset and transverse offset in case of single-mode dispersion shifted trapezoidal as well as dispersion flattened graded and step W fibers. Here, we employ the recently developed simple series expression for fundamental modal field for such fibers. The evaluation of the concerned parameters based on our formalism requires very little computations. We show that our estimations match excellently with the exact numerical results in case of the said fibers. Further, splices being highly tolerant with respect to longitudinal separation, we restrict our investigations to the cases of transverse and angular mismatches only. The present study should find application in all optical technology involving said kinds of fiber.     

Simple high-order Galerkin finite element scheme for the investigation of both guided and leaky modes in anisotropic planar waveguides

A simple high-order Galerkin finite element scheme is formulated to compute both the guided and leaky modes of anisotropic planar waveguides with a diagonal permittivity tensor. Transparent boundary conditions derived from the Sommerfield radiation conditions are used to model the fields at the computational boundaries that allow the radiation into the high index cladding/substrate and decay into the low index cladding/substrate, hence work for both guided and leaky modes. Richardson's extrapolation is employed to achieve high-order accuracy by only using simple first-order-polynomial basis functions. Schemes up to sixth-order of accuracy in the effective index are demonstrated. The resulted non-linear sparse matrix eigenvalue equation is solved using an iterative procedure. The ability of the scheme to compute leaky and guided modes of various structures with isotropic and anisotropic materials, step and graded index profiles is demonstrated; including its applications to investigate the properties of ARROW structures.     

Analysis of erbium doped holey fiber using fundamental space filling mode

Erbium-doped holey fiber with hexagonal lattice was modeled by using effective index method. In order to calculate the equivalent step index of the periodic structure of the cladding holey optical fiber, all-vectorial fundamental space filling mode approach was utilized. By using EH11 mode, we have numerically solved the rate equations of a three-level pumping scheme for a fiber laser. The obtained results have shown a good agreement with the other experimental results, recently. The results have predicted amplifiers with gain efficiencies as high as 10 dB/mW.     

掺铒孔辅助导光光纤的特性研究与优化设计

掺铒孔辅助导光光纤是由掺铒的高折射率纤芯、低折射率包层和少量的空气孔组成. 采用有限元法分析了掺铒孔辅助导光光纤的模式特性；给出了数值计算截止波长和模场直径的方法；提出了改进的平均粒子数反转度迭代算法来数值计算掺铒光纤放大器的增益和噪声系数. 研究空气孔对掺铒孔辅助导光光纤的截止波长、模场直径和放大器的增益系数的影响. 发现：减小相对孔芯距的值，可使截止波长向短波长移动，减小模场直径的值；当孔的相对大小较大时，截止波长、模场直径和增益的最大值基本上不随孔的相对大小的增大而改变. 最后，综合考虑掺铒光纤基模和二阶模的截止波长、与普通单模光纤的熔接损耗、放大器的增益和噪声系数等因素，优化设计了掺铒孔辅助导光光纤的四个结构参量——纤芯半径、纤芯与包层的折射率差、相对孔芯距和孔的相对大小. 关键词： 孔辅助导光光纤 掺铒光纤 光纤放大器 有限元法     

手征参数对光纤中模式特性的影响

对圆芯和包层都是手征介质的阶跃型手征光纤进行了解析求解，导出了模式特征方程，给出了手征光纤中模式场，光强和光功率分布的表达式。分别研究了纤芯和包层中的手征参数对模式特性的影响．。     

一种新的阶跃折射率光纤本征函数表达形式

为了阐明阶跃折射率光纤的模式特性,根据电磁波辐射的能量守恒定律和经过狄拉克函数奇异性修正的亥姆霍兹方程,通过数学推导和证明得出:柱面径向行波场的本征函数是经过狄拉克函数修正的整数阶汉克尔函数,阶跃折射率光纤模式场的本征函数是零、一阶贝塞尔函数经过狄拉克函数修正的零、一阶诺埃曼函数和虚参量汉克尔函数.该结论揭示了光纤芯层和包层模式场分别是径向驻波场和倏逝波场的本质,并基此推导出新的光纤模式特征方程,模式存在条件,模式数目和符合光纤实际的基模归一化截止频率的理论值.     

Refractometer based on a tapered Mach–Zehnder interferometer with Peanut-Shape structure

A novel refractometer based on tapered Mach–Zehnder modal interferometer (MZI) is proposed and experimentally demonstrated. This sensor is composed of a pair of Peanut-Shape structures and an embedded taper – the former excites high-order cladding modes, while the latter enhances the evanescent field. As the effective refractive index (RI) of cladding is based on the changes of surrounding RI, thus extinction ratio will change due to the alteration of the distribution of power in the fiber which is induced by various differences of core and cladding for RI. As a result, the maximum RI sensitivity of 240.78 extinction ratio/RIU (refractive index unit) is achieved within the range from 1.3334 to 1.4081.     

Uniform Core Field in Symmetrical Planar Waveguides and Circular Fibers with Nonlinear Claddings

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