Determination of GR-IN optical fibre parameters from transverse interferograms considering the refraction of the incident ray by the fibre

The core–cladding refractive index difference Δn and the index gradient profile parameter of the graded index (GR-IN) optical fibre has been determined. The curve representing the real path, in the core region, due to refraction of the beam and the change in the exit wavefront are considered. Multiple-beam Fizeau fringes and two-beam interference Pluta polarizing microscope, are used for this investigation. A new method, based on a derived mathematical expression, is used with a prepared computer program to estimate the fringe shift inside GR-IN of the fibre core. The estimated and experimental values of the fringe shift, along the core radius, are used to obtain the refractive index profile of the optical fibre. A comparison between the new method and a previous model considering the refraction has been shown. Microinterferograms are given for illustrations.     

双包层稀土掺杂光纤抽运吸收特性的分析

建立了复折射率纤芯结合有限差分束传播法的双包 层稀土掺杂光纤抽运吸收效率数值模型,利用该模型对几种常 用内包层外边界结构下双包层稀土掺杂光纤的抽运吸收系数进 行了详细的分析,得出相应双包层光纤的抽运吸收特性. 分析结果对双包层稀土掺杂光纤的优化设计具有重要的指导意义.     

Automatic determination of refractive index profile of fibers having regular and/or irregular transverse sections considering the refraction of light rays by the fiber

A new model, using non-destructive two- and/or multiple-beam interferometric techniques, is suggested for measuring the refractive index profile of fibers having regular and/or irregular cross-sectional shape taking into consideration the refraction of the light rays by the fiber. The proposed model is applied for three different fibers having different cross-sectional shapes and different refractive index profiles. These fibers are PPT, homogeneous fiber, with circular cross-section, graded index optical fiber of circular cross-sectional shape and Dralon fiber of irregular cross-section. To validate the proposed model it is used, firstly, to calculate the index profile for a standard PPT fiber. Secondly, the calculated results for the irregular Dralon fiber and GR-IN optical fiber are compared with that calculated using other conventional method. From this comparison, we recommend that the refraction must be taken into account to obtain accurate results especially for birefringent fibers and graded index optical fibers.     

光学马格努斯效应中的横向角移分析

从平面角谱理论出发,建立了光束在空气和玻璃界面折射的传输模型.基于这一模型,揭示了光学马格努斯效应中的横向角移现象.对于特定的线偏振和椭圆偏振光束,其折射场重心出现了横向角移,而当入射光束为圆偏振时,横向角移则会消失.在正负折射率界面,光束的横向角移产生了反转现象,这是由于光束在左手材料中发生了负衍射.超高折射率可明显地减少横向角移,而超低折射率则可显著地增强横向角移.这些发现将为如何调控和增强光学马格努斯效应提供理论依据. 关键词： 光学马格努斯效应 横向角移 圆偏振     

Influence of temperature on the optical and structural properties along the diameter of optical fibres

Multiple-beam Fizeau fringes technique with an opto-thermal device is used to study the effect of temperature on the optical properties of Philips graded-index optical fibres. The refractive index profile of the optical fibre is measured at different temperatures. From these profiles the opto-thermal coefficient, the profile shape parameter α, the cladding/core maximum refractive index difference Δn and some guidance parameters of the optical fibre that play an important role in communication are determined. The variation of oscillation and dispersion energies along the diameter of the optical fibre (energy profile) are calculated at different temperatures. An empirical formula of the energy profile is obtained. Microinterferograms are given for illustrations.     

Numerical ray tracing through a modified cladding fiber optic segment sensors

By using 3-D geometric optics, the effect of a modified cladding on the transmission of light through optical fiber is investigated. Analysis of the light transmission of the optical fiber as function of the modified cladding refraction index and length are presented for various input illumination focused and compared with 3-D ray theory. Applications to chemical sensors are also discussed.The intensity of light signal transmitted through an optical fiber, which its cladding over a finite length is removed, is used as a sensor of refractive of liquids, in which the fiber is immersed. The transmitted light intensity is measured as a function of liquid refractive index for different lengths of the unclad section of the fiber and at each unclad length its sensitivity to change in refractive index of liquid is presented.     

Refractive index profiling of a GRIN optical fiber using a modulated speckled sheet of light

A method for calculating the refractive index of GRIN optical fiber from its transverse interference pattern is presented.In this method the transverse interference fringe pattern through an optical fiber using a sheet of light is applied to get the refractive index profile of it. The optical fiber is not immersed in a matching liquid as used in different techniques [Barakat N, El-Hennawi HA, El-Zaiat SY, Hassan R. Pure Appl Opt 1996;5:27].In this method a sheet of He–Ne laser light is allowed to illuminate the fiber. The light sheet is divided into two parts, the first is refracted through the fiber while the second is used as a reference beam. Interference pattern will be obtained between these two rays displaying the refractive index variation along the fiber radius.The fringe shift of such interference pattern has been measured and used to calculate the deflection angle of light refracted by the fiber and the cladding. An equation is derived to calculate the refractive index profile difference ratio δn at different positions across the fiber cross section in terms of the corresponding deflection angle and is verified experimentally.The optical path difference between these two rays (refracted and reference beam divided by the fiber) has been derived and the fringe shift obtained has been used to calculate the refractive index profile of the fiber.Introducing a ground glass screen on the passage of the two light beams (refracted and reference beam divided by the fiber), two superimposed identical speckle patterns are formed leading to the formation of a third speckle pattern modulated by a grid structure displaying the optical thickness of the fiber.     

Determination of the refractive index of fibres using the modified area method: I. Homogeneous fibres

The mathematical formulae for determining the mean refractive indices and birefringence of homogeneous fibres are modified. This modification depends on calculating the area under the fringe shift and cross-sectional area of homogeneous fibres having nearly circular cross-sectional area taking the refraction of the incident light beam by the fibre into consideration. The mathematical analysis for two-beam and multiple-beam interferometric techniques is dealt with. These formulae are applied to polypropylene fibres with draw ratios of 3.5 and 4 using the two techniques. A comparison between the results when using the new formulae and when neglecting the refraction has been studied. The diffraction of a He–Ne laser beam is used for determining the shape of the cross-sectional area of these fibres. Microinterferograms are given for illustration.     

超细低水峰抗弯损光纤的设计及制作

采用全合成预制棒制造法（VAD＋OVD）和改进的G.652.D光纤拉制法制造光纤.研究了工艺中光纤芯径的大小、第一包层的厚度、芯包折射率差、芯包比等参量与光纤弯曲性能的关系,并据此制作了几种超细低水峰抗弯损光纤.该光纤的裸光纤直径约80 μm,涂覆后成品光纤直径约140 μm,当弯曲半径不小于7.5 mm时,能够在1 260～1 625 nm整个波段内满足DWMD的传输要求.     

Design of temperature-compensated elliptical core birefringent fibres

A new type of temperature compensated birefringent optical fibre is reported. The proposed fibre is designed aiming to minimising the stress birefringence by matching the thermal expansion coefficients between the core and the cladding and maximising the geometric birefringence by increasing the refractive index difference between the core and the cladding and increasing the core ellipticity. The optimum dopant concentrations satisfying the requirements is determined by solving a set of nonlinear algebraic equations. The fibre aimed at satisfying the requirements is fabricated and characterised. The experimental results show that the temperature dependence of the fibre birefringence is 6.97 × 10⁻⁴/°C. Methods of further improvement of the compensation are discussed and an alternative dopant material, titanium, for the improvement is suggested.     

Investigation of various transmission properties and launching techniques of plastic optical fibres suitable for transmission of high optical powers

The significant parameters for plastic fibres with various core/cladding combinations are given: refractive index, numerical aperture, critical angle of total internal reflection at the core/cladding interface and maximum angle of aperture. The output power of a plastic fibre (PS/PMMA) was measured as a function of the angle of incidence. The results are interpreted using the ray optical fibre transmission model. Various launch-loss-reducing optical end-face working procedures are compared. We also investigated a method to avoid Fresnel reflection losses by a Brewster angled fibre input end-face for a linearly polarized light beam. The transverse and longitudinal intensity distribution of the output beam of a PS/PMMA fibre was measured. We conclude that a single large core clad plastic fibre is a promising alternative to a multi-glass fibre bundle for some applications.     

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     

Measuring method for the refractive index profile of optical glass fibres

A new method for measuring the refractive index profile of optical glass fibres is described. This simply monitors the reflection of a focused laser beam from a polished fibre end face. Detailed tests on the accuracy and resolution of the method are described and the index profiles of several fibres are given as an example of its feasibility.     

Design and analysis of a kind of large flattened mode optical fibre

In this paper, a refractive index profile design enabling us to obtain a flat modal field around the fibre centre is investigated. The theoretical approach for designing such multilayer large flattened mode (LFM) optical fibres is presented. A comparison is made between the properties of a three-layer LFM structure and a standard step-index profile with the same core size. The obtained results indicate that the effective area of the LFM fibre is about twice as large as that of the standard step-index fibre, but the LFM fibre has less effective ability to filter out the higher order modes than the standard step-index fibre with the same bending radius.     

一种适用于任意折射率分布的等效折射率方法

提出了一种新的等效折射率方法,可以将光波导的两维折射率分布精确等效成一维折射率分布。从波动方程出发,通过严格的数学推导,得到了一维等效折射率分布的表达式。该等效折射率分布由二维光波导的模场分布和折射率分布决定。在此等效过程中,几乎无任何近似,因此具有比传统等效折射率方法(EIM)更高的精度,而且不受波导截止条件的限制,并适用于任意的折射率分布结构。以SOI(silicon-on-insulator)脊型光波导为例,给出新方法的一个具体等效实施过程,比较了新方法与传统等效折射率方法计算得到的等效模场分布及等效折射率,结果显示本文方法的有更高的计算精度。最后,文中给出了一个利用这种等效方法计算弯曲波导损耗的例子。新方法可以使对三维结构(截面为任意折射率分布)的模拟简化成二维模拟。     

Refractive index design and validation for evanescent field power maximization in optical fibre sensors

The viability and operation of evanescent field-based optical fibre sensors is largely determined by the fraction of the total supported modal field power in the evanescent field. As this fraction is highly dependent on the refractive index profile of the fibre, one design strategy for fibre sensors is to maximize this field power fraction over the class of all refractive index profiles. This paper documents this design strategy for circular geometry optical fibres, where the goal is to maximize the evanescent field power fraction for a particular mode via the selection of an optimal refractive index profile. The axially symmetric profiles obtained approximate “holey” annular structures, the performance of which can be validated using existing waveguide analysis techniques.     

Bending loss analyses of photonic crystal fibers based on the finite-difference time-domain method

This is a report on an effective simulation method for the bending loss analyses of photonic crystal fibers. This method is based on the two-dimensional finite-difference time-domain algorithm and a conformal transformation of the refractive index profile. We observed the temporal dynamics of light waves in a bent fiber in a simulation and obtained the bending loss as a function of bend radius and optical wavelength for the commercial photonic crystal fibers. The accuracy of this method was verified by good agreement between the simulation and experimental data.     

Nonparaxial propagation of Hermite-Laguerre-Gaussian beams in uniaxial crystal orthogonal to the optical axis

Analytical expressions for the three components of the nonparaxial propagation of a Hermite-Laguerre-Gaussian （HLG） beam in uniaxial crystal orthogonal to the optical axis are derived. The intensity distribution of an HLG beam and its three components propagating in a uniaxial crystal orthogonal to the optical axis are demonstrated by numerical examples. Although the y and z components of an HLG beam in the incident plane are both equal to zero, they emerge upon propagation inside the uniaxial crystal. Moreover, the beam profile of the x component is relatively stable and the beam profiles of the y and z components have the same evolution law. If the ratio of the extraordinary refractive index to the ordinary refractive index is larger than unity, the beam profile of the HLG beam is elongated in the x direction and generally rotates clockwise. Otherwise, the beam profile of the HLG beam is elongated in the y direction and generally rotates anticlockwise. This research is beneficial to the optical trapping and nonlinear optics involved in the rotation of a beam profile.     

Morse势阱中线性和三阶非线性光折射率的改变

利用量子力学中的密度矩阵算符理论和迭代方法,导出莫尔斯（Morse）势阱中线性和三阶非线性光折射率改变的解析表达式,并以典型的GaAs／AlGaAs Morse势阱为例进行数值计算。数值结果表明,随着入射光强度增强,总的折射率改变将减少;随着势阱参数a的增大,总的折射率改变将减小;而随着载流子浓度的增加,总的折射率改变将增加。结果表明要获得较大的折射率改变,则需选取较小的入射光强度,较小的参数a,较大的载流子浓度,从而为实验研究提供理论依据。     

An Optical Differentiator Based on a Three-Layer Structure with a W-Shaped Refractive Index Profile

An optical differentiator based on a three-layer resonant structure with a W-shaped refractive index profile is proposed. The differentiation operation is performed in reflection and is associated with the resonant excitation of an eigenmode of the structure localized in the central layer. The presented results of numerical simulations demonstrate the possibility of spatial differentiation of the transverse profile of an incident optical beam, temporal differentiation of the envelope of an incident optical beam, and simultaneous spatial and temporal differentiation with a high quality. The proposed structure can find applications in designing analog optical computing and optical information processing systems.