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.     

Multiple-beam interference fringes applied to investigate the index profile of the optical fiber dip

A numerical-based phase shift method is presented to study optical fibers having a dip in the refractive index profile at the center of the core. Mathematical expressions for the shape of multiple-beam Fizeau fringes crossing a graded-index optical fiber (GRIN) comprising a central graded-index dip or GRIN fiber with a constant refractive index dip, immersed in a silvered liquid wedge, are derived. The index profile parameters of the central dip are determined by comparing the theoretical fringe shape across the fiber cross-section and the experimental fringe shape obtained from micro-interferograms of the wedge interferometer.     

Influence of refractive profile shape on the distribution of modal attenuation in planar structures with absorption cover

The paper illustrates the influence of refractive profile shape in a sensor planar structure on the distribution of modal attenuation. Depending on the shape of refractive profile, the dependence of modes attenuation on their order can be an increasing function, decreasing function or non-monotonic one. The problem is discussed basing on the example of parabolic, exponential, Gaussian and linear profiles of refractive index. For the linear refractive profile, we present the influence of the gradient of waveguide’s refractive index and the influence of the thickness and refractive index of sensitive layer on the distribution of modal attenuation. Theoretical predictions are experimentally verified for two different refractive profiles. Theoretical predictions are excellent agreement with experimental results.     

Investigation of refractive index profile and mode field distribution of optical fibers using digital holographic phase shifting interferometric method

In this paper a digital holographic phase shifting interferometric method is used to characterize the graded index (GR-IN) optical fibers. Off-axis digital holographic Mach–Zehnder like arrangement in aid of phase shifting tool is applied. Numerical reconstruction of phase shifted holograms is applied to calculate the optical phase difference distribution in the image plane, and then the optical phase differences across GR-IN fibers are extracted considering image enhancement and noise reduction steps. Also, a simple algorithm is presented to modify the position of the extracted optical phase differences across the fibers to be perpendicular to x-axis, so that it becomes easy to calculate the mean optical phase differences along the fiber. The mean optical phase differences in combination with multilayer model are applied to calculate the refractive index profiles across GR-IN optical fibers. An analytical model is presented to predict the mode distribution associated with the effective indices and the propagation coefficient of the parabolic refractive index profile GR-IN fiber.     

Automatic fringe analysis of the induced anisotropy of bent optical fibres

A new theoretical model considering the refraction of the incident light beam by the fibre is suggested to determine the refractive index profile of bent optical fibres. This new model (slabs model) considering the cross section of the bent optical fibre consists of large number of slabs. The slabs model bases on the refraction of the incident beam by the fibre. The refractive index profile of the optical fibre cladding before bending obtained using the automated Fizeau interferometer with the aid of suggested model is compared with other models such as, the homogenous model and the multilayer model to verify the ability of this slab model. The refractive index profile of the bent optical fibre cladding is investigated using this suggested model. In addition, the new model is used to obtain the induced birefringence and the guiding parameters. The bending radius is recommended to be greater than 7.1 mm for the used optical fibre. The consideration of the refraction increases the accuracy of the results.     

套管辅助法测量异型预制棒折射率分布

基于光束扫描法的光纤预制棒折射率测试仪主要适用于直径和长度在一定范围内的圆柱形样品折射率分布的测试。提出一种套管辅助法可实现更短长度、更细直径和变直径样品的折射率测试。该方法将待测样品居中放置于一个尺寸符合测试要求的圆柱形套管内,并在套管内注入折射率匹配油,使其没过待测样品后按常规步骤进行测试。对比实验结果表明,套管辅助法与直接测量法的偏差与仪器的测量误差相当。采用套管法,获得了预制棒拉丝终止后变径区不同位置折射率的径向分布,可为拉丝过程的研究提供参考。     

聚焦法测量塑料光纤折射率分布的可行性研究

结合理论分析和实验验证,探讨了聚焦法测量塑料光纤纤芯的折射率分布的可行性。结果表明,对GI-POF而言,聚焦法是一种简单可行的技术.但是对SI-POF,由于入射光线在光纤边界处发生交叉,聚焦法不能精确测量其折射率分布.     

Determination of the optical and geometrical properties of fibres having skin–core structure

A method is suggested to determine both the refractive index and the transverse sectional shape and area of fibres, having skin–core structure, at the same time for the same region of the fibre. The method depends on using a fibre rotator device attached with Pluta polarizing interference microscope, to record the variation of the fibre thickness at each angle of rotation. Nylon 6 fibres having skin–core structure were used in this study. Beck-line method was used to determine the refractive index of the skin for light vibrating parallel and perpendicular to the fibre axis. To confirm the results of the suggested method, the optical microscope was used to determine the transverse sectional shapes of bundles of nylon 6 fibres. The mean refractive indices of the skin and core of nylon 6 fibres were determined. Microinterferograms are given for illustration.     

Analytical relation between effective mode field area and waveguide dispersion in microstructure fibers

For optical fibers exhibiting a radially symmetric refractive index profile, there exists an analytical relation that connects waveguide dispersion and the Petermann-II mode field radius. We extend the usefulness of this relation to the nonradially symmetric case of microstructure fibers in the anomalous dispersion regime, yielding a simple relation between dispersion and effective mode field area. Assuming a Gaussian mode distribution, we derive a fundamental upper limit for the effective mode field area that is required to obtain a certain amount of anomalous waveguide dispersion. This relation is demonstrated to show excellent agreement for fiber designs suited for supercontinuum generation and soliton lasers in the near infrared.     

Wave localization in two dimensional parabolic periodic refractive index profiles: a 4th order Runge–Kutta study

In this work, we have studied the wave localization in a two dimensional parabolic periodic refractive index profile. Our calculations have been performed by developing a 4th order Runge–Kutta method. Effects of different parameters in refractive index profile and incident wave shape on the wave intensity and shape in the future are shown. Effects of the mentioned parameters on localization degree and total momentum of the system are also investigated. We find different parameters change intervals within which the excitation disperses. Thus no bound state is possible. Finally, we show when a bound state is present.     

Transmission characteristics of graded-index fibers

The use of graded-index fibers for optical communication systems is now under consideration for numerous civil and military applications, and in these either LED or laser sources can be developed. The bandwidth of the system depends on the source linewidth, the dispersion of refractive index in the fiber, the strength of excitation of the modes by the source, and the extent of mode mixing caused, by example, by microbending. In fibers with refractive-index profiles that have a nearly parabolic dependence upon radius, pulse broadening is a slight, but small departures from an optimum profile can cause a dramatic decrease in bandwidth. It is of considerable importance to predict the bandwidth of fibers from a knowledge of the refractive-index profile and source geometry. The purpose of the first part of this paper is to compare two computational methods by which the propagation characteristics of a fiber, hence the impulse response and system bandwidth, may be determined. In the second part, we shall describe a computer program that determines the excitation of modes in an arbitrarily graded refractive index fiber for a model of laser source.     

Refraction of an astigmatic laser beam in a transition layer of a stratified liquid

Refraction of an astigmatic laser beam in a transition layer formed at the boundary between two liquids with different optical characteristics is studied theoretically and experimentally. An algorithm of calculating a ray trajectory in the transition layer of a stratified liquid is considered. The profile of the refractive index in the medium is modeled for three different distributions: linear, sinusoidal, and tangential. Computer modeling based on the above models allowed obtaining two- and three-dimensional images of the laser beam (refractograms) inside and outside of the medium. The influence of the beam parameters and the experimental layout on the shape of refractograms is studied, and optimal experimental conditions are determined. The experimental arrangement for detection of 2D and 3D refractograms by the laser refractography method is described. An experimental technique is developed, and digital registration of the experimental refractograms is carried out. Adaptation of special software for processing 2D refractograms allowed retrieving the refractive index profile in the transition layer of a liquid. Based on the tangential model of the diffusion layer in a saltstratified liquid, the values of the refractive index were obtained that allowed determining the salinity profile in the given layer.     

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.     

Mode analysis of realistic optical waveguide structures and microstructured holey fibers by modal field evolution

In this article, we describe a useful technique for calculating modes of practical optical waveguides having two-dimensional arbitrary transverse refractive index profile. The method uses a finite difference platform for evaluating Helmholtz's equation in scalar and semivectorial forms through a field evolution algorithm. The method is straightforward, easy to handle and does not involve any complex analysis or matrix formulation. We tested the accuracy of our analysis approach by applying it on a large number of realistic waveguide problems having known results or results available in the literature. The formulation has facilitated us to study the modal properties, viz., field distribution, birefringence, dispersion and mode effective area, of a variety of practical two-dimensional structures namely, planar structure, coupler, semiconductor optical waveguides, optical fibers and arbitrary profile microstructured fibers which are uniquely important in photonics and guided-wave devices. The algorithm will therefore be very useful in designing and studying any arbitrary-structure waveguides, and to explore new geometry and properties.     

Automatic refractive index profiling of fibers by phase analysis method using Fourier transform

Automatic fringe pattern analysis is a powerful and inexpensive digital image-processing technique. It is used to analyze the fringe pattern obtained by different optical techniques, such as multiple-beam Fizeau fringes. To perform accurate and fast automatic measurement of fiber refractive index profile, phase analysis method has been used with the Fourier transform technique. In this paper, the refractive index profiles of polyethylene fibers with different draw ratios are presented by two methods, fringe shift method and phase analysis method. A comparison between the results obtained is presented.     

Brillouin gain analysis for fibers with different refractive indices

We studied an anomalous result in the measured stimulated Brillouin scattering threshold for single-mode optical fibers with different refractive index profiles and effective areas. It was found that, in addition to the optical effective area, the refractive-index-dependent interaction between the optical and the acoustic fields must be considered in order to account for the differences in the stimulated Brillouin scattering threshold between fiber types. A detailed analytical formalism describing the acousto-optic interaction was derived to accommodate the influence of the index profile design on Brillouin scattering.     

Determination of propagation constants in a Ti:LiNbO3 optical waveguide by using finite element and variational methods

The finite element and variational methods are used to determine the propagation constants in a titanium indiffused lithium niobate waveguide with the reconstructed refractive index profile (in depth) from the near field measurements. A subsequent second diffusion of magnesium affects the shape of the calculated electric field and we have defined an effective depth of the profile.     

Kinetics of the refractive index change in the core of active fibers, doped with Yb3+ and Er3+ ions, under pulsed optical pumping

The kinetics of refractive index change (RIC) in the core of Yb³⁺/Er³⁺ fibers at a radiation wave-length lying beyond the range of resonant absorption of active ions under pulsed pumping of fiber laser has been analyzed. The measurement of RIC kinetics with a Mach-Zehnder interferometer makes it possible to separate the contributions of the electronic and thermal RIC mechanisms and determine quantitatively the temperature profile inhomogeneity in the fiber. The measured values are compared with the numerical estimates derived from the spectral properties of the active medium in order to check the modern models of RIC in active fibers.     

Recovery of Graded Index Profile of Planar Waveguide by Cubic Spline Function

A method is proposed to recover the refractive index profile of graded waveguide from the effective indices by a cubic spline interpolation function. Numerical analysis of several typical index distributions show that the refractive index profile can be reconstructed closely to its exact profile by the presented interpolation model.     

Modulation of absorption and refractive index in Er3 -doped fibers

Modulation of the absorption and refractive index in Er³⁺-doped fibers for a signal wavelength in the 1550-nm band and a pump wavelength of 980 nm is investigated. The experimental results are compared with a model that takes into account optical transitions between the ground state and the metastable state in Er³⁺. Good agreement between the experiment and the model is obtained apart from a wavelength-independent constant in the refractive index modulation, which is discussed.