3D refractive index profile for the characterization of necking phenomenon along stretched polypropylene fibres

The phenomenon of neck formation in polymers has attracted considerable attention. During the cold-drawing process an initial undrawn material is transformed into anisotropic one across a narrow transition region called ‘neck’. The Video Opto-Mechanical (VOM) device attached with multiple-beam Fizeau fringes techniques are used to stretch polypropylene (PP) fibres. A iPP sample is stretched to have a neck at room temperature. The optical properties of the deformed material over the necking region are examined. Another PP sample is stretched (without necking deformation) at room temperature and the optical properties are also examined. The task of this study is to characterize and assess the necking phenomenon along cold-drawn polypropylene (iPP) fibre axis. The effect of necking on the optical properties of the fibre is confirmed by the determination of the 3D refractive index profile at different regions along the deformed PP fibre. Also the orientation function is calculated for the necked sample. The contour lines of microinterferograms are given for illustrations.     

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.     

Detection of necking deformation along polypropylene fibres axis at low draw ratios using multiple-beam microinterferometry

A modified drawing device attached with an automated system for producing multiple-beam Fizeau fringes in transmission is used to study the mechanical deformation along polypropylene (PP) fibres at low draw ratios. Two drawing processes are used for drawing PP fibres. In the first process (fast drawing), the necking deformations are formed at draw ratios from 1.2 to 1.9 along the fibre axis. While in the other process (slow/step drawing), these deformations disappeared. The refractive indices calculated at different positions along the fibre axis during the fast- and slow-drawing processes. To overcome the formation of necking deformation along the PP fibres during fast-drawing process, the slow-drawing technique is recommended. Microinterferograms are given for illustration.     

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.     

An interferometric method for determining the mean refractive indices of highly birefringent fibres

An interferometric method with its mathematical derivation is suggested to determine the mean refractive indices and birefringence of highly birefringent fibres using multiple-beam Fizeau fringes in transmission. The application of this method depends on measuring the cross-sectional area of the fibre and the area enclosed under the fringe shift. It is very difficult to measure the area enclosed under the fringe shift in case of highly birefringent fibres, as these fibres have a relatively large optical path difference and a bad connection with the surrounding medium fringe. This difficulty is solved using the suggested method. Poly(aryel ether ether ketone) (PEEK) and poly(ethylene 2,6-naphthalene-dicarboxylate) (PEN) were used as applied examples of highly birefringent fibres for the suggested method. The refractive indices and birefringence of polypropylene fibre with draw ratio 4 are determined using the suggested and conventional methods. The results of the two methods are compared and it is found to be in agreement with the previously published data. The diffraction of He–Ne laser beam was used to determine the mean value of cross-sectional areas of fibres. Microinterferograms and tables are given for illustrations.     

On line interferometric investigation of the neck propagation phenomena of stretched polypropylene fibre

On line interferometric investigation of the neck propagation phenomenon of stretched fibre is carried out using an automatic multiple-beam Fizeau fringes technique. It was observed that under such a deformation condition, a neck deformation is formed and propagated steadily towards the gripped ends of the stretched sample. The neck propagation was recorded carefully during the course of the tests by means of a CCD camera. The fringe shift profile due to the neck formation was analyzed during the propagation stage. A polypropylene (PP) sample was stretched until a neck deformation is formed at room temperature. The 3D time-refractive index profile is investigated to clarify the fixed profile of propagation. The obtained microinterferograms are clarifying the fixed neck profile during the propagation of necking phenomena. The speed of neck propagation was calculated. The dependence of the propagation on the drawing speed and draw ratio was investigated.     

Detecting and avoiding the necking deformation along polypropylene fibre axis using the fringe pattern analysis of multiple-beam microinterferometry

A fibre-drawing device attached with the system for producing multiple-beam Fizeau fringes in transmission is used to optimize the optical properties during the cold drawing of polypropylene (PP) fibres. This system is automated for interference pattern analysis. Two drawing processes for the PP fibres are applied and investigated. The first one is fast drawing in which the necking deformation is predicted and the other is the slow (step) drawing in which the necking can be avoided. The refractive index profiles (n and n) of PP fibres are determined at different positions along the fibre axis during the fast and slow drawing processes. The fibre interference patterns are automatically digitized and stored in a computer storage media. The slow drawing technique for PP fibres is recommended to overcome the deformation difficulties along the fibre axis due to necking during the drawing processes. Microinterferograms in case of light vibrating parallel and perpendicular to the fibre axis are given for illustration.     

Chromatic and opto-mechanical dispersion of some characteristic parameters of optical fiber undergoing macrobending

Bending of optical fiber leads to an induced-anisotropy in the index profile that influences many important guiding fiber parameters. An analytical method is described for the measurement of refractive-index-wavelength dispersion in bent optical fibers. Multiple-beam Fizeau fringes technique at transmission is used to analyze the opto-mechanical properties and induced-index anisotropy in a standard single-mode fiber undergoes pure mechanical macrobending. The shift in Fizeau fringes is employed to evaluate the dispersion of the cladding material of the bent fiber. The radial variations in Cauchy’s coefficients and the associated variations of some fiber parameters due to macrobending are carried out. The radial profiles of some material parameters such as oscillation energy, dispersion energy, lattice energy and material dispersion are measured as well. The presented method is capable to achieve quantitative and qualitative measurements, which is not available with other methods. The method has a good index resolution in the order of 10⁻⁴ and spatial resolution of 1.3 μm.     

Automatic determination of refractive index profile, sectional area, and shape of fibers having regular and/or irregular transverse sections

A new method based on a mathematical model and a computer program is suggested to determine the refractive index profile of fibers having regular and/or irregular transverse sectional shape. Microinterferogram of both multiple-beam Fizeau fringes and the duplicated image from two-beam interference microscope are used for the determination of refractive index profile, cross-sectional area and shape of three different types of fibers. To confirm the suggested model, the calculated area and the shape of the transverse section of these fibers are compared with those results obtained using conventional methods.     

Theoretical model for the transverse interference pattern of GRIN optical fiber using a laser sheet of light

A new technique (El-Ghandoor et al., Opt. Laser Technol. 31(7) (1999) 481–488) has been applied to study the shape of transverse interference fringes, instead of multiple beam Fizeau fringes (Marhic, Stein, Appl. Phys. Lett. 35 (1975) 1678–1682), from a GRIN optical fiber. In this technique, a laser light sheet is used to illuminate and pass directly through the optical fiber. Theoretical expressions are derived for the optical path differences of three groups of interference beams. The first one passes through the cladding, the core, and then the cladding once again; the second passes through the cladding only, and the third passes through the surrounding air. Theoretical expressions for the shape of transverse interference fringes formed across isotropic non-absorbing optical fibers are also calculated.     

A subfringe integration method for multiple-beam Fizeau fringe analysis

Some aspects concerning the subfringe integration method in interferogram analysis have been investigated and modified. The modified algorithm, introduced in this paper, is capable of reconstructing the phase in the presence of noise or errors in carrier frequency. The subfringe integration method was applied to analyze two computer simulated patterns of equispaced Fizeau fringes using N bucket integration. Also, it is used to analyze the multiple-beam Fizeau fringe. The refractive index profile of polyethylene fiber is obtained by using two methods, subfringe integration method, and Fourier transform method. A comparison between the obtained results using the maintained methods is presented.     

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.     

Multi-mode opto-thermo-mechanical stretching system for determination of 3D refractive index along the axis of stretched and/or heated fibres

A multi-mode opto-thermo-mechanical stretching system was modified to study the changes in the 3D of optical and structural properties of stretched fibre along its axis. The structural deformation of isotactic Polypropylene, (iPP), fibres was studied at different draw ratios. The modified system coupled with Pluta polarising interference microscope was used to determine the variation of the birefringence in three dimensions during stretching process. Using this modified system, the multi-necking was detected. Subfringe analysis technique was used to determine the phase distribution of the obtained microinterferograms, which were given for illustration.     

光纤拉曼放大器中增益的偏振相关特性研究

提出了一种改进的、可用于计算偏振相关拉曼增益的光纤拉曼放大器的非线性耦合波方程。建立了单模双折射光纤拉曼增益的数学模型,分析了线偏振抽运光以与光纤快轴成45°激励的单模双折射光纤拉曼放大器模型与实际具有随机双折射的光纤拉曼放大器的拉曼增益偏振相关特性的等价性。基于上述模型,提出了一个可定量表征单模光纤偏振模色散统计特性的拉曼增益偏振相关因子,用以替代常规的光纤拉曼放大器非线性耦合波方程中的偏振相关因子。计算结果与已报道文献的实验数据非常吻合。同时对抽运增益在同向和反向抽运方式下截然不同的增益偏振相关特性给出了合理的解释。     

Highly accurate film thickness measurement based on automatic fringe analysis

This paper describes an automated multiple-beam interferometry for measuring a calibrated step height of (27.00 ± 3.00) nm nominally. The fringes captured from the multiple-beam Fizeau–Tolansky interferometer were thinned by using a written program to obtain accurate measurement. We claim that multiple-beam interferometry based on automatic fringe thinning process can provide a real time solution for calibrating step heights precisely and with high accuracy. The uncertainty budget of the multiple-beam interferometry method due to incomplete parallelism of the incident beam and the inhomogeneity of the reflecting layers was calculated automatically with a written ray tracing program. The uncertainty budget in multiple-beam interferometry was estimated to be of the order of 3.00 nm.     

Mehrstrahlinterferenzen in konvergentem Licht

Formulae describing sharpness and luminosity of multiple-beam interference fringes produced by convergent rays are deduced and tested experimentally by means of measurements on interference filters. Further, the application of these formulae upon two problems of practical importance is discussed; i.e. upon the permissible deviation from collimation when Fizeau fringes are being used (Tolansky), and also upon the diameter of the output diaphragm behind a Fabry-Pérot-interferometer adapted for direct recording.     

Fabrication and study of microstructured optical fibers with elliptical holes

We report the fabrication of what are believed to be the first microstructured optical fibers with uniformly oriented elliptical holes. A high degree of hole ellipticity is achieved with a simple technique that relies on hole deformation during fiber draw. Both form and stress-optic birefringence are characterized over a broad wavelength range. These measurements are in excellent agreement with numerical modeling and demonstrate a birefringence as high as 1.0 x 10(-4) at a wavelength of 850 nm.     

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.     

矩形点阵微结构聚合物光纤偏振特性研究

采用全矢量平面波方法,以聚合物为基材,研究了矩形点阵微结构聚合物光纤的传输模场和偏振性质.结果发现,矩形点阵微结构聚合物光纤基模两个正交偏振态不再简并,模场呈现类矩形且具有较强的线偏振特性;该光纤模式双折射产生于包层孔结构分布的不对称性,减小包层纵向孔间隔和横向孔间隔之比η值,双折射明显增强,适当调节η,可在更宽频带范围内实现高双折射单模运行.     

The PMD of sinusoidally spun fibers in the presence of random birefringence perturbations

Although fiber spinning is known to reduce polarization mode dispersion (PMD) effects in optical fibers, relatively few studies have been performed of the dependence of the reduction factor on the strength of random birefringence fluctuations. In this paper, we apply a general mathematical model of random fiber birefringence to sinusoidally spun fibers. We find that while even in the presence of random birefringence perturbations the maximum reduction of PMD is still obtained when the phase matching condition is satisfied, the degree of PMD reduction and the probability distribution function of the DGD both vary with the random birefringence profiles.