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.     

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.     

Determining the opto-mechanical and geometrical properties of high-density polyethylene fibres

A method is described to determine the opto-mechanical and geometrical properties of high-density polyethylene, HDPE, fibres at the same time for the same region from the fibre. Variations of the transverse sectional shapes, areas, optical and mechanical properties of fibres during the cold drawing process were investigated. A rotator-mechanical drawing device was used for rotating the fibre around its longitudinal axis during the cold drawing process. The Pluta polarizing two-beam interference microscope was attached with the rotator-mechanical drawing device for detecting these variations under the interferometer. The rotator-mechanical drawing device permits determining the tensile stress–strain curve, Poisson's ratio and strain optical coefficient for HDPE fibres. Also, it permits determining the refractive index profile of the drawn fibres taking into considering the transverse sectional area and the enclosed area under the fringe shift. The optical orientation factor and orientation angle was calculated for HDPE fibre to clarify the orientation of molecules during the cold drawing process. Microinterferograms are utilized for illustrations.     

Automatic fringe analysis of two-beam interference patterns for measurement of refractive index and birefringence profiles of fibres

Automatic fringe pattern analysis is a powerful and inexpensive digital image-processing technique. Two-beam polarizing interference Pluta microscope [Pluta M. Opt Acta 1971;18:661, Pluta M. J Microsc 1972;96:309] is automated by the computer-aid via CCD camera and digital frame grabber. Software program is prepared to deal with the duplicated (separated and overlapped) Microinterferograms produced by two-beam polarizing microscope. It also gives an accurate and fast automatic measurement of refractive index and birefringence profiles for fibres. In this paper, the refractive index and birefringence profiles of two different types of fibres, basalt and polypropylene (PP) fibres are presented. A new method to determine the birefringence profile of fibres from non-duplicated microinterferogram is suggested. The cold drawing process for PP fibres is studied.     

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.     

Interferometric determination of the refractive indices and birefringence of some highly oriented fibres

Variable wavelength interferometric technique (VAWI) is a direct method for determining the refractive indices and birefringence of highly oriented fibres. This method uses the polarizing interference Pluta microscope with a monochromatic light from wedge interference filter that provides a continuously variable wavelength. The standard calibration process of the Pluta polarizing interference microscope is carried out and a calibration graph is obtained. The refractive indices and birefringence of PEN, CONEX and TECHNORA were measured over the visible range of the spectrum and the constants for the Cauchy's dispersion formula were determined. The oscillation and dispersion energies were calculated from the measurements of the refractive index.     

Circularly birefringent optical fibres: new proposals

This paper deals with a family of azimuthally inhomogeneous fibres whose guided modes have been shown, in a previous paper, to have analytical expressions. It elaborates on the per-unit-length torque-induced circular birefringence as a function of the geometrical parameters and of the refractive indices. Recipes are given for enhancing the birefringence above that of an azimuthally homogeneous fibre. The coupling loss, which is unavoidable when such a fibre is fed by a circularly symmetrical fibre or beam, is shown not to be a major concern.     

Enhancement of fringe visibility in a fibre interferometer

A simple method for increasing fringe visibility of an interference pattern in a Mach-Zehnder type fibre interferometer is presented. In order to obtain high visibility, two elliptically polarized waves emitted from fibres with birefringence are transformed into two linearly polarized waves of equal amplitude and with parallel planes of polarization by using ordinary optical components. Instability of fringe patterns due to temperature fluctuation of the air surrounding the fibres is also discussed.     

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.     

Step index fibre using laser interferometer

A model is suggested to describe the fringe shift which occurs due to the phase variations of cladded glass fibre introduced between the two plates of the liquid wedge interferometer illuminated with a He–Ne laser. The fringe shift of the phase object which appears in the denominator of the Airy distribution formula of the multiple beam interference is represented in the harmonic term. An experiment is conducted using liquid wedge interferometer where the step index glass fibre of a nearly quadratic thickness variation is introduced between the two plates of the interferometer. The obtained fringe shift shows a good agreement with the proposed quadratic model. The Matlab code is written to plot the interferometer fringes comprising the shift of the step index fibre. Secondly, recognition of elliptical fibres is outlined using tomographic imaging. Finally, results and concluding remarks are given.     

Polarization-maintaining photonic crystal fibre

Photonic crystal fibres (PCFs) offer new possibilities of realizing highly birefringent fibres due to a higher intrinsic index contrast compared to conventional fibres. In this paper, we analyse theoretically the modal properties of a kind of polarization-maintaining PCF, namely the elliptical hole photonic crystal fibre (EHPCF) with a central small elliptical hole introduced in the core region. We demonstrate the possibility of achieving large birefringence with zero walk-off in the single-mode regime. This PCF also exhibits unusual dispersion properties. Several hundred nanometres of ultra broadband flattened dispersion near the wavelength 1.55μm is achieved in this EHPCF with a central small hole of d_c=0.4Λ.     

Polarisation-sensitive four-wave mixing and soliton self-frequency shift effect in the highly birefringent photonic crystal fibre

By adjusting the polarisation state of the pump at 805 nm parallel to slow (x) and fast (y) axes of the highly birefringent photonic crystal fibre with zero dispersion wavelengths 790 nm and 750 nm, this paper demonstrates the efficient polarisation-sensitive four wave mixing involved in pump, anti-Stokes and Stokes signals and soliton self-frequency shift effects induced by the phase-matching between red-shifted solitons and blue-shifted dispersive waves. If the reduction of coupling efficiency to the circular pump laser mode or other circular fibres due to asymmetry of the core is neglected, more than 98% of the total input power is kept in a single linear polarisation. Controlled dispersion characteristic of the doublet of fundamental guided-modes results in achieving light field strongly confined in principal axes of photonic crystal fibre, and enhancing the corresponding nonlinear-optical process through the remarkable nonlinear birefringence.     

Calculation of geometrical birefringence from two-dimensional refractive-index profile in single-mode fibres

We present two numerical approaches to calculate the geometrical birefringence from two-dimenslonal refractive-index profile in single-mode fibres. One is the improved perturbation model theory, the other is based on the general solution of noncircular uniform optical waveguide in an arbitrary coordinate system. Using these methods, we can obtain not only the magnitude of geometrical birefringence, but also the orientation of birefrlngent axes. We report the calculation results of geometrical birefringence in a real single-mode fibre.     

Highly birefringent photonic crystal fibers with flattened dispersion and low effective mode area

A highly birefringent index-guiding photonic crystal fibers with flattened dispersion and low effective area is proposed by introducing elliptical air holes in the cladding and small holes both in the core area and in the cladding. With the plane wave expansion (PWE) method, the birefringent, dispersion and effective area of the fundamental modes in such photonic crystal fibers are analyzed in detail. The simulation result shows that high birefringence with a magnitude of the order of 10⁻³, flattened chromatic dispersion from 1100 nm to 1800 nm and low effective area (which mean high nonlinearity) are obtained. Furthermore, the influences on the birefringence and dispersion by geometrical parameters have also been discussed and a modest number of design parameters are given.     

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.     

Polarization and modal field properties of quinquangular-core photonic crystal fibers

A kind of highly birefringent quinquangular-core photonic crystal fiber(Q-PCF) structure is proposed and analyzed by full-vector finite element method(FEM) . The modal field,effective index,and birefringence properties are investigated. From the numerical results,it is found that the birefringence of the new polarization-maintaining PCFs is at least five times larger than that of the standard highly birefringent hexagonal PCFs(H-PCFs) with the same hole pitch,hole diameter,and whole hole area as that of the new PCFs at 1 550 nm. Moreover,the modal field of the new PCFs could be better restricted than that of the standard highly birefringent H-PCFs;hence,the loss of fibers could be reduced.     

Measurement of the spectral dispersion curves of low birefringence polymer fibres

A method is suggested to overcome the difficulties of measuring the spectral dispersion of low birefringence fibres, that produce small optical path difference, δ<3λ, where δ is the optical path difference and λ is the wavelength of light used. This method depends on variable wavelength interferometry (VAWI). The suggested method is used to measure the spectral dispersion of birefringence of polypropylene fibre with a draw ratio 4 (low birefringence fibre). This method is also used to measure the spectral dispersion of birefringence of a polyester staple from ICI (high birefringence fibre). Also, the conventional VAWI method is used to measure the spectral dispersion of this fibre to confirm the results obtained by the suggested method. Microinterferograms are given for illustration.     

Temperature dependence of birefringence in olarization-maintaining photonic crystal fibres

In this paper,the temperature dependence of birefringence in polarization maintaining photonic crystal fibres(PMPCFs) is investigated theoretically and experimentally.Utilizing the structural parameters of the PM-PCF samples in the experiment,two effects leading to the birefringence variation under different temperatures are analysed,which are the thermal expansion of silica material and the refractive index variation due to the temperature variation.The actual birefringence variation of the PM-PCF is the combination of the two effects,which is in the order of 10-9 K-1 for both fibre samples.Calculation results also show that the influence of refractive index variation is the dominant contribution,which determines the tendency of the fibre birefringence variation with varying temperature.Then,the birefringence beat lengths of the two fibre samples are measured under the temperature,which varies from -40℃ to 80℃.A traditional PANDA-type polarization maintaining fibre(PMF) is also measured in the same way for comparison.The experimental results indicate that the birefringence variation of the PM-PCF due to temperature variation is far smaller than that of the traditional PMF,which agrees with the theoretical analysis.The ultra-low temperature dependence of the birefringence in the PM-PCF has great potential applications in temperature-insensitive fibre interferometers,fibre sensors,and fibre gyroscopes.     

Measurement of mechanical deformation of dielectric fibres by a light scattering method

This paper describes an experimental method to detect quantitative changes of both refractive index and diameter of unclad dielectric fibres, such as fused silica fibre and nylon 6 fibre, due to tensile stress. The technique employed here is based on the variation in the position of a fringe in back-scattered light, which is generated when a laser beam is incident at a right angle to the axis of the fibre. This procedure makes it possible to measure refractive index, diameter and ellipticity to within an accuracy of 0.048%, 2.6% and 0.05%, respectively.     

空气孔正方形排列的低损耗高双折射光子晶体光纤的数值模拟

提出了一种正方形排列渐增空气孔高双折射光子晶体光纤，并利用多极方法对光纤基模的模场分布、色散、双折射以及损耗特性进行了数值模拟.模拟结果表明利用这种结构可以在包层空气孔层数较少的情况下实现极低的限制损耗，通过调节内层空气孔的分布可以有效地控制光纤的双折射和色散特性.本结果对高双折射光子晶体光纤的制备具有一定的指导意义. 关键词： 光子晶体光纤 双折射 限制损耗 多极方法