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.     

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.     

Geometric optics analysis of non-circular,graded-index fibres

The cross-sections of practical optical fibres do not have perfect circular symmetry. The appropriate mathematical representation of the refractive index profile is discussed and it is shown that the basic power law profile in circular fibres should be replaced by a grading functionF which is a homogeneous function of thex andy coordinates. Multimode optical fibres of this type are analysed using geometric optics. General properties of ray paths are described. The fundamental quantities of interest in fibre optics (power acceptance, ray transit time, impulse response) are shown to depend on the degree of homogeneity ofF but not on its specific form. Thus, fibres need not have circular symmetry in order to retain the desirable properties of the circular power law fibres. Ray paths and classifications are analysed in detail for elliptical, parabolic-index fibres. Splicing losses are examined and are shown to be not drastically dependent on deviations from circular symmetry.     

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.     

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.     

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.     

Orientation distribution of fibres in a channel flow of fibre suspension

The orientation and concentration distributions of fibres in laminar and turbulent channel flows are investigated numerically. The obtained results are in good agreement with the experimental data. In the laminar flow regime, more fibres orient to the flow direction as the Reynolds number increases. The shear rate of fluid around a fibre plays an important role in determining the orientation distribution of fibres, while the fibre density and the fibre aspect-ratio have marginal influence on the orientation distribution. In the turbulent regime, the orientation distribution of fibres becomes more homogeneous with the increase of Reynolds number, and the concentration profile is flatter than that in the laminar regime. The fluctuating intensity of fibre velocity in the downstream direction is larger than that in the lateral directions.     

Transmission properties of all-silica fibres for high-power Nd:YAG lasers

The transmission properties of two different types of all-silica fibres, step index and graded-index fibres, are investigated using a multimode high-power cw Nd:YAG rod laser. The reflections from the fibre surface back into the laser cavity affect the laser power and the beam parameters, waist diameter and divergence. A set-up for simultaneously measuring these values in front of and behind a fibre is presented. The maximum laser power transmitted by fibres is dependent upon the beam parameters, the fibre design and the surface conditions. An upper limit for the maximum divergence which can be coupled into a fibre with a certain numerical aperture without loss is given. The beam parameters behind the fibre, related to the input parameters, are presented.     

Electromagnetic wave refraction on the interface of absorptive and transparent isotropic media and non-resonant excitation of surface waves

New formulae for the angles of refraction at the interface of the absorbing/transparent isotropic media are derived from Maxwell's equations. Using the time-averaged Poynting vector for the direction of the beam of light, the noncoincidence of incidence and refraction planes is predicted for the mixed polarization of incident wave. The angle between the refracted beam and incidence plane is especially large for the condition of non-resonant excitation of surface electromagnetic waves at a flat interface of absorptive-transparent media.     

Tunnelling rays in graded-index fibres

An analysis of the role of tunnelling rays in pulse propagation in graded-index fibres is presented. Tunnelling ray attenuation is handled by using the generalized parameter technique which allows attenuation coefficients to be dispensed with and relevant families of tunnelling rays to be identified. Results are given for impulse response pulse widths and shapes. Incorporation of tunnelling ray pulse contributions into the formalism for determining optimum refractive-index profiles is presented. For most cases, tunnelling ray effects are small, but significant corrections may be necessary when measurements are made on short lengths of fibre.     

Perturbation theory of optical fibres with power-law core profile

The characteristics of graded-index optical fibres with power-law core profile and homogeneous cladding have been studied using perturbation theory. Analytical expressions are derived for the cut-off frequency, propagation constant and, in the case of leaky modes, the attenuation coefficient of an arbitrary mode on such a fibre. For the case of monomode fibres, excellent agreement is found with existing theoretical results for the propagation constant of the HE₁₁ mode and cut-off frequency of the TE₀₁ mode.On leave from Department of Physics, IIT, New Delhi, India.     

Far-field techniques for the characterization of single-mode fibres

The characterization of single-mode fibres is important not only for determining the system parameters for a particular fibre, but also for the specification of fibres for manufacturing purposes. We present a detailed analysis of two new methods of characterizing single-mode fibres. The strip integrated far-field method involves measuring the light power passed by a thin slit scanned across the far-field pattern and the area integrated far-field method involves measuring the light power passed by a knife edge scanned across the far-field pattern. It is shown that, for either method, the measured data is related to the transverse offset transmission coefficient by the Fourier-cosine transform and hence that the far-field r.m.s. spot-size can be directly calculated. Noise analysis shows that the area integrated far-field method is superior to the strip integrated far-field method and similar to the far-field mask method when a broadband light source is used to measure the far-field r.m.s. spot-size. It is also shown that the area integrated far-field method has smaller systematic errors than the far-field mask method.     

Methods to determine surface energies of natural fibres: a review

To tailor the interaction across composite interfaces especially for the development of green composites, i.e. composites made completely from renewable materials, information about the fibre surfaces is required. We review the current state of the art of methods to determine the surface tension of natural fibres and discuss the advantages and disadvantages of techniques used. Although numerous techniques have been employed to characterise surface tension of natural fibres, it seems that commonly used wetting techniques are very much more affected by the non-ideal character of natural fibres. Inverse Gas Chromatography (IGC) is a much better suited technique to determine the surface energetic properties of natural fibres than wetting techniques. The surface tension of natural reinforcements, determined using IGC, was reported for nanosized bacterial cellulose as well as bamboo, cornhusk, flax, hemp and sisal, covering a wide range of cellulose content. The effect of methods to separate/extract fibres from the plants as well as of a few surface modification procedures on the fibre surface properties is also reviewed. The dispersive part of the natural fibre surface tension γ ^d _S varies from 32 to 61 mJ/m². The fibre surface tension increases with increasing cellulose content of natural fibres. We also found that a higher basicity (Donor Number, K _B to Acceptor Number, K _Aratio) was observed for fibres containing more cellulose. This may be reflective of higher crystalline cellulose content in the surfaces of the fibres, as only the ether linkage of the cellulose is labile for hydrogen bonding.     

Guided modes in fibres with parabolic-index core and homogeneous cladding

Mode propagation characteristics of parabolic-index fibres with a homogeneous cladding are studied by using vector wave analysis. By investigating the asymptotic behaviour of the eigenvalue equations and the field components at cut-off and far from cut-off, a comprehensive and consistent scheme for the designation of the various modes is established. Strong similarities with step index fibres are found for both the mode designation schemes and the degeneracy properties among the hybrid modes as well as the TE_0m and TM_0m modes. This suggests that the technique employed in this paper can be applied to other types of graded-index fibres. In addition, numerical results obtained by solving the eigenvalue equations for a wide range of parameters are presented, which verify the theoretical predictions. Comparisons with the infinite-core approximation (ICA) and the field decomposition technique (FDT) are given. It is shown that neither the ICA nor FDT are applicable for modes near cut-off.Work supported in part by the Department of Communications, Canada.     

Beam delivery characteristics of optical fibres for carbon monoxide lasers

An experimental investigation has been conducted of the propagation characteristics of several types of optical fibres which are candidates for use in optical beam delivery systems for carbon monoxide lasers. Both solid core (chalcogenide) fibres and hollow core (with dielectric or dielectric coated metal) waveguides have been investigated. Such experiments have included an assessment of both the power transmission characteristics, and the effects of waveguide transmission on the optical quality of the beam at the exit of the fibre. The experiments indicated lowest loss for the chalcogenide solid core fibre with a value of 0.4 dB m⁻¹.     

Adiabatic bend transitions for large mode area fibres

Adiabatic bend transitions in large mode area multimode fibres were investigated theoretically using the beam propagation method. Adiabatic bend transducers preserve the power of guided light in the fundamental mode while guiding from one level of curvature to another for improved operation of mode filters and fibre amplifiers. A method is shown and used to find the optimised guidance path. Applications of these transducers include modal power back-converters, and guidance paths into and out of higher order mode filtering devices which work on bending.     

Evaluation of splice loss in single-mode graded index fibres by a simple technique

We present simple and accurate analytical expressions for the evaluation of splice loss in single-mode graded index fibres. Our analysis is based on simple series expression for fundamental mode of such fibres which we have developed recently. Since splices are highly tolerant for longitudinal separation, we restrict our analysis to cases of transverse offset and angular tilt only. The concerned calculations require much less computations. With examples of step and parabolic index fibres, we show that our predictions agree excellently with the exact results. A useful collection of integration and differentiation formulae involving Bessel functions is presented in the appendix for ready reference to engineering problems of similar computational context.     

Refractive index profile optimisation for the design of optical fibres

Owing to advanced manufacturing techniques, it is possible to produce cylindrical single-mode fibres with nearly arbitrary refractive index profiles. For the design of optical fibres automated optimisation schemes have yet to be exploited. We have employed deterministic local, and stochastic global optimisation schemes for the minimisation of a cost function based on dispersion, dispersion slope, macro-bending losses and mode-field diameter, on the space of continuous piecewise linear dopant concentration profiles. For the local schemes (modified and quasi Newton), it appears possible to select a few initial profiles, such that the optimisation results are close to the “global optima” (within 8%), found using global schemes (simulated annealing and differential evolution), while reducing computation times significantly (minutes instead of days). For the local schemes, the cost function gradient is required. Fréchet derivatives are more efficient than finite-difference approximations. A sensitivity analysis provides useful information for manufacturers regarding the required profile accuracy. A comparison of our optimised fibre designs with commercially available optical fibres demonstrates that existing fibres can be improved.