Polarization mode coupling in long single-mode fibres

In this paper we look at the polarization state evolution of light propagating in long, birefringent, single-mode fibres in the presence of mode coupling. We show first that there always exist two orthogonal linear input polarizations which lead to linear output polarization for monochromatic light. The applicability of the coupled power equations is discussed and it is shown that they cannot be used with only two propagating modes. A more detailed analysis is then carried out for a uniform coupling and the effect of the spectral width of the source is investigated. Some insight into the time-dependent propagation is also given. Experimental results illustrate the theoretical considerations.     

Light polarization modulation in single-mode optical fibres

A theoretical and experimental study of light polarization modulation in single-mode anisotropic optical fibres is presented. The problem of increasing polarization modulation efficiency in slightly and strongly anisotropic fibres is considered. The requirements to be met by the optical configuration for efficient polarization modulation with both slightly and strongly anisotropic fibres are discussed. The polarization modulation signal is found to be immune to external effects on the fibre under compensated birefringence. An experimental polarization modulation-based fibredyne video transmission data highway is presented.     

Curvature and microbending losses in single-mode optical fibres

Curvature of a single-mode optical fibre gives rise to two principal forms of additional transmission loss, namely transition loss and pure bend loss. The transition loss and the associated ray radiation, which have been observed at the beginning of a bend, can be satisfactorily explained by a modified coupled-mode theory. The radiation modes are represented by a quasi-guided mode having an average propagation constant _e. The introduction of a gradual change of curvature reduces the transition loss much more than the pure bend loss. Analysis of the microbending loss shows that the transition component is a maximum at a given correlation length which can be simply expressed in terms of _e. The contributions of both transition and bend components to the total microbend loss have been derived for the case of a randomly-curved fibre for several autocorrelation and density functions.     

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.     

Polarization characteristic calculation of three-layer elliptical single-mode fibres

A vector solution is obtained for fields of fundamental modes of an elliptical three-layer optical fibre, which is valid for small ellipticity of boundaries between the layers and for arbitrary differences of core and cladding indices. The modal birefringence is investigated as a function of fibre parameters on the basis of this solution. It is shown that the two-step fibre birefringence is larger than the W-fibre birefringence for equal differences of the core and inner cladding indices. The relationship is inverse for equal differences of the core and outer cladding indices. The correlation between the birefringence value and the effective diameter of the single-mode fibre is discussed.     

Effective cut-offs for modes on helical fibres

Every mode of a single-mode or multimode helical fibre is always leaky but, for practical purposes, can be treated as being bound with an effective cut-off wavelength. The leakage loss for each mode is quantified, showing that, for fixed core offset and source wavelength, the cut-off pitch increases with increasing mode order. The value of the cut-off pitch for each mode is in agreement with experimental measurements.     

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.     

Equivalent step-index (ESI) profile of elliptical-core single-mode fibres

The spectral dependence of the spot size of the elliptical-core single-mode fibre was measured along the major and minor axes using the transverse offset technique. Characteristics of this dependence may be applied for ESI determination of elliptical-core single-mode fibres.     

Analysis of splice loss in single-mode fibres using a Gaussian field approximation

By using a Gaussian field approximation to the fundamental mode in a single-mode fibre, a very simple formula is derived for the splice loss in the two fibres when transverse, longitudinal and angular misalignments exist simultaneously. It is shown that the effects of the three misalignments on the splice loss are more significant for step-index fibres than for parabolic-index fibres, and also that matching oil in the gap between the fibres is effective for the end separation, but produces a reverse effect for the tilt. Calculated coupling efficiency between step-index fibres is compared with the experimental data reported so far, and good agreement between them is observed.     

Bend loss calculation in single-mode graded-index fibers using variational fields

Calculation of bend loss for single-mode graded-index fibers utilizes the fundamental modal field. Using some of the single and two parameter scalar variational approximations available in the literature for this mode, the bend loss has been computed. The exact results are obtained using a well known numerical method. The accuracies of the results obtained from the use of these variational fields have been compared.     

Microlens fabrication on single-mode fibres for efficient coupling from laser diodes

An analysis of the etching process for forming a truncated conical microlens on the end surface of a single-mode fibre (SMF) so as to improve its coupling efficiency with a laser diode (LD) has been carried out. This is followed by a simple geometric-optics and electromagnetic analysis to calculate this coupling efficiency, when the lens is formed on a SMF fabricated by the MCVD technique. The theory is supported by measurements which gave a maximum coupling efficiency of 57%.     

旋转光纤对二阶偏振模色散的影响

论述了单模光纤生产过程中旋转光纤对二阶偏振模色散的影响. 从理论上指出虽然旋转光纤 有助于减小一阶偏振模色散，但是同时会使二阶偏振模色散增大，这对10 Gb/s以上速率的 光纤通信系统是个重要的问题. 关键词： 二阶偏振模色散 旋转光纤 动态方程     

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.     

Polarization properties of a single-mode gas laser in transverse magnetic fields

The effect of transversally applied magnetic fields on the polarization behavior of a single-mode gas laser is theoretically investigated, stressing the importance of the additivity of respective contributions influencing the time evolution of polarization parameters. By adding a new element to the existing theory, namely the contribution of magnetic-field-free regions in the active medium, and by considering the relatively large effects that small cavity anisotropies can cause, several apparent discrepancies between experiments and existing theory are resolved.     

Topology of toroidal helical fields in non-circular cross-sectional tokamaks

The ordinary differential magnetic field line equations are solved numerically; the tokamak magnetic structure is studied on Hefei Tokamak-7 Upgrade （HT-TU） when the equilibrium field with a monotonic q-profile is perturbed by a helical magnetic field. We find that a single mode （m, n） helical perturbation can cause the formation of islands on rational surfaces with q=m/n and q=（m±1,±2,±3,...）/n due to the toroidicity and plasma shape （i.e. elongation and triangularity）, while there are many undestroyed magnetic surfaces called Kolmogorov-Arnold-Moser （KAM） barriers on irrational surfaces. The islands on the same rational surface do not have the same size. When the ratio between the perturbing magnetic field Br（r） and the toroidal magnetic field amplitude Bφ0 is large enough, the magnetic island chains on different rational surfaces will overlap and chaotic orbits appear in the overlapping area, and the magnetic field becomes stochastic. It is remarkable that the stochastic layer appears first in the plasma edge region.     

A study of the propagation characteristics of W-type single-mode fibers using variational fields of single-clad single-mode fibers

A number of single and two parameter scalar variational fields approximating the fundamental mode of single-clad fibers are available in the literature. The present work aims at checking if these fields can also explain the propagation characteristics of W-type or double-clad single mode fibers with similar accuracies. To assess the accuracies, numerical solution of scalar wave equation is required. A method for solving the scalar wave equation numerically has also been proposed. Investigation shows that the single parameter fields are not very suitable for the W-type fibers. At least a two parameter variational field should be used.