Parallel-beam impulse response of multimode fibres: numerical results

Impulse responses are calculated for parallel-beam injection into fibres having-type profiles with a varying from 1 to 8. The responses obtained exhibit characteristic features which can guide the interpretation of experimental investigations of such fibres. The ray model is used and leaky-mode attenuation is taken into account. Finally, the dependence of the transmitted power on the injection angle is investigated, suggesting a possible functional relation to the index profile.     

Application of nonlinear oscillator theory to multimode fibres

By returning to the ray path equations and using mathematical methods taken over from the theory of nonlinear oscillators, we derive a new formalism for calculating transit times in power-law fibres with small additional refractive index profile perturbations. The formalism has the following important attributes: the structure is simple, the unperturbed fibre analytic result plus a separate term explicitly related to the perturbation; the results are wholly analytical in many cases of interest; and in contrast to older methods, the only integrals to be evaluated have well-behaved integrands involving only the profile perturbation function and they can be evaluated easily using experimental data points. The extension to perturbations varying along the fibre length is made and the analytic form of the result, again explicitly exhibiting the influence of the perturbations, enables us to observe quite generally that perturbations which average out to zero over the fibre length will have a minor effect on individual times and hence pulse dispersion.     

Ray theory of graded non-circular optical fibres

Both bound and tunnelling rays exist in multimode graded fibres which do not have circular symmetry; however, the fraction of energy in the tunnelling rays is generally less than that in a similar circular fibre, especially for near-parabolic profiles. For a large class of non-symmetric profiles, no tunnelling rays can propagate.     

Numerical evaluation of the impulse response of multimode optical fibers

Abstract

A numerical technique based on ray optics is presented that provides the impulse response of multimode optical fibers having arbitrary smooth index profiles and arbitrary material dispersion. The variation of dn/dλ ₀ as a function of n when the dopant concentration varies is obtained from Fleming⁽¹⁾ measurements on bulk samples. This technique is applied to germania-doped multimode fibers with power-law profiles and various values of Δ ≡ Δn/n Previous results⁽²⁾ are shown to be invalid when Δ ? 0.005. By successive approximations, optimum profiles that minimize the impulse response widths for quasi-monochromatic sources are found. For these optimum profiles, the quasi-monochromatic root-mean-square (rms) impulse response width is found to be of the order of 150 Δ²nsec/km, in agreement with a recent analytical result.⁽³⁾     

Numerical evaluation of the impulse response of multimode optical fibers

A numerical technique based on ray optics is presented that provides the impulse response of multimode optical fibers having arbitrary smooth index profiles and arbitrary material dispersion. The variation of dn/dλ₀ as a function of n when the dopant concentration varies is obtained from Fleming⁽¹⁾ measurements on bulk samples. This technique is applied to germania-doped multimode fibers with power-law profiles and various values of Δ ≡ Δn/n Previous results⁽²⁾ are shown to be invalid when Δ ≳ 0.005. By successive approximations, optimum profiles that minimize the impulse response widths for quasi-monochromatic sources are found. For these optimum profiles, the quasi-monochromatic root-mean-square (rms) impulse response width is found to be of the order of 150 Δ²nsec/km, in agreement with a recent analytical result.⁽³⁾     

Approximations in the evaluation of the impulse response of nearly parabolic fibres

Formulae are derived giving the flight time of a ray impinging on a nearly-parabolic fibre whose core index profile includes a fourth order perturbation term in addition to the usual second order term of parabolic profiles. The method is applied to the case of parallel beam injection to calculate the impulse responses of nearly parabolic fibres characterized either by a fourth order term or by an value very close to 2. Numerical results are given for parameters typical of silica fibres made by the CVD technique.     

Transmission properties of cabled multimode optical fibres

The study of real multimode fibres suggests a division into two main classes: very-low-dispersion fibres, employed in high-capacity transmission systems, for which a bandwidth limitation occurs in the repeater spacing; and other fibres. Surprisingly, for the fibres in the first class, the cabling process need not be too sophisticated and expensive, provided that no bandwidth limitations arise from material dispersion. In fact, in this case, the bandwidth limitation can be partly relaxed owing to the fibre perturbation.     

Optimization of inexpensive step-and-graded index multimode fibres

For local network applications, inexpensive multimode optical fibres are needed. The Axial-Lateral Plasma Deposition (ALPD) process developed in France is capable of providing low cost fibres. However the index profile needs to be optimized in order to obtain –6 dB bandwidths about 100 MHz km. In the present paper we report the results of an optimization procedure based on ray theory.     

Theory of scattering in multimode optical fibres

The problem of scattering in multimode optical fibres is treated in a rigorous way by means of both a ray and a statistical approach. These two methods are interlaced and harmonized. Applications to microbending, ellipticity, core radius and maximum numerical aperture variations, and fluctuations of index profile shape are performed. Useful results about power distribution and fibre attenuation are derived in each case.     

Theory of dispersion in lossless multimode optical fibres

Using the ray propagation model generalized expressions for the impulse response of multimode fibres have been derived. The analysis has been applied to lossless fibres for pulses having both gaussian and lambertian spatial distributions as well as impulse and gaussian temporal distributions. Detailed results are given for output pulse shapes and fibre dispersions for various configurations.     

Theory of power coupling between multimode optical fibres

In this paper power coupling between two multimode optical fibres is investigated. A formalism (based on a geometrical approach) suitable for analysing any coupling configuration between fibres with any index profile and any radiance distribution is presented. The model is applied to obtain coupling losses both in uniformly excited parabolic- and step-index fibres, in the presence of all kinds of coupling errors. Numerical results of extensive utility are shown and useful asymptotic expressions of coupling efficiency, valid for small values of coupling error parameters, are derived together with some practical rules for error combination. Mention is also made of some experimental results we have obtained, which corroborate some previous assertions. The work can supply a useful tool in the design of joints and connectors between single fibres or optical cables.     

Low-pass filter characteristics of multimode graded index fibres

On the basis of ray model solutions, the response of a lossless multimode graded-index fibre to a modulated source is calculated. The results demonstrate great sensitivity of the bandwidth of the fibre to small variations in index profile.     

Studies of radiative losses from multimode optical fibres

We describe measurements in which the radiative losses from a multimode fibre have been resolved into three components. These are the Rayleigh Scatter component from the material, the loss by tunnelling from the modes closest to cut-off into the surrounding material, and the forward scatter loss caused by imperfections in the fibre that are large compared to a wavelength.     

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.     

Simplified theory of the impulse response of an optical degenerate four-wave mixing cell

It is shown that the linearized theory of transient degenerate four-wave mixing (DFWM) is analogous to the case of a linear string with nonrigid support, imbedded in a repulsive quadratic potential. The dispersion relation for the latter permits an extremely simple derivation of the impulse response of a finite-length DFWM cell.     

Ray theory of microbending

A ray theory is given for randomly bent (two-dimensional) optical fibers that have arbitrary index profiles and arbitrary curvature spectra. Simple closed form results are given for power-law profiles and spectra. No approximation is made besides the small bending approximation and the paraxial ray optics approximation. In particular, the coupling between all modes is effectively taken into account.     

Limitations in the perturbation analysis of bent finite-clad fibres and waveguides

The transverse shift in the field distribution and the correction to the propagation constant of the fundamental and symmetric cladding modes on bent finite-clad single-mode fibres and slab waveguides are evaluated from perturbation theory for effective index values extending below the cladding index. Analytical results are derived in both geometries for the step-profile that are valid within the overall limitations of the theory. However, it is found that, for the fibre geometry only, the method breaks down at certain discrete wavelengths because of degeneracies that occur between the HE₁₂ (LP₀₂) and TE₀₁ (LP₁₁) mode propagation constants.     

Frequency-dependent steady-state distribution of optical power in multimode fibres

A new approach to the steady-state solution of the optical power flow equation in multimode fibres is presented. It takes into account the dependence on the modulation frequency of the optical guided power, starting from a very general trial solution. The steady-state attenuation coefficient and optical power distribution (in amplitude and delay) can be numerically evaluated for any kind of index profile and fibre perturbation.