Pulse propagation in multimode fibres

The Gloge model for mode-coupled pulse propagation in a step index fibre has been re-examined and a dynamic model proposed to explain the significance of the pulse-broadening regime in which the pulse width varies asL. This leads to the conclusion that the critical factor controlling such propagation is the existence of a particular distribution of power which is a function of space, time and angle.     

Pulse propagation through a nonlinear optical amplifier

We report an investigation of pulse propagation through a recently proposed nonlinear amplifier composed of asymmetrical twin-core fibre. While the pulse is amplified and the associated noise is suppressed, we find that the pulse is strongly chirped. While the chirp in the centre of the pulse can be easily eliminated by inserting a short piece of dispersive fibre right after the amplifier, the chirp in the wings may remain and lead to the eventual destruction of the pulse. This residual chirp can be removed through a damped and radiative oscillation by judicious adjustment of the parameters of the amplifier and the dispersive fibre. Finally, we consider the effect of noise in the pulse. We discovered a threshold of the noise amplitude below which the noise is suppressed (which must be a characteristic asset of the nonlinear amplifier). Above the threshold, the noise tends to shift the centre of the pulse.     

Optimum profiles for dispersive multimode fibres

A simple closed-form expression is given for the index profile of multimode fibres with arbitrary dispersion providing transmission capacities as large as 1.6/ ² Mbit/s km, wheren/n. Our result reduces to a previous result of Marcatili for the special case of circularly symmetric fibres. A transmission capacity of 150 Mbit/s over a 10 km long fibre appears possible with LED sources operating at optimum wavelengths for the medium.     

Pulse propagation in optical fibres with index profiles slowly varying along their length

This paper describes the formalism for calculating the effect of profile variations along the fibre on transit times and path parameters for rays in multimode fibres. The ideal case of power-law profiles is considered in detail and it is shown that when the exponentq is given byq=q ₀+f (z), the fibre may be described by an equivalent exponentq _e. Simple formulae forq _e in terms of the average properties off(z) are given. The ray parameter varies and this is shown to have only a minor effect on transit time, but does imply that some rays suffer an attenuation when0. If the amount of dopant in any crosssection is assumed constant, the fibre radius must vary whenq varies and profiles with this attribute are examined and shown to have ray behaviour similar to that described above.     

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.     

Minimum total dispersion in multimode graded-index fibres

This paper points out that, in impulse response calculations by the method of Gloge and Marcatili, the condition that the equal propagation constant lines and the equal group delay lines coincide is not satisfied except for a power law index profile. The group delay time is derived in this paper, by a perturbation method. The optimum index profile is determined from the measured refractive indices data of several doped silica glasses.It is found that (1) the optimum value of the fourth order coefficient is not so different from the value which minimizes the modal dispersion, except in the short wavelength region, (2) the wavelength which minimizes the total dispersion is near 1.30m and (3) a B₂O₃ doped fibre has a small profile dispersion and a small total r.m.s. width.     

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.     

Pulse amplification characteristics of multimode fiber amplifier

Under small signal situation, the analytical expression for describing the output signal emitted from an Yb³⁺-doped fiber amplifier with a Gaussian input pulse signal is deduced, by full considering both fiber guided modes’ propagation constant and filling factor, which depend on the signal frequency. Pumped by continue wave (CW) source, the analytical expressions of the small signal gain and each guided mode's output power are obtained. Based on these analytical expressions, the various intensity distributions of output pulses amplified by the fiber amplifier with different Gaussian input pulse widths are analyzed.     

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.     

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.     

Wavelength dependent propagation in optical multimode fibers

Under various assumptions concerning the wavelength dependence of the refractive index of a fiber whose radial dependence is not an “a priori” known function of r, a method is described to obtain a closed form expression for the flight time of a ray in a multimode fiber. Consequently, the refractive index n(r) is shown to be the solution of a differential equation. Thus, for these selected profiles, we avoid the problem of the high precision required in the calculation of the flight time of a ray, a problem that arises frequently if the impulse response is to be reconstructed from a large number of rays, and transpose it to the determination of a single function of r, namely the refractive index.     

Dispersion of tubular modes propagating in multimode optical fibres

We have already used interferometric techniques for measuring, first, the impulse response of optical fibres and further the different times of flight of modes of a multimode fibre. Apart from time of flight, our set-up provides the intramodal dispersion of each mode (d² β/dω ²). To demonstrate, we have measured the modal dispersion difference between two tubular modes that were selectively excited in a multimode graded index fibre. For comparison, a theoretical expression has been derived, based on a ray optics approach.     

The preparation of multimode glass- and liquid-core optical fibres

A preform technique for drawing cladded-glass and hollow fibres suitable for application to optical communications is described. The parameters which need to be controlled are discussed and the preparation of the preforms is described. The resulting fibres have a high geometric uniformity and a probe beam remains largely at the same angle to the axis after more than 10⁶ reflections at the core/cladding interface. Fibre attenuations of 150, 60 and 5.8 dB km^–1 have been obtained with commercial glasses, preforms made from a special melt at Sheffield University [5], and a commercial liquid, respectively. The fibre drawing process does not appear to introduce any additional impurities and heat treatment has produced a significant reduction of transmission loss in glass fibres.     

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.     

Beam propagation in elliptical fibres

We apply an operator method, based on the scalar wave equation, to study the propagation of a Gaussian light beam in an optical fibre with an arbitrary, elliptically symmetric refractive-index profile. We discover that ray optical results, while not capable of predicting the rapid distortion of an optical beam in a non-ideal refractive-index profile, successfully simulate the general form of the optical power distributions, even in non-ideal profiles. We find that the propagation patterns for elliptical fibres with and without a strongly scattering central index dip show several unexpected similarities.