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.     

Rays and time dispersion in multimode graded core fibres

The propagation of a bundle of rays in a multimode graded core fibre is investigated. The analytical conditions for minimizing time dispersion for the bundle of rays are found and tested on a number of profiles including the so called alpha profile. Finally an estimate of the width of the impulse response is given and applied to different profiles.     

Core fields in graded fibres with non-circular index contours

Fields in the cores of graded non-circular optical fibres are analysed using a new method. It is shown that the scalar wave equation in elliptical co-ordinates can be separated for many realistic non-circular profiles, thus allowing calculation of fields by a double WKB method, The boundaries separating oscillatory and evanescent regions are found by simple analysis of algebraic equations, This method supports and further explains previous analysis which used geometric optics.     

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 multimode fibres

To evaluate their communication potential, measurements have been made on multimode glass fibres. Detector limited pulses of 180 psec risetime from a Ga-As laser were transmitted through various lengths of fibre. After a 120 m length the risetime was still not greater than 450 psec. Measurements with a mode locked He-Ne laser, done on shorter lengths of fibre, agreed with the above results.     

Geometric optics approach to light acceptance and propagation in graded index fibres

The methods of geometric optics are applied to light acceptance and propagation in graded index fibres. The symmetry of the basic ray equations reveals ray path invariants. Rays are classified into bound, tunnelling and refracting rays. The role of source properties in exciting different ray types is analysed. Pulses are considered in terms of absolute widths, r.m.s. widths and complete shape detail. Optimization formulae are obtained. The incorporation of attenuation mechanisms is described and the effects of an absorbing core are analysed in detail.     

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.     

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.     

All-fiber multimode interference bandpass filter

A novel design for an all-fiber bandpass filter based on a multimode interference reimaging phenomenon is presented. The filter has achieved low insertion loss with adequate bandwidth and isolation for coarse wavelength-division multiplexing. The filter can easily be made with any central wavelength that is compatible with the single-mode fiber used for its construction. The measured filter performance matches the theoretical predictions well. The filter can have broad applications in fiber-optic telecommunications, spectroscopy, and sensing.     

Bandwidth of multimode fibres with random fluctuation in the index profile: a Monte-Carlo approach

Random variations of the index profile along the length of a multimode fibre are analysed by means of a Monte-Carlo technique, within the framework of the WKBJ approximation, assuming linear profile dispersion. Previous results (concerning fibres with deterministic profile variations) would suggest that very broad bandwidths could be obtained even in the presence of strong deviation from uniformity, with a suitable choice of the average profile. On the contrary, our analysis shows that similar results are obtained only under restrictive assumptions. In particular, if the random fluctuations are specified in terms of their r.m.s. deviation, then the probability of getting a broad bandwith is always significantly less than unity, no matter how accurate the choice of the average profile.     

Thermal emission characteristics of a graded index semitransparent medium

This paper develops a numerical model for thermal radiative transfer in a two-dimensional semitransparent graded index medium. A piecewise continuous refractive index model, the linear refractive index bar model, is presented. This model is established based on three hypotheses, and has a higher precision than the bar model used previously. This paper also studies the thermal emission from a two-dimensional graded index medium, which is scattering or non-scattering. We find that it can present an obvious pattern of directional distribution at times. The refractive index distribution and absorption coefficient are the two main influential factors. This finding differs from the common belief that thermal sources, such as the incandescent filament of a light bulb, emit a quasi-isotropic light. The finding also suggests that there maybe other important applications of artificial GRIN materials.     

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.     

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.     

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.     

金属包层渐变折射率介质光波导的传输特性与损耗

用金属包层介质光波导损耗的微扰理论及藉助多层近似法用递推公式分析渐变折射率波导传播常数的方法,对几种类型的金属包层渐变折射率介质光波导的传输特性与损耗进行分析和讨论,得到了与精确数值计算结果相吻合的结果.     

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.