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.     

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.     

渐变折射率波导传播特性微扰计算的代数递推公式

应用量子力学的超位力定理（HVT）和赫尔曼－费恩曼（Hellmann-Feynman）定理（HFT），导出了用微扰法计算渐变折射率平面波导传播常数各级近似值的代数递推公式，并给出了由传播常数近似值计算模场近似表达式的代数式。计算了几个典型实例，此法的特点是便于直接计算任意级近似的传播常数及模场分布，且可推广到二维波导的计算。     

梯度折射率介质中高斯光束的非线性传输特性

 利用无像差自聚焦理论研究了梯度折射率非线性Kerr介质中高斯光束的传输特性,得到了高斯光束光斑半径和波面曲率半径的表达式。解析结果清楚地表明了衍射、自聚焦以及梯度折射率效应之间的竞争对高斯光束传输行为的影响。梯度折射率效应使光束自聚焦的距离缩短。     

梯度折射率介质中高斯光束的非线性传输特性

利用无像差自聚焦理论研究了梯度折射率非线性Kerr介质中高斯光束的传输特性,得到了高斯光束光斑半径和波面曲率半径的表达式。解析结果清楚地表明了衍射、自聚焦以及梯度折射率效应之间的竞争对高斯光束传输行为的影响。梯度折射率效应使光束自聚焦的距离缩短。     

Modelisation de la propagation dans les fibres optiques

This paper presents a new method for investigating the effects of mode conversion due to microbends on the transmission characteristics (attenuation, frequency response ...) of multimode optical fibres. The method applies to both step-index and graded-index fibres and takes into account any dependence of the mode coupling coefficient upon propagation angle. The general theory of propagation with mode coupling is developed and we introduce the concept of modes. The propagation problem is then simplified by using hypotheses based on exerpimental results and the solution is obtained with the help of a computer. Practical results concerning the increase of attenuation due to microbends are presented, from which the precautions to be taken when cabling fibres are deduced. It is also shown that in every practical case encountered, the prediction of the total attenuation and of the frequency response of a given fibre, when the launching conditions are specified is obtained from analytical expressions which approximate well with the exact results obtained from the computer. All these results make the method powerful and very useful for system designers when evaluating the effect of introducing an optical fibre into a transmission system.     

Interferometric studies on the influence of temperature on the optical and dispersion parameters of GRIN optical fibre

Opto-thermal device attached to automate Fizeau interferometer is used to investigate the influence of temperature on opto-thermal properties of multimode graded-index (GRIN) optical fibre in the range from 27 to 54 °C. The effect of temperature on the refractive index profile of fibre is studied. The optical parameters and the opto-thermal coefficient of this fibre are determined. Also the variation of oscillation and dispersion energies, zero dispersion wavelengths, coupling efficiency, normalised frequency, number of propagation modes with the temperature and the material dispersion with the wavelength at different temperatures are calculated. Microinterferograms are given for illustration.     

A numerical technique for solving the scalar wave equation for Gaussian and smoothed-out profiles

A numerical technique, based on transforming the scalar wave equation to a finite interval before discretization is applied, is proposed for the solution of the scalar wave equation defining the modal fields and propagation constants of optical fibres. It is used to compute the propagation constants and modal fields of weakly guiding fibres of circular cross-section when the refractive index profile has a Gaussian or smoothed-out form. The smoothed-out profiles are studied because they vary continuously from the Gaussian to the step profile. Results are compared with and shown to be accurately approximated by simply explicit functions, dependent only on the fibre parameter.     

Bandwidths of single-mode and multimode optical fibre

An analysis is given of the effect of carrier spectral width on bandwidth of optical fibre transmission lines and a simple generalized expression is deduced relating carrier bandspread and maximum permissible pulse rate. It is shown that for the case of a semiconductor laser carrier source the bandwidth of a multimode fibre can be made to approach that expected from single-mode and graded-index fibres.     

Upper limit of bandwidth improvement by optical equalization of graded-index fibres

Optical equalization was suggested as a means for increasing the bandwidth of optical fibre communication links when non-optimal graded-index fibre profiles are available. In this paper it is shown that by proper choice of the length as well as of the index of the compensating fibre one can significantly increase the bandwidth capability of the link. An upper limit of this improvement is derived, which is much larger than that obtained with alternating fibres of equal lengths.     

The effect of cladding loss in graded-index fibres

We present quantitative results for the effect of cladding absorption on the transmitted power and impulse response of a typical multimode, graded-index fibre that is excited by a Lambertian source. Power attenuation is due to the absorbing cladding material and the radiation loss of the tunnelling rays. Graded-index fibres are shown to be far less susceptible to the effect of cladding absorption than step-index fibres.     

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.     

Comparative spectral attenuation measurements on optical fibres: final report by members of COST 208

Comparative spectral attenuation measurements on a graded-index fibre have been perfomed by nine participants, covering the range 700–1800 nm. Details of measurement equipment and techniques are being reported. Since the attenuation of a graded-index fibre depends on the energy distribution launched into the fibre, only careful control of this parameter leads to comparable results. A method was developed to check the energy distribution in the fibre over a broad spectral range. By this method agreement of attenuation values to within ± 5% from 800 to 1500 nm has been achieved. This is about half of the deviation found in other comparison measurements which are usually restricted to one or two wavelengths.     

WKB analysis of guided and semileaky modes in graded-index anisotropic optical waveguides

WKB analysis of graded-index anisotropic optical waveguides is briefly presented. The angular dependencies of the propagation characteristics of both guided and semileaky modes are calculated numerically for the out-diffused and in-diffused LiNbO₃ waveguides with parabolic index profile. The results for the out-diffused waveguide are compared with those obtained from the rigorous theory and the applicability of the WKG method is discussed for semileaky mode loss calculations. The angular dependence of the propagation constants of a TiO₂-diffused LiNbO₃ waveguide is demonstrated experimentally, too.     

Free wave propagation in two-dimensional periodic plates

The propagation of flexural waves in a two-dimensional periodic plate which rests on an orthogonal array of equi-spaced simple line supports has been investigated. A type of plane wave motion has been considered. An energy method has been developed to predict the frequency of wave propagation in terms of the propagation constants. A Galerkin type of analysis has been used, incorporating assumed complex modes of wave motion for the identical rectangular elements of the periodic plate. Expressions for the frequency have been obtained firstly by using simple polynomial modes for the plate displacements, and then (alternatively) by using characteristics beam function modes. The use of these different modes has first been demonstrated by applying them to the analysis of wave propagation in periodic beams. A single polynomial mode which satisfies the geometric and wave-boundary conditions of the periodic plate element leads to an elegant expression relating the frequency and the wave propagation constants in the first propagation band. The frequencies so obtained compare well with those found from a multi-mode, characteristic beam function analysis. The latter involves much more algebra, is solved as an eigenvalue problem, and yields the frequencies in as many propagation bands as are desired. The bounding frequencies and corresponding wave motions in the first and higher propagation bands have been identified, and it has been shown that the propagation bands can overlap. Consideration has been given to one-dimensional “strip” structures which are equivalent to the two-dimensional plate when a plane wave in a general direction is propagating. Furthermore, it is shown that the natural frequencies of finite rectangular periodic plates can be obtained very simply from the results of the wave propagation analysis.     

Length-dependent effects due to leaky modes on multimode graded-index optical fibres

The radiation losses of tunnelling leaky modes in graded-index optical fibres are calculated theoretically, and it is shown that the near-field intensity profile has a length dependence. Consequently measurements of the near-field intensity distribution do not give the refractive index profile directly, and a correction factor must be applied. We have investigated this factor and find that it depends only on a single normalisation parameter involving fibre length, core radius and normalised frequency. A further use of the correction factor is to determine the total power attenuation due to the loss of leaky modes.     

Optical fibre beam delivery of high-energy laser pulses: beam quality preservation and fibre end-preparation

This paper investigates the extension of optical fibre beam delivery to high-brightness applications, in particular laser percussion drilling, where both a good beam quality and high peak power are required. Beam quality preservation through a number of optical fibres is studied both experimentally and by using a ray propagation model. It is determined that in order to achieve the beam quality required for percussion drilling (M²<30) the largest fibre which can be used is 400 μm diameter. The laser-induced damage threshold is measured for a number of 400 μm fibres, and a CO₂ laser-annealing technique is shown to increase the damage threshold by a factor of 10, allowing 28 J, 1 ms pulses to be transmitted.     

Thermal Diffusion Process Estimation for Fabrication of Graded Plastic Optical Fibre

Thermal diffusion of dopants is investigated in the process of generating the graded-index profile of plastic optical fibres. Because the diffusion coefficient in high polymers has been shown to depend strongly on dopant concentration, it is allowed in this work to vary with the radial coordinate of the multistep-core fibre. A novel multi-layer model is presented for solving the diffusion equation with the variable diffusion coefficient. It is solved by the finite difference method. The solution determines the dopant diffusion profile in the fibre. It is verified against a solution from the literature and two cases of fibres with diffused profiles. The application is demonstrated on two examples of graded-index plastic optical fibres, one originally with a two-step and the other with four-step core. The results indicate that closer to the core-cladding interface, the computed diffused profile with variable diffusion coefficient D is closer to target profile than the profile obtained with constant D for the same time of thermal process.     

Simplified universal dispersion curves for channel waveguides

Simplified universal dispersion curves for graded-index diffused channel waveguides have been obtained with the new normalized WKB equation using the effective index method. It is shown that, similarly to planar guides, the propagation constant of all the guided modes of a particular channel can be obtained by two parameters, called the normalized mode orders. The dispersion relations between the propagation constant and the normalized mode order of the channel have been obtained for a number of profile shapes and waveguide dimensions.     

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.