Light propagation in multi‐step index optical fibres

This paper reviews the theoretical analysis of light propagation we have carried out on multimode multi‐step index (MSI) optical fibres. Starting from the Eikonal equation, we derive the analytical expressions that allow calculating the ray trajectories inside these fibres. We also analyse the effects of leaky rays on the transmission properties of MSI fibres. For this purpose, a single analytical expression for the evaluation of the ray power transmission coefficient is calculated. Afterwards, we investigate the effects of extrinsic and intrinsic coupling losses on the performance of MSI fibres, providing analytical expressions to calculate the coupling loss and, also, determining the most critical parameters. Finally, we carry out a comprehensive numerical analysis of the fibre bandwidth under different source configurations.     

The nonlinear dynamical stabilization of ps-pulses in gradient index optical fibres

The new possibilities of controlled nonlinear evaluation of short pulses in gradient index optical fibres, connected with the fundamental and higher modes of the fibre geometry and with the pulse envelope are analysed. The possibilities for using these phenomena for increasing the quantity of information transmitted by such pulses are discussed. The preferred regions for employment of both soliton and non-soliton powerful pulses in optical communication systems are identified.     

多量子阱波导等效折射率的新公式

利用转移矩阵技术,建立了薄膜近似下的多量子阱波导芯子区域等效折射率的解析公式。该公式是偏振态和量子阱波导折射率分布的函数。     

折射率渐变透镜的数值设计

传统折射率渐变透镜的设计要求初级馈源天线具有稳定的相位中心,这就限制了透镜的应用范围。为拓宽透镜的应用范围,提出了一种折射率渐变透镜的数值设计方法,通过对馈源天线的极化电场离散采样获得相位信息,并据此设计透镜,随后用金属短线结构的新型人工电磁材料来实现这种透镜。这种设计方法简单灵活,对馈源天线没有限制。以经典矩形贴片天线为例,比较了贴片天线和透镜天线的回波损耗和远场方向图,结果表明运用这种方法设计的透镜使贴片天线的增益提高了2 dB,口径效率从62%提高到了99%。     

折射率渐变透镜的数值设计

传统折射率渐变透镜的设计要求初级馈源天线具有稳定的相位中心,这就限制了透镜的应用范围。为拓宽透镜的应用范围,提出了一种折射率渐变透镜的数值设计方法,通过对馈源天线的极化电场离散采样获得相位信息,并据此设计透镜,随后用金属短线结构的新型人工电磁材料来实现这种透镜。这种设计方法简单灵活,对馈源天线没有限制。以经典矩形贴片天线为例,比较了贴片天线和透镜天线的回波损耗和远场方向图,结果表明运用这种方法设计的透镜使贴片天线的增益提高了2 dB,口径效率从62%提高到了99%。     

Highly nonlinear chalcogenide fibres for all-optical signal processing

Chalcogenide glasses offer many attractive properties for all-optical signal processing including large Kerr nonlinearity (up to 500 × silica glass), an intrinsic ultrafast response time and low to moderate two-photon absorption (TPA). These properties together with the convenience of a fibre format allow us to achieve all-optical signal processing at low peak power and in a very compact form. In this paper, several nonlinear processing functions will be demonstrated including: femto-second pedestal free, pulse compression; all-optic wavelength conversion; and all-optical regenerator. In addition, we show enhanced nonlinearity for more efficient signal processing by tapering the As₂Se₃ fibre. These applications show chalcogenide glass fibres are very promising candidate materials for nonlinear all-optic signal processing.     

A general strategy for designing seamless multiscale methods

We present a new general framework for designing multiscale methods. Compared with previous work such as Brandt’s systematic up-scaling, the heterogeneous multiscale method (HMM) and the “equation-free” approach, this new framework has the distinct feature that it does not require reinitializing the microscale model at each macro time step or each macro iteration step. In the new strategy, the macro- and micro-models evolve simultaneously using different time steps (and therefore different clocks), and they exchange data at every step. The micro-model uses its own appropriate time step. The macro-model runs at a slower pace than required by accuracy and stability considerations for the macroscale dynamics, in order for the micro-model to relax. Examples are discussed and application to modeling complex fluids is presented.     

BDF-like methods for nonlinear dynamic analysis

We present several time integration algorithms of second-order accuracy that are numerically simple and effective for nonlinear elastodynamic problems. These algorithms are based on a general four-step scheme that has a resemblance to the backward differentiation formulas. We also present an extension to the composite strategy of the Bathe method. Appropriate values for the algorithmic parameters are determined based on considerations of stability and dissipativity, and less dissipative members of each algorithm have been identified. We demonstrate the convergence characteristics of the proposed algorithms with a nonlinear dynamic problem having analytic solutions, and test these algorithms with several three-dimensional nonlinear elastodynamic problems involving large deformations and rotations, employing St. Venant-Kirchhoff and compressible Neo-Hookean hyperelastic material models. These tests show that stable computations are obtained with the proposed algorithms in nonlinear situations where the trapezoidal rule encounters a well-known instability.     

Refractive index profile optimisation for the design of optical fibres

Owing to advanced manufacturing techniques, it is possible to produce cylindrical single-mode fibres with nearly arbitrary refractive index profiles. For the design of optical fibres automated optimisation schemes have yet to be exploited. We have employed deterministic local, and stochastic global optimisation schemes for the minimisation of a cost function based on dispersion, dispersion slope, macro-bending losses and mode-field diameter, on the space of continuous piecewise linear dopant concentration profiles. For the local schemes (modified and quasi Newton), it appears possible to select a few initial profiles, such that the optimisation results are close to the “global optima” (within 8%), found using global schemes (simulated annealing and differential evolution), while reducing computation times significantly (minutes instead of days). For the local schemes, the cost function gradient is required. Fréchet derivatives are more efficient than finite-difference approximations. A sensitivity analysis provides useful information for manufacturers regarding the required profile accuracy. A comparison of our optimised fibre designs with commercially available optical fibres demonstrates that existing fibres can be improved.     

Mechanism for designing metallic metamaterials with a high index of refraction

We introduce a mechanism for creating artificial high refractive index metamaterials by exploiting the existence of subwavelength propagating modes in metallic systems. As an example, we investigate analytically and numerically metal films with a periodic arrangement of cut-through slits. Because of the presence of TEM modes in the slits, for TM polarization such a system can be rigorously mapped into a high refractive index dielectric slab when the features are smaller than the wavelength of light. The effective refractive index is entirely controlled by the geometry of the metal films, is positive, frequency independent, and can be made arbitrarily large.     

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.     

Circularly symmetric modal interferometers: Equalization wavelength and equivalent step determination for matched-cladding fibers

An LP₀₁-LP₀₂ modal interferometer fabricated from a standard matched-cladding telecommunication fiber is studied in the visible wavelength range. Its spectral response in the vicinity of the LP₀₁/LP₀₂ equalization wavelength is used to characterize the fiber by the determination of an equivalent step 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.     

Measuring method for the refractive index profile of optical glass fibres

A new method for measuring the refractive index profile of optical glass fibres is described. This simply monitors the reflection of a focused laser beam from a polished fibre end face. Detailed tests on the accuracy and resolution of the method are described and the index profiles of several fibres are given as an example of its feasibility.     

Transformation methods for solving nonlinear field equations

The collection of extended canonical transformations of first-order contact manifolds is studied. This collection is shown to form a group under target-source composition and to contain the group of all first prolongations of point transformation of the underlying graph space and all isogroups of completely integrable horizontal ideals. Extended canonical transformations are compared and contrasted with Bäcklund transformations. These results are used to construct an extended Hamilton-Jacobi method for systems of nonlinear PDE. The collection of all extended canonical transformations is also shown to contain infinitely many one-parameter families of transformations, but there is no Lie group structure that contains these one-parameter families, in general. Conditions are obtained under which a one-parameter family of extended canonical transformations will map a solution of the fundamental ideal that characterizes a given system of PDE into a one-parameter family of solutions. These results are applied to the -Gordon equation _x1 = () and to the Navier-Stokes equations.     

Comparison of nonlinear dynamic methods and perturbation methods for voice analysis

Nonlinear dynamic methods and perturbation methods are compared in terms of the effects of signal length, sampling rate, and noise. Results of theoretical and experimental studies quantitatively show that measurements representing frequency and amplitude perturbations are not applicable to chaotic signals because of difficulties in pitch tracking and sensitivity to initial state differences. Perturbation analyses are only reliable when applied to nearly periodic voice samples of sufficiently long signal lengths that were obtained at high sampling rates and low noise levels. In contrast, nonlinear dynamic methods, such as correlation dimension, allow the quantification of chaotic time series. Additionally, the correlation dimension method presents a more stable analysis of nearly periodic voice samples for shorter signal lengths, lower sampling rates, and higher noise levels. The correlation dimension method avoids some of the methodological issues associated with perturbation methods, and may potentially improve the ability for real time analysis as well as reduce costs in experimental designs for objectively assessing voice disorders.     

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.