Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides

AbstactAbstact This paper reviews numerical and approximate methods for the modal analysis of general optical dielectric waveguides with emphasis on recent developments. Six groups of methods are reviewed, covering (1) the finite-element method, (2) the finite-difference method, (3) the integral-equation method, (4) methods based on series expansion, (5) approximate methods based on separation of variables, and (6) methods that do not fit into the above groups, ranging from the specialized ones for analysing restricted classes of waveguides to the most general ones for analysing inhomogeneous, arbitrarily-shaped, anisotropic waveguides. Some suggestions with regard to the selection of methods for particular applications are given.     

A new semi-analytical method for the analysis of tapered optical waveguides

Tapered waveguide are used in number of integrated optic devices such as directional couplers, modulators, switches mode converters, etc. Most of the methods analyzing tapered waveguide are numerical in nature. In this paper we present a simple, fast and accurate semi analytical method for z-varying waveguide. However, very few idealized structures can be analyzed directly. The present method consists of separating transverse and longitudinal variation in the wave equation, leading to a differential equation with z-varying coefficients for the field variation along z-axis. For the transverse variation local normal theory is applied. Now this equation is applied to specific taper geometries like linear down taper. Computational are done assuming typical values. We observe variation of power mode profile and mode width. Waveguide loss is also including in the analysis. Finally the analytical simulation results have been verified by the commercial Opti-BPM software.     

A new approach for analysis of closed dielectric waveguides

The dispersion characteristics of a class of closed dielectric waveguides are investigated by the method which combines the building-block approach of mul timode network theory with rigorous mode matching procedure. Several numerical examples for different guiding structures have been given by the approach. The same structures are also analyzed with the finite element method and the EDC method for comparison. The calculations show that the present approach yields as highly accurate results as the finite element method while almost retaining the simplicity of the EDC method, and justify the utility of the present method     

光波导等参元分析

本文提出一套用于分析任意介质光波导的等参元算法,它基于严格的E_z-H_z变分公式,采用八节点曲边四边形单元。这种类型的等参元分析法尤其适用于研究各种具有曲边边界的复杂光波导和光波导器件。作为例子,文中把这一方法用于分析阶跃型光纤,渐变型光纤、各向同性以及各向异性光纤耦合器。     

Analytic approach to dielectric optical bent slab waveguides

A rigorous classical analytic frequency domain model of confined optical wave propagation along 2D bent slab waveguides and curved dielectric interfaces is investigated, based on a piecewise ansatz for bend mode profiles in terms of Bessel and Hankel functions. This approach provides a clear picture of the behaviour of bend modes, concerning their decay for large radial arguments or effects of varying bend radius. Fast and accurate routines are required to evaluate Bessel functions with large complex orders and large arguments. Our implementation enabled detailed studies of bent waveguide properties, including higher order bend modes and whispering gallery modes, their interference patterns, and issues related to bend mode normalization and orthogonality properties.     

A theoretical analysis of scattering loss from planar optical waveguides

We derive analytical expressions for the scattering loss in planar optical waveguides whose surface roughness can be described by an exponential or Gaussian autocorrelation function. Our results show, for the first time, the explicit dependence of the loss coefficient on all the waveguide parameters. In addition, we show that for any waveguide there is a simple upper limit for the scattering loss.     

Leaky mode analysis of circular optical waveguides

A leaky mode is a bound mode below its cut-off frequency. It attenuates in the direction of propagation and approximates the portion of the radiation field within the optical waveguide that is significant far from the source. The characteristics, including attenuation coefficients, of leaky modes on the circular fibre are compared with those of the more familiar slab waveguide. Except for the HE_1m leaky modes, leaky modes attenuate much faster on the slab than on the circular fibre. The greater the /(azimuthal field variation) the smaller the attenuatioN. Thus, theI?1 leaky modes are important even at great distances from the source. An effective cut-off frequency is proposed. Above this frequency the mode is either weakly leaky or trapped. An expression for the number of weakly leaky and trapped modes is given. The power of leaky modes due to illuminating one end of the fibre is determined. The effect of material absorption is considered.     

Comparison of a vectorial and new semivectorial finite-difference approach for optical waveguides

In this article, a new semivectorial finite-difference method is presented. By comparing the results obtained by the new approach with a vectorial method, it is shown that the accuracy is still very high with costs reduced by a factor of two. This revised version was published online in November 2006 with corrections to the Cover Date.     

A propagating beam method analysis of nonlinear effects in optical waveguides

We extend the propagating beam method to nonlinear media and subsequently analyse several examples of three and four photon processes in optical waveguides.     

Vectorial wave-matching mode analysis of integrated optical waveguides

For mode fields of integrated optical waveguides with piecewise constant and rectangular permittivity profile, Maxwell's equations reduce to the two-dimensional Helmholtz wave equation, supplemented by continuity requirements on the boundaries between different media. Two basic components of the mode field are expanded into factorizing harmonic or exponential functions, separately on each rectangular region. We determine approximations for guided modes and propagation constants by means of a minimization procedure based on a least squares expression for the mismatch in the continuity requirements. Results for the hybrid mode fields of typical sample waveguides classify this approach as competitive with and superior to alternative methods for vectorial mode analysis, although some open questions remain.     

改进的光波导标量近似有限元分析

本文首次将波矢量的匹配条件应用于标量近似有限元法求解条形波导,从而将二维问题简化成两个一维问题.其结果除了具有标量近似有限元法的一切优点外,还为节省计算机的存储和时间提供了一条新的途径.     

Mode energy transformation between two connected multimode general square-law-index optical waveguides

A coherent states method is used to investigate the mode coupling coefficients in the most general buttjoint problem for two multimode general square-law-index optical waveguides, when two different waveguides with elliptical cross-sections are to be butt-jointed with axis displacement, tilt and some turning of symmetry axes with respect to each other. The explicit expressions for the mode coupling coefficients and recurrence relations for the mode overlap integrals are obtained; the sum rules for the mode coupling coefficients are formulated and a method of experimental data analysis is proposed for this general problem. The method of calculating mode coupling coefficients is proposed for the case of the butt-joint problem when the waveguide cross-sections are only partially overlapping and then it is used to investigate the influence of misalignment on mode power distribution and pulse dispersion in the second waveguide. The experimental data are compared and it is shown that the coupling coefficients obtained in square-law-index model can be used in dispersion calculations forα-profile fibres in the case when the valueα is not far from the valueα=2.     

Matrix method for analysis of optical waveguides and quantum well structures

The one dimensional wave equation

A theoretical analysis of mode-mixing in optical waveguides with nearest-neighbour mode coupling

Properties of the solutions of the coupled equations describing the flow of average mode power in optical waveguides are investigated. All of the important properties and their theoretical foundations are first reviewed for systems with arbitrary coupling and loss coefficients. It is then shown that, for the special class of systems with nearest-neighbour coupling, the solutions are expressible in terms of orthogonal polynomials. In particular, for systems obeying a quasi-uniform loss model and having coupling coefficients with simple dependence on mode number (uniform or linear), the solutions are associated with the classical polynomials. As illustrations of this analysis, the characteristics of optical power flow in three such systems are studied in detail. These include a slab-waveguide with uniform coupling, the corresponding cylindrical waveguide with uniform coupling, and a parabolic-index fibre with linear coupling dependence.     

A new theory of rectangular optical waveguides

A new theoretical treatment of the dispersion theory for rectangular optical waveguides is presented. The theoretical basis of the effective dielectric constant method is investigated, and it shows how corrections can be calculated systematically. The result is a new set of eigenvalue equations, simple in form, and which provide very accurate values for the propagation constant.     

Design and analysis of a low loss and large-tolerance optical interface for large-area optical waveguides

An alternative interface structure design of a large-area optical waveguide for a large-area optical printed circuit board using a step-out fabrication technique is proposed. To investigate the misalignment tolerances and coupling excess losses, we simulated and compared our proposed structure to a typical straight core structure. As a result, the proposed structure was found to significantly improve the misalignment tolerance by more than 2 times and successfully conduct a data-link based on large area optical waveguide of 50 cm ×?50 cm.     

A simple iterative finite-element approach for the analysis of TM guided waves in uniaxial planar waveguides

An efficient computer-aided solution procedure based on the finite-element method is developed for the analysis of TM waves in slab uniaxial waveguides. In this approach, self-consistent solutions are obtained by using a simple iterative scheme. Propagation constants and field profiles for TM guided waves in a uniaxial planar waveguide are given and compared with analytical results.     

Theoretical analysis of bragg electrostrictive mixing in optical waveguides

A theoretical analysis of electrostrictive mixing in optical waveguides using the power balance approach is presented. The high optical power densities attainable in optical waveguides provide a means to make this effect appreciable to generate acoustic surface waves of the Rayleigh type. The tensor property of the acoustic wave and the transverse field distributions of the optical and acoustic waves are included in the analysis. Numerical calculation for a tellurite glass, fused quartz waveguide structure indicates a possibility for cw operation.     

Zero-birefringence photosensitive polyimides for optical waveguides

Zero-birefringence (delta n < 1 x 10(-6)) photosensitive fluorinated polyimides are synthesized for use in polymer optical waveguides. To obtain zero birefringence, the UV exposure time and copolymer content of photosensitive polyimides are controlled. Zero birefringence combined with photoprocessing of the material has excellent potential for applications in high-performance wavelength division multiplexing components such as polarization-independent arrayed waveguide gratings and Bragg wavelength filters.