Analysis Of Optical Waveguides Research Articles

A new approach to scalar and semivector mode analysis of optical waveguides

A new numerical method, based on the mapping to a molecular dynamics for extracting extreme eigenvalues and the corresponding eigenmodes, is applied for analyzing optical waveguides. We have utilized this method for the scalar and semivector mode analysis of arbitrary-shaped optical waveguides. The accuracy of the method is assessed for a graded slab-waveguides by comparing the result with analytical solutions. In addition, taking into account three well known rib-waveguides and a directional coupler as practical examples, the efficiency of our method is demonstrated. In comparison with results obtained by other numerical methods, it is shown that the method is very powerful for the analysis, modeling and optimum design of lossless optical waveguides.

Molecular Dynamics Approach to the Mode Analysis of Optical Waveguides

A novel numerical method, based on a molecular dynamics algorithm for coupled harmonic oscillators, is applied to the mode analysis of arbitrary-shaped optical waveguides. We describe in detail the relationships between the vibrational equation of motion for lattice dynamics and the discretized form of the wave equation for light. This mapping is useful for the analysis of the characteristics of optical waveguides. The efficiency of the method is demonstrated by application of the method to the mode analysis of a semiconductor rib-waveguide.

The perfectly matched layer boundary condition for modal analysis of optical waveguides: leaky mode calculations

The perfectly matched layer (PML) boundary condition is applied to modal analysis for optical waveguides. It is demonstrated that the PML is suitable and effective in computation of leaky modes.

Vector analysis of optical dielectric waveguide bends using finite-difference method

A full-vectorial analysis of optical dielectric waveguide bends using the finite-difference method has been developed. The formulation was based on the transverse electric field components, E/sub r/ and E/sub z/. To set up the boundary conditions at each dielectric interface, the continuity of E/sub /spl theta//, H/sub /spl theta//, and the tangential component of the electric field, and the discontinuity of the normal component of the electric field were satisfied. The finite-difference scheme was modified to satisfy these boundary conditions. The results of the analysis using the current method is compared with previous results. The optimal offset for 90/spl deg/ bends was obtained, and the losses for these optimal bend structures are also presented.

Equivalent-optical-waveguide model for the analysis of optical waveguides by means of an asymptotic effective-index method

We present a theoretical method that makes it possible to analyze three-dimensional (3-D) integrated optical waveguides with arbitrary refractive-index profiles. With this method it is easy to obtain effective indexes, propagation constants, and coupling-switching properties of planar and channel optical waveguides. This theoretical approach involves one's modeling the original optical waveguide by means of an equivalent optical waveguide whose effective index is evaluated by the application of a technique that we call the asymptotic effective-index method. The numerical values show good convergence and accuracy for effective indexes, propagation constants, and coupling-switching characteristics. Theoretical and experimental results are given.

A new technique of analysis of anisotropic channel optical waveguides using the propagating beam method

A new technique of analysis of anisotropic channel optical waveguides using the propagating beam method

Mode analysis of optical waveguides: a new approach

We propose a new numerical method for extracting extreme eigenvalues and the corresponding eigenmodes for very large Hermitian matrices. The method is applied, for what we believe is the first time, to the mode analysis of arbitrarily shaped optical waveguides. Compared with results obtained by other numerical methods, it is shown that our method is powerful with respect to the analysis, modeling, and optimum design of lossless optical waveguides.

Application of the transmission line matrix method to the analysis of slab and channel optical waveguides

The applicability of the three-dimensional vectorial transmission line matrix (TLM) method to the analysis of optical waveguiding structures is demonstrated. Any waveguide geometry, even incorporating anisotropic materials, can be treated by taking into account the coupling between all optical field components. The application of the TLM method to optical waveguides is shown to be both efficient and accurate. The dispersion curve for the fundamental TE-like mode of a typical rib dielectric waveguide as well as its electric-field pattern is obtained by the use of the TLM method. Numerical comparisons with the integral-formulation technique, the effective-index method, the finite-difference analysis, the spectral-index method, and the beam-propagation technique are also included.

Vectorial finite element modelling of 2D leaky waveguides

An accurate finite element method is described for the analysis of leaky optical waveguides with arbitrary cross-section and inhomogeneous anisotropic dielectrics including loss or gain. The method leads to the iterative solution of a nonlinear matrix eigenvalue problem without compromising the sparsity of the resultant matrices which depend only on the mesh topology. >

Analysis of single-mode optical waveguides by means of an equivalent optical waveguide technique

We present a theoretical method that makes it possible to analyze 3-D integrated optical waveguides with arbitrary refractive-index profiles. With this method it is easy to obtain effective indices, propagation constants, and coupling/switching properties of planar and channel optical waveguides. This theoretical approach involves modeling the original optical waveguide by means of an equivalent optical waveguide whose eftective index is evaluated by applying a technique that we call the asymptotic eftective-index method. The numerical values show good convergence and accuracy for effective indices, propagation constants, and coupling/switching characteristics. Theoretical and experimental values are given.

Vector and quasi-vector solutions for optical waveguide modes using efficient Galerkin's method with Hermite-Gauss basis functions

An efficient vector formulation and a corresponding quasi-vector formulation for the analysis of optical waveguides are presented. The proposed method is applicable to a large class of optical waveguides with general refractive index profile in a finite region of arbitrary shape and surrounded by a homogeneous cladding. The vector formulation is based on Galerkin's procedure using Hermite-Gauss basis functions. It is shown that use of Hermite-Gauss basis functions leads to a significant increase in computational efficiency over trigonometric basis functions. The quasi-vector solution is obtained from the standard scalar formulation by including a polarization correction. The accuracy of the scalar, vector, and quasi-vector solutions is demonstrated by comparison with the exact solution for the fundamental mode in a circular fiber. Comparison of the modal solutions obtained with the various methods for optical waveguides with square, rectangular, circular, and elliptical core demonstrate the accuracy and advantage of the quasi-vector solution.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modal analysis of optical waveguides using prony's method and bpm

AbstractWe present the application of Prony's method to the problem of computing the complex propagation constants of guided optical modes from data obtained with the beam propagation method (BPM). Prony's method provides accurate results for the complex propagation constants and also gives the amount of power carried by each of these modes as well as their relative phases, for both absorbing and nonabsorbing waveguides. © 1994 John Wiley &amp; Sons, Inc.

Comparison of two interactive finite-element programs for analysis of optical and microwave waveguides

This paper presents a comparison of two- finite-element programs developed for accurate cross-sectional analysis of arbitrary optical and microwave waveguiding structures. Both techniques were developed in response to the growing demand from scientists and engineers for application-specific expert systems, and employ advanced interactive pre- and post-processing facilities. They show good agreement, strongly complement one another, and could form the core of a whole library of similar "intelligent" software for computer-assisted analysis and design, with a wide range of possible applications within both supercomputer and workstation environments.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Finite element analysis of the ARROW leaky optical waveguide

The implementation of the finite element method is much simplified when studying lossless, bounded structures. An approach is described which estimates the solution of a leaky waveguide, the rib ARROW (antiresonant reflecting optical waveguide), by a perturbation of the solution of a similar, but bounded, FEM model. By focusing on designs with low rib heights, the quasi-TE characteristic of the hybrid mode of interest is exploited, simplifying the solution. It is shown that lower rib heights result in lower leakage attenuation. This approach is shown to compare favorably to the effective index method. >

Finite element analysis for lossy optical waveguides by using perturbation techniques

A finite element analysis, based on the variational procedure, is used to find the modal loss or gain for both the TE and TM modes with the application of the perturbation technique. Results for the modal gain for the buried heterostructure diode laser are presented, as well as the loss estimation for both the TE and TM modes for the asymmetrical multilayer metal-clad planar optical waveguides. The results obtained agree very well, for a wide range of loss/gain values, with the previously published work using alternative approaches.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Bidirectional eigenmode propagation analysis of optical waveguides based on method of lines

The eigenmode propagation algorithm based on the method of lines is extended to treat wave propagation in longitudinally varying and strongly reflecting waveguides with high refractive index contrast. The analysis includes multiple reflections, radiation loss and absorption by lossy dielectrics. Results for the power flow in a corrugated slab waveguide are in excellent agreement with the literature.

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

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.

Impedance boundary method of moments for accurate and efficient analysis of planar graded-index optical waveguides

An impedance boundary method of moments (IBMOM) is proposed to accurately and efficiently compute the propagation characteristics including the number of guided modes of general graded-index dielectric slab waveguide structures. The method is based on Galerkin's procedure in the method of moments and employs the exact impedance boundary condition at the interfaces between the graded-index region and constant-index cladding. Legendre polynomials are utilized in the field expansion. Computational results are shown for waveguides with various inhomogeneous refractive index profiles. The results indicate that typically five Legendre polynomials are sufficient for accurate solutions of the dominant TE and TM modes in optical waveguides having a finite region of inhomogeneous refractive index. Diffused optical waveguides with untruncated index profiles as well as coupled dielectric waveguides can be accurately analyzed using ten Legendre polynomials. >

Synthesis and analysis of planar optical waveguides with prescribed TM modes

An inverse-scattering approach to designing optical waveguides with prescribed propagation characteristics of TM modes is presented. The refractive-index profile of the waveguide is formulated as a solution to a nonlinear differential equation whose forcing function is the potential obtained from the application of inverse-scattering theory. This method can reconstruct smooth refractive-index profiles for planar waveguides that support single modes or multimode. The cases of both zero and nonzero reflection coefficients characterizing the transmission properties of waveguides are discussed. A direct analysis technique based on a finite-difference scheme has been formulated to verify the results obtained by the inverse-scattering method, and the two approaches are in excellent agreement.

Improved variational analysis of inhomogeneous optical waveguides using Airy functions

Variational trial fields that are based on modified Airy functions are proposed to obtain the propagation characteristics of inhomogeneous planar optical waveguides. Comparison is made with other recently proposed trial fields to demonstrate the improved accuracy obtained through the use of these Airy function trial fields. The probable reason that the proposed fields are better suited than others is that, unlike the others, they depend on the profile shape. The argument of the Airy function trial field is also sensitive to the rate of change of the profile. The fields are thus better matched to the exact field, improving the variational results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>