A novel method is presented for the analysis of dielectric waveguides. This method provides four major new contributions: (1) a transformation of variables is introduced that allows propagation constants to be computed directly; (2) H/sub 1/ (curl) tangential vector finite elements are applied to dielectric waveguides to obtain reliable approximate electromagnetic fields; (3) the Lanczos algorithm is modified to solve the required eigenmatrix equation efficiently; and (4) the reaction principle is used to provide a posteriori error estimates for use in adaptive mesh refinement. The method produces reliable solutions and applies to structures that contain both electric and magnetic inhomogeneities. The answers are refined adaptively to generate waveguide eigenmodes to a specified accuracy. Numerical results of an image guide, a microstrip transmission line, and a pedestal-supported stripline are shown. Computed solutions agree very well with previously published results. >

Full-wave analysis of dielectric waveguides using tangential vector finite elements

A simple accurate method, which automatically takes full account of the discontinuities in the normal electric field components across any arbitrary distribution of internal dielectric interfaces, is presented for the determination of polarised solutions of the Helmholtz wave equation. The application of the shifted inverse power iteration method to the resulting matrices, enables any required propagation eigenvalue (not necessarily the fundamanetal mode) to be determined, together with its corresponding electric field profile. It is found that the results, which are presented for various semiconductor rib waveguide structures, compare favourably with published vector finite element and scalar results.

Semivectorial polarised finite difference method for optical waveguides with arbitrary index profiles

https://ntrs.nasa.gov/api/citations/19950021305/downloads/19950021305.pdf

The Origin of Spurious Solutions in Computational Electromagnetics

A class of dielectric waveguide structures using a rectangular dielectric strip in conjunction with one or more layered dielectrics is analyzed with a finite-difference method formulated directly in terms of the wave equation for the transverse components of the magnetic field. This leads to an eigenvalue problem where the nonphysical, spurious modes do not appear. Moreover, the analysis inclndes hybrid-mode conversion effects, such as complex waves, at frequencies where the modes are not yet completely bound to the core of the highest dielectric constant, as well as at frequencies below cutoff. Dispersion characteristic examples are calculated for structures suitable for millimeter-wave and optical integrated circuits, such as dielectric image lines, shielded dielectric waveguides, insulated image guides, ridge guides, and inverted strip, channel, strip-slab, and indiffused inverted ridge guides. The numerical examples are verified by results available from other methods.

Finite-Difference Analysis of Rectangular Dielectric Waveguide Structures

A method for calculating the modes of arbitrarily shaped dielectric waveguides is presented. It consists of expanding the field in a two-dimensional Fourier series. The expansion is used to convert the scalar wave equation into a matrix eigenvalue equation. To facilitate calculation of the matrix elements, the waveguide geometry is approximated by a number of rectangles of constant refractive index. The accuracy of the method is demonstrated by calculating the dominant mode of a circular optical fiber and comparing it with the exact solution. The method well-fitted the experimental data on dielectric film waveguides on silicon, including data on waveguide-to-fiber butt-coupling loss, waveguide far-field angles, and the coupling length of directional couplers. >

Solution of the scalar wave equation for arbitrarily shaped dielectric waveguides by two-dimensional Fourier analysis

A method for computing the modes of dielectric guiding structures based on finite differences is described. The numerical computation program is efficient and can be applied to a wide range of problems. We report here solutions for circular and rectangular dielectric waveguides and compare our solutions with those obtained by other methods. Limitations in the commonly used approximate formulas developed by Marcatili are discussed.

/pdf/computer-analysis-of-dielectric-waveguides-a-finite-2t6ae0t80r.pdf

Computer Analysis of Dielectric Waveguides: A Finite-Difference Method

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Computer Analysis of Dielectric Waveguides: A Finite-Difference Method