Explanation of errors inherent in the effective-index method for analyzing rectangular-core waveguides

Abstract

It is shown that use of the effective-index method for a rectangular-core waveguide is equivalent to analysis of a pseudorectangular-core waveguide, the dielectric constant of which is higher in some of the cladding regions than that of the actual waveguide. This explains why the effective-index method gives higher values for the propagation constants for the various guided modes than other methods and different results depending on whether one starts with the longer dimension or the shorter dimension to construct the effective-index waveguide.

A conceptual model of light coupling by pillar diffraction gratings

“…The justification for the use of the procedure used in the EIM can be understood by examining the mathematical basis of the method. When we apply the EIM to a structure we are assuming that the dielectric function profile of interest can be approximated by a separable profile 7,21 i.e., n 2 ͑x,y͒ Х n app 2 ͑x,y͒ = n app,x 2 ͑x͒ + n app,y 2…”

Radiation in bent asymmetric coupled waveguides

“…All the 3D vector mode field calculations in this work have been performed using the wgms3d [24,27] software package. A very common approach to this problem is also based on its reduction to a 2D geometry, using the EIM [14,15]. Solutions for the 2D effective problem are then sought for by different means [16,17,10,18,19,20,21,22,23].…”

“…In the EIM, a semivectorial approach with pure TE or TM polarized fields is being used [15]. By assuming the separability of both the field components and the refractive index [14,15], the problem is first analyzed in one of the transverse spatial dimensions, producing the effective indices for the analysis along the orthogonal transverse direction. The intrinsic error in the effective index model [15] is due to: (a) the semi-vectorial approach to a full vector problem and (b) the fact that the refractive index is actually non-separable.…”

Silicon‐On‐Insulator (SOI) Photonics

“…Many authors have considered the accuracy of the method and produced examples of good agreement with more rigorous theory, or relatively poor agreement (see for example [1,2,3]). The general conclusions are that the method becomes inaccurate for complex structures, poorly confined modes, or large index steps; hence care must be exercised using this, or indeed any other, approximate method.…”