 
Summary: A VECTORIAL VARIATIONAL MODE SOLVER AND
ITS APPLICATION TO PIECEWISE CONSTANT AND DIFFUSED WAVEGUIDES
O. (Alyona) Ivanova, Remco Stoffer, Manfred Hammer, E. (Brenny) van Groesen
University of Twente, MESA+
Institute for Nanotechnology, P.O. Box 217, 7500 AE Enschede, The Netherlands
o.v.ivanova@math.utwente.nl
Abstract A Variational Vectorial Mode Solver for 3D dielectric waveguides with arbitrary 2D cross
sections is proposed. It is based on expansion of each component of a mode profile as a superposition of
some a priori defined functions defined on one coordinate axis times some unknown continuous coefficient
functions, defined on the other axis. By applying a variational restriction procedure the unknown coefficient
functions are determined as an optimum approximation of the true vectorial mode profile. A couple of
examples illustrate the performance of the method.
I. INTRODUCTION
Optical waveguides are main ingredients in many integrated optical circuits, and design tools for these waveguides
are of great importance. Detailed overviews of such techniques are presented in [1, 2]. In this paper we extend
the scalar Variational Mode Expansion Method [3] to fully vectorial simulations of lossless isotropic dielectric
waveguides with in principle arbitrary refractive index distribution. The validity of the method is checked for
a waveguide with nonrectangular piecewiseconstant refractive index distribution and a diffused waveguide.
II. VARIATIONAL VECTORIAL MODE SOLVER
A. Problem Formulation
