 
Summary: A variational mode expansion mode solver
O. V. Ivanova, M. Hammer, R. Stoffer, E. van Groesen
MESA+ Institute for Nanotechnology, AAMP group, University of Twente,
P.O. Box 217, 7500 AE, Enschede, The Netherlands
A variational approach for the semivectorial modal analysis of dielectric waveguides with arbitrary piecewise
constant rectangular 2D crosssections is developed. It is based on a representation of a mode profile as a super
position of modes of constituting slab waveguides times some unknown continuous coefficient functions, defined on
the entire coordinate axis. The propagation constant and the lateral functions are found from a variational prin
ciple. It appears that this method with one or two modes in the expansion preserves the computational efficiency
of the standard effective index method while providing more accurate estimates for propagation constants, as well
as welldefined continuous approximations for mode profiles. By including a larger number of suitable trial fields,
the present approach can also serve as a technique for rigorous semivectorial mode analysis.
1 Introduction
A variety of methods has been developed for the modal analysis of dielectric waveguides. References [1], [2], [3]
present a detailed overview of the techniques. Among these, one of the most popular approximate approaches is
the Effective Index Method (EIM) [4]. While being rather intuitive and computationally very efficient, the inherent
approximations limit the range of its applicability: problems that occur are e.g. undefined effective indices in a
slab region below cutoff and, as a result, only rather heuristically defined field profiles. Several methods exist that
in certain respects might be viewed as improvements of the EIM; we mention the (Film) Mode Matching Method
(MMM) [5] [6], in which the total field is expanded in the terms of the local slab modes and later matched across
