 
Summary: A Variational Vectorial Mode Solver
O.V. (Alyona) Ivanova, Remco Stoffer, Manfred Hammer and E. (Brenny) van Groesen
MESA+ Institute for Nanotechnology, AAMP group, University of Twente, The Netherlands
o.v.ivanova@math.utwente.nl
A variational method for the fully vectorial mode analysis of lossless dielectric waveguides with piecewise
constant rectangular refractive index distributions is proposed.
Summary
An extension of the scalar Mode Expansion Mode Solver [1] to fully vectorial simulations is dis
cussed. The method uses a six component variational formulation of the Maxwell equations [2] to
gether with approximations of each component of the vector field by specific superpositions of some
given basis functions, depending on one of the coordinates, times unknown coefficient functions that
are defined on the entire second coordinate axis. In principle there is some freedom in choosing the
basis functions; we use the vector field components of modes of the constituting vertical slices of the
waveguide.
It turns out that with our field template the problem of finding the unknown lateral coefficient
functions reduces to finding those, which correspond to only two field components; the computational
effort becomes comparable to the scalar case [1] or the Film Mode Matching method [3].
Just like the scalar approach this method can be used with only a few terms in the expansion
for rough approximations; the technique can then be compared to a semivectorial Effective Index
Method. With a suitable choice of basis fields a reasonable approximation can be achieved with a rel
