 
Summary: Variational modelling for integrated optical devices
Seminar Mathematical Physics, Autumn 2002
E.(Brenny) van Groesen (groesen@math.utwente.nl)
AAMP, University of Twente
version 23 September 2002
Abstract
Variational modelling is the use of a variational structure of a problem to simplify the model or
to find approximations of the solutions in a consistent way. In both cases the consistent use of the
variational structure consists in restricting the relevant functionals to smaller sets and consider the
EulerLagrange equation on the restricted set instead of on the original set. One type of restriction
may be to specialise the set of phenomena. To find approximate solutions, parameterized manifolds
of functions are used to restrict the functional; either lowdimensional manifolds of appropriate
`trial'functions, or highdimensional linear subspaces for numerical discretizations.
In these notes another type of restriction will be discussed. We describe how typical problems
for alloptical devices in integrated optics have to be considered on unbounded domains. The
variational structure is then exploited to confine the problem to a finite domain by restriction
to functions that satisfy, or approximate, the equations on the exterior domain. For a typical
reflection problem this leads to boundary conditions that are `transparent' for apriorily unknown
radiation and transmittance, but allow a prescribed influx of light into the structure.
1 Prelim: Macroscopic Maxwell Equations
