 
Summary: Ef®cient interface conditions based
on a 5point ®nite difference operator
R . S T O F F E R
Faculty of Applied Physics and Faculty of Mathematical Sciences, University
of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
H . J . W . M . H O E K S T R A
Lightwave Device Group, Faculty of Applied Physics, University of Twente,
PO Box 217, 7500 AE Enschede, The Netherlands
Received 14 January; revised and accepted 31 March 1998
A new 5point ®nite difference operator is developed for integrated optics simulations.
Interfaces are taken into account accurately. The eigenvalues of the discretization
matrix converge rapidly, according to ODx4
. Implementation of the operator in a beam
propagator leads to a highly ef®cient computation scheme.
1. Introduction
When designing devices in integrated optics, it is usually necessary to perform simulations
on these structures, since normally no analytical solutions are known. Therefore, it is
necessary to have beam propagation methods and mode solvers that are as accurate and as
fast as possible.
Both beam propagation methods and mode solvers rely on accurate approximation of
