Summary: New true fourth-order accurate scalar
beam propagation methods for
both TE and TM polarization
R . S T O F F E R 1
, P . A . A . J . B O L L E R M A N 1
, H . J . W . M . H O E K S T R A 1
E . V A N G R O E S E N 2
A N D F . P . H . V A N B E C K U M 2
Faculty of Applied Physics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;
Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, The
Received 5 November 1998; accepted 24 February 1999
Abstract. New 2D scalar beam propagation methods for both TE and TM polarization are presented.
Both second- and fourth-order accurate schemes, in the lateral stepsize, are shown. The methods use
uniform discretization and can handle arbitrary positions of interfaces between materials with dierent
refractive indices. Either Transparent Boundary Conditions or Perfectly Matched Layers are used at the
boundary of the computational window.