TY - JOUR
T1 - Modified S-matrix algorithm for the aperiodic Fourier modal method in contrast-field formulation
AU - Pisarenco, M.
AU - Maubach, J.M.L.
AU - Setija, I.D.
AU - Mattheij, R.M.M.
PY - 2011
Y1 - 2011
N2 - The Fourier modal method (FMM) is a method for efficiently solving Maxwell’s equations with periodic boundary conditions. In order to apply the FMM to nonperiodic structures, perfectly matched layers need to be placed at the periodic boundaries, and the Maxwell equations have to be formulated in terms of a contrast (scattered) field. This reformulation modifies the structure of the resulting linear systems and makes the direct application of available stable recursion algorithms impossible. We adapt the well-known S-matrix algorithm for use with the aperiodic FMM in contrast-field formulation. To this end, stable recursive relations are derived for linear systems with nonhomogeneous structure. The stability of the algorithm is confirmed by numerical results.
AB - The Fourier modal method (FMM) is a method for efficiently solving Maxwell’s equations with periodic boundary conditions. In order to apply the FMM to nonperiodic structures, perfectly matched layers need to be placed at the periodic boundaries, and the Maxwell equations have to be formulated in terms of a contrast (scattered) field. This reformulation modifies the structure of the resulting linear systems and makes the direct application of available stable recursion algorithms impossible. We adapt the well-known S-matrix algorithm for use with the aperiodic FMM in contrast-field formulation. To this end, stable recursive relations are derived for linear systems with nonhomogeneous structure. The stability of the algorithm is confirmed by numerical results.
U2 - doi:10.1364/JOSAA.28.001364
DO - doi:10.1364/JOSAA.28.001364
M3 - Article
VL - 28
SP - 1364
EP - 1371
JO - Journal of the Optical Society of America A, Optics, Image Science and Vision
JF - Journal of the Optical Society of America A, Optics, Image Science and Vision
SN - 1084-7529
IS - 7
ER -