In this work, a new implementation of the finite-difference (FD) modal method (FDMM) based on an iterative approach to calculate the eigenvalues and corresponding eigenfunctions of the Helmholtz equation is presented. Two relevant enhancements that significantly increase the speed and accuracy of the method are introduced. First of all, the solution of the complete eigenvalue problem is avoided in favor of finding only the meaningful part of eigenmodes by using iterative methods. Second, a multigrid algorithm and Richardson extrapolation are implemented. Simultaneous use of these techniques leads to an enhancement in terms of accuracy, which allows a simple method such as the FDMM with a typical three-point difference scheme to be significantly competitive with an analytical modal method.
© 2013 Optical Society of America
Diffraction and Gratings
Original Manuscript: August 16, 2013
Revised Manuscript: October 21, 2013
Manuscript Accepted: October 21, 2013
Published: November 13, 2013
Igor Semenikhin and Mauro Zanuccoli, "Computationally efficient finite-difference modal method for the solution of Maxwell’s equations," J. Opt. Soc. Am. A 30, 2531-2538 (2013)