Goal oriented adaptive finite element method for precise simulation of optical components

Adaptive finite elements are the method of choice for accurate simulations of optical components. However as shown recently by Bienstman et al. many finite element mode solvers fail to compute the propagation constant's imaginary part of a leaky waveguide with sufficient accuracy. In this paper we show that with a special goal oriented error estimator for capturing radiation losses this problem is overcome.

[1]  Matti Lassas,et al.  Complex Riemannian metric and absorbing boundary conditions , 2001 .

[2]  Frank Schmidt,et al.  Solving Time-Harmonic Scattering Problems Based on the Pole Condition II: Convergence of the PML Method , 2003, SIAM J. Math. Anal..

[3]  O. Martin,et al.  Green's tensor technique for scattering in two-dimensional stratified media. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  S. Burger,et al.  JCMmode: an adaptive finite element solver for the computation of leaky modes , 2005, SPIE OPTO.

[5]  Rolf Rannacher,et al.  A posteriori error control for finite element approximations of elliptic eigenvalue problems , 2001, Adv. Comput. Math..

[6]  Rolf Rannacher,et al.  An optimal control approach to a posteriori error estimation in finite element methods , 2001, Acta Numerica.

[7]  Matti Lassas,et al.  Analysis of the PML equations in general convex geometry , 2001, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[8]  L. Zschiedrich,et al.  J an 2 00 6 Advanced Finite Element Method for Nano-Resonators , 2006 .

[9]  Stefano Selleri,et al.  Modelling leaky photonic wires: A mode solver comparison , 2007 .

[10]  Peter Monk,et al.  The Perfectly Matched Layer in Curvilinear Coordinates , 1998, SIAM J. Sci. Comput..

[11]  Frank Schmidt,et al.  Solving Time-Harmonic Scattering Problems Based on the Pole Condition I: Theory , 2003, SIAM J. Math. Anal..

[12]  Frank Schmidt,et al.  A New Approach to Coupled Interior-Exterior Helmholtz-Type Problems: Theory and Algorithms , 2002 .

[13]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .