The search for a reliable, low-cost, general-application modeling tool has been assuming a growing importance among integrated optics theoreticians. For example, finite-difference (FD) based algorithms have given rise to commercial photonic CAD software programs that are less expensive, from both financial and computational points of view, than finite-elements (FEM) based ones. On the other hand, the former show some computational drawbacks that do not permit to consider them as of truly general application, while the latter provide extremely reliable modeling tools. Recently, a few numerical techniques (alternative to both FD and FEM methods) have been proposed, mainly in view of an improvement in flexibility and a reduction in computational cost. In particular, methods based on the Galerkin approach and Krylov reduction have proven particularly effective for the solution of the Helmholtz equation in a very wide class of integrated optical structures. Moreover, these methods are very promising from the point of view of reliability and are computationally non-expensive. Here, we present the implementation of one of such numerical techniques, the so-called Arnoldi-Galerkin method, together with that of a home-made FEM software program. A comparison with the results from other algorithms is shown as well.
In search of highly effective modeling tools for the CAD of photonic devices and components
BELLANCA, Gaetano;
2001
Abstract
The search for a reliable, low-cost, general-application modeling tool has been assuming a growing importance among integrated optics theoreticians. For example, finite-difference (FD) based algorithms have given rise to commercial photonic CAD software programs that are less expensive, from both financial and computational points of view, than finite-elements (FEM) based ones. On the other hand, the former show some computational drawbacks that do not permit to consider them as of truly general application, while the latter provide extremely reliable modeling tools. Recently, a few numerical techniques (alternative to both FD and FEM methods) have been proposed, mainly in view of an improvement in flexibility and a reduction in computational cost. In particular, methods based on the Galerkin approach and Krylov reduction have proven particularly effective for the solution of the Helmholtz equation in a very wide class of integrated optical structures. Moreover, these methods are very promising from the point of view of reliability and are computationally non-expensive. Here, we present the implementation of one of such numerical techniques, the so-called Arnoldi-Galerkin method, together with that of a home-made FEM software program. A comparison with the results from other algorithms is shown as well.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
