Optical scattering problems in guided wave photonics are addressed. We represent the unknown optical fields as superpositions of 1D slab modes bounded by PMLs. By applying a variational principle, the problems are reduced to lower dimensional systems of differential equations for the unknown coefficient functions, which are solved using the finite elements method. Dirichlet to Neumann maps allow influx to be prescribed and radiation to freely pass the computational window boundaries. Expansions with one or a few modes give a quick, effective index-like approximation; more modes provide more accurate solutions. We give examples for a series of 2-D configurations, where reliable reference data is available.
|Title of host publication||First International Workshop on Theoretical and Computational Nano-Photonics TaCoNa-Photonics, Conference Proceedings|
|Place of Publication||Karlsruhe, Germany|
|Publisher||University of Karlsruhe|
|Number of pages||1|
|ISBN (Print)||not assigned|
|Publication status||Published - 3 Dec 2008|
Ivanova, A., Stoffer, R., & Hammer, M. (2008). A dimensionality reduction technique for scattering problems in photonics. In First International Workshop on Theoretical and Computational Nano-Photonics TaCoNa-Photonics, Conference Proceedings (pp. 47). Karlsruhe, Germany: University of Karlsruhe.