Investigation of methods to set up the normal vector field for the differential method

Stephan Rafler; Peter Götz; Matthias Petschow; Thomas Schuster; Karsten Frenner; Wolfgang Osten

doi:10.1117/12.780482

25 April 2008 Investigation of methods to set up the normal vector field for the differential method

Stephan Rafler, Peter Götz, Matthias Petschow, Thomas Schuster, Karsten Frenner, Wolfgang Osten

Author Affiliations +

Proceedings Volume 6995, Optical Micro- and Nanometrology in Microsystems Technology II; 69950Y (2008) https://doi.org/10.1117/12.780482
Event: SPIE Photonics Europe, 2008, Strasbourg, France

Abstract

In Fourier modal methods like the RCWA and the Differential Method the Li-rules for products in truncated Fourier space have to be obeyed in order to achieve good convergence of the results with respect to the mode number. The Lirules have to be applied differently for parts of the field that are tangential and orthogonal to material boundaries. This is achieved in the Differential Method by including a field of vectors in the calculation that are normal to the material boundaries. The same can be done laterally in each layer of an RCWA calculation of a 2-D periodic structure. It turns out that discontinuities in the normal vector field can disturb the computation especially when metallic materials are dominant in the structure which would make the usefulness of the normal vector method questionable. So it is of great importance to investigate how normal vector fields can be established with as few discontinuities as possible. We present various methods for the 2-D RCWA and the 1-D and 2-D Differential Method and compare the respective convergence behaviors. Especially we emphasize methods that are automatic and require as few user input as possible.

Citation Download Citation

Stephan Rafler, Peter Götz, Matthias Petschow, Thomas Schuster, Karsten Frenner, and Wolfgang Osten "Investigation of methods to set up the normal vector field for the differential method", Proc. SPIE 6995, Optical Micro- and Nanometrology in Microsystems Technology II, 69950Y (25 April 2008); https://doi.org/10.1117/12.780482

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