Local normal vector field formulation for periodic scattering problems formulated in the spectral domain

Abstract

We present two adapted formulations, one tailored to isotropic media and one for general anisotropic media, of the normal-vector field framework previously introduced to improve convergence near arbitrarily shaped material interfaces in spectral simulation methods for periodic scattering geometries. The adapted formulations enable the definition and generation of the normal-vector fields to be confined to a region of prolongation that includes the material interfaces but is otherwise limited. This allow for a more flexible application of geometrical transformations like rotation and translation per scattering object in the unit cell. Moreover, these geometrical transformations enable a cut-and-connect strategy to compose general geometries from elementary building blocks. The entire framework gives rise to continuously parameterized geometries.

A 3D spatial spectral integral equation method for electromagnetic scattering from finite objects in a layered medium

“…(4) yields poor convergence since it violates the Li-rules (1996). We propose to use a normal-vector field approach (Popov and Nevire 2001; Beurden and Setija 2017). In Dilz et al.…”

“…(2017) it is shown that when the Li-rules are satisfied, good convergence is reached in a continuous spectral discretization in a formulation similar to the RCWA formulation by Granet and Guizal (1996). We follow the same approach as Popov and Nevire (2001), Beurden (2011, 2012), Beurden and Setija (2017), van Beurden (2013) in constructing normal-vector fields and the following is intended as a short summary of that method.…”

“…2008; Götz et al. 2008; Beurden and Setija 2017) can be a good tool to systematically construct an auxiliary field .…”

“…More intricate objects can then be constructed from combinations of a variety of such objects. More details and examples of this construction can be found in Beurden and Setija (2017). …”

“…Here, we propose a generalization of this method to three dimensions. Inspired by Beurden and Setija (2017), we show that a normal-vector field formulation (Popov and Nevire 2001) can be used for three-dimensional scattering to replace the field-material interaction.…”