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

Area of Science:

• Computational physics
• Numerical methods
• Materials science

Background:

• Spectral simulation methods are crucial for analyzing periodic scattering geometries.
• Accurate handling of material interfaces is essential for simulation convergence.
• Existing methods face challenges with arbitrarily shaped interfaces.

Purpose of the Study:

• To adapt the normal vector field framework for improved spectral simulations.
• To enhance convergence near complex material interfaces in periodic scattering.
• To enable flexible and continuous parameterization of geometries.

Main Methods:

• Developed two adapted formulations of the normal vector field framework: one for isotropic and one for anisotropic media.
• Confined normal vector field generation to a limited prolongation region around material interfaces.
• Utilized geometrical transformations (rotation, translation) for individual scattering objects.
• Implemented a cut-and-connect strategy to construct complex geometries from basic building blocks.

Main Results:

• Achieved improved convergence in spectral simulations near arbitrarily shaped material interfaces.
• Enabled flexible application of geometrical transformations per scattering object.
• Facilitated the composition of general geometries using elementary building blocks.
• Resulted in a framework for continuously parameterized geometries.

Conclusions:

• The adapted normal vector field framework significantly enhances spectral simulations for periodic scattering.
• The new methods offer greater flexibility in defining and manipulating complex geometries.
• This work provides a robust approach for creating continuously parameterized scattering systems.