Fast iterative, coupled-integral-equation technique for inhomogeneous profiled and periodic slabs

Area of Science:

• Electromagnetics
• Computational Physics
• Materials Science

Background:

• Scattering from periodic structures is crucial in optics and photonics.
• Existing methods struggle with complex geometries and material variations.
• Efficient computation is needed for analyzing advanced optical components.

Purpose of the Study:

• Develop a fast computational technique for plane-TE-wave scattering.
• Address scattering from 2D inhomogeneous periodic structures with curvilinear boundaries.
• Enhance existing integral equation methods for broader applicability.

Main Methods:

• Derivation of coupled-integral-equations (CIEs) in the spectral domain from volume electric field integral equations.
• Iterative solution of CIEs using the biconjugate gradient stabilized method.
• Development of an efficient preconditioning operator (PO) based on analytical inversion for accelerated convergence.

Main Results:

• The CIE technique demonstrates linear arithmetic complexity and memory requirements.
• The proposed preconditioning operator significantly speeds up the iterative solution.
• Numerical studies confirm the technique's potential and flexibility across various material parameters.

Conclusions:

• The developed fast CIE technique offers an efficient solution for scattering problems.
• The method is applicable to a wide range of periodic 2D inhomogeneous structures.
• It provides accurate results for structures with diverse dielectric and metallic components.