Stabilized scattering matrix formulation for 2D periodic multilayer dielectrics

This paper proposes an alternative semi-analytical Fourier modal method adapted for general periodic anisotropic gratings made of dielectrics with moderate to low index profiles corresponding to materials ranging from conventional dielectric 3D printing materials to ceramic materials. The proposed method is closely related to the classical rigorous coupled wave analysis built on scattering matrices; however, a key difference is that the new scheme relies on the recently reported concept of stabilized wave propagation operators, leading to improved numerical stability and accuracy for a wider range of structures where, <i>e.g.</i>, evanescent waves are present. Multilayer structures can be handled in a stable manner using the dissipative property of the Redheffer star product for cascading scattering matrices from which the reflection and transmission of the whole structure is derived. Numerical examples of practical interest as well as importance for future development demonstrate the accuracy, efficiency, and stability of the method through comparison with solutions obtained by finite elements and results published in the literature.