Stable GSTC Formulation for Maxwell’s Equations

We revisit the classical zero-thickness generalized sheet transition conditions (GSTCs) that are a key tool for efficiently designing metafilms able to control the flow of light in the desired way. It is shown that it is more convenient to use an enlarged formulation of the GSTC in which the original metafilm is replaced by GSTCs that exclude the layer from the physical or computational domain. These new “layer” transition conditions have the same form as their “sheet” analogs; hence, they do not necessitate additional complications in their use, and their advantage is that they provide a well-posed problem and, hence, guarantee the stability of numerical schemes in the time domain. These assessments are demonstrated for an all-dielectric structure; the effective susceptibility tensors are derived due to asymptotic analysis combined with homogenization technique, and bounds for the susceptibilities entering the balance of energy are provided. While negative constant susceptibilities appear in the classical zero-thickness GSTCs, their values in the enlarged formulation are always positive, which ensures the stability of the effective problem. The validation of the effective model is provided by means of comparison with direct numerics in two and three dimensions.