# Comparison of Tensor Boundary Conditions (TBCs) with Generalized Sheet Transition Conditions (GSTCs)

## TL;DR

This paper analyzes the relationship between Tensor Boundary Conditions (TBCs) and Generalized Sheet Transition Conditions (GSTCs), showing their equivalence under certain conditions and highlighting limitations in modeling complex metasurfaces.

## Contribution

It establishes the equivalence between TBCs and a subset of GSTCs, and discusses how extending TBCs affects their ability to model metasurfaces.

## Key findings

- TBCs with 3 scalar parameters are equivalent to a subset of GSTCs.
- Extending TBCs to tensor parameters aligns with tangential GSTCs.
- Extended TBCs lack polarization physics of sheet media.

## Abstract

This paper compares Tensor Boundary Conditions (TBCs), which were introduced to model multilayered dielectric structures, with Generalized Sheet Transition Conditions (GSTCs), which have been recently used to model metasurfaces. It shows that TBCs, with their 3 scalar parameters, are equivalent to the direct-isotropic -- cross-antiisotropic, reciprocal and nongyrotropic subset of GSTCs, whose 16 tangential (particular case of zero normal polarizations) or 36 general susceptibility parameters can handle the most general bianisotropic sheet structures. It further shows that extending that TBCs scalar parameters to tensors and allowing a doubly-occurring parameter to take different values leads to a TBCs formulation that is equivalent to the tangential GSTCs, but without reflecting the polarization physics of sheet media, such as metasurfaces and two-dimensional material allotropes.