A Vectorial Discontinuous Galerkin Time-Domain Method Incorporating Generalized Sheet Transition Conditions

Generalized Sheet Transition Conditions (GSTCs) in Electromagnetic Metasurface Modeling

“…Some methods for implementing these simplifications and calculation of the tensors are presented in [48]. Although, to our best knowledge, there is no commercial electromagnetic software on the market using GSTCs [50], [51], different numerical methods have employed GSTCs for electromagnetic simulation of metasurfaces, e.g., the discontinuous Galerkin time-domain (DGTD) in [50], [51], the finite difference time-domain (FDTD) in [12], [52], the finite-element method (FEM) in [53], the finite difference frequency-domain (FDFD) in [54], the spectral-domain integral equations (SD-IEs) in [55], the multifilament current (MFC) in [56], the IE-based method of moments (IE-MoM) in [57]. In [50], for example, they introduced the "virtual edges" after and before the metasurface to incorporate the DGTD method on GSTCs (see Fig.…”

“…However, it is worth noting that in some cases, it is convenient to assume that the metasurface has zero normal polarizability or susceptibility components; the number of tangential susceptibilities can be reduced to 16, as shown in (52) [48], [84]. Therefore, ( 48) and ( 49) can be written as (51).…”

“…The array equation specified in (52) involves 16 unknown variables, which results in a heavily underdetermined system that is not well-constrained when combined with the matrix equivalents of (51) [48]. In order to solve the inverse synthesis problem presented in (51), there are three primary approaches discussed in [48]. (I) Variable reduction method: This aims to reduce the 16 unknown variables to four, making system (51) solvable or determinate.…”

“…Currently, commercial full-wave simulators can model various boundary conditions, including the perfectly matched layer (PML), perfect electric conductor (PEC), periodic boundary condition, radiation boundary condition, and perfect magnetic conductor (PMC) [12]. As already mentioned, there has not been any commercial simulation tool capable of incorporating GSTCs [50], [51]. The importance of these numerical method examples lies in paving the way for further research in developing GSTCs modeling for designing various metasurface applications with shorter simulation times [50], [51].…”

“…As already mentioned, there has not been any commercial simulation tool capable of incorporating GSTCs [50], [51]. The importance of these numerical method examples lies in paving the way for further research in developing GSTCs modeling for designing various metasurface applications with shorter simulation times [50], [51].…”