Second-Order Procedure for Modeling Dielectric Material Interfaces in Structured Nonorthogonal Finite-Difference Discretizations of Maxwell's Equations

Structured nonorthogonal finite-difference discretizations of Maxwell's equations are often employed to incorporate curved dielectric material interfaces. As part of this process, it is necessary to employ an adequate procedure to enforce the tangential field continuity conditions at the locations of the interfaces where the components of the permittivity tensor are discontinuous. This contribution proposes a second-order domain-splitting procedure that can accomplish this task without assuming that the permittivity tensor components are piecewise constant or diagonal. As explained, this feature is needed to exploit the full geometrical flexibility of structured grid generation. The proposed domain-splitting procedure consistently yields a global error that is second-order accurate even in extreme cases where the components of the permittivity tensor have a change of sign or a sharp jump.