An exploration of the electromagnetic boundary conditions for two-dimensional materials with out-of-plane polarization

We investigate the consequences of the electromagnetic boundary conditions governing isotropic 2D materials with out-of-plane (OOP) polarization, inserted between two distinct dielectric media. In extending the classical set of jump conditions, we introduce an effective screened OOP polarization density to account for arbitrary dielectric surroundings and derive modified Fresnel reflection coefficients. We compare several models of dielectric screening against ellipsometric phase data for graphene-on-substrate configurations, revealing that although current experimental precision does not conclusively favour one model, the differences are measurable. Furthermore, we derive a plasmon dispersion relation for doped graphene showing a non-monotonic character resulting from coupling between the in-plane and OOP polarization mechanisms at low frequencies. Supplementary Information: The online version contains supplementary material available at 10.1007/s00340-026-08630-3.