Electromagnetic Theory of Metasurface Perfect Magnetic Conductor (PMC)

Abstract: Artificial magnetic conductors (AMCs) mimic the idealized boundary condition of a perfect magnetic conductor (PMC), which reflects electromagnetic waves with a preserved electric field and inverted magnetic field. Despite their usefulness, existing AMC implementations often rely on complex or impractical designs, and lack a clear electromagnetic theory explaining their behavior, especially under oblique or polarization-diverse incidence. This work addresses these limitations by presenting a rigorous electromagnetic framework for PMC metasurfaces based on dipolar and quadrupolar surface susceptibilities within the generalized sheet transition conditions (GSTCs) formalism. We show that achieving polarization- and angle-independent PMC behavior requires a specific set of heteroanisotropic (nonlocal) susceptibilities, and we derive closed-form expressions for angular scattering that include higher-order multipole contributions. A physically realizable, asymmetric metasurface structure is then designed to satisfy these theoretical conditions. Despite its geometric asymmetry, the proposed structure exhibits a isotropic PMC response at resonance, confirmed by full-wave simulations and multipolar susceptibility extraction. These results demonstrate how properly engineered surface multipoles can yield angularly independent magnetic boundary conditions using only thin, passive metallic layers. This work bridges the gap between AMC design and electromagnetic theory, and enables a new class of angle-independent metasurface reflectors for more accurate simulations, optimizations and innovative AMC designs.