Abstract
The conditions securing stability in configurations that employ gain media, carry vital information for the operation and functionality of the respective systems. These constraints are determined for a generic photonic setup comprising two concentric, passive or active, cylindrical impedance metasurfaces, by assuming their size small compared to the oscillation wavelength. Such an approximation, permits the analytical determination of the unstable poles across the complex frequency plane, which is otherwise a computationally cumbersome task. The absorbing and scattering response of the structure, when excited by various primary sources, unveils the dynamics behind the supported resonances and reveals the limits in its performance while respecting stability restrictions. The reported results may assist substantially the modeling and stable design of devices involving this ubiquitous cylindrical component in numerous applications spanning from radiation pattern control and angular momentum transformation to active cloaking and reconfigurable wavefront manipulation.