Absorption and amplification singularities in metasurface etalons with gain

Passive reflective metasurfaces can possess perfect absorption conditions: Singular scattering anomalies at which all impinging light is absorbed. Perfect absorption is a common yet powerful metasurface design option with applications in energy harvesting, sensing, and more. Less common is the inclusion of optical gain to the system, which can give rise to a singular condition for perfect amplification. We analyze absorption and amplification singularities in plasmon antenna metasurface etalons with gain with a simple transfer matrix model. Our etalon follows the Salisbury screen design: A metal ground plate spaced by dielectric medium from an array of resonant plasmonic scatterers. We include frequency dispersive models for gain media and discuss the limitations of time reversal symmetry arguments for relating gain singularity conditions (reflectivity poles) to the well-known perfect absorption conditions (reflectivity zeros) of metasurface etalons. We show that for metasurface etalons with both gain and loss, gain can induce both perfect absorption and gain singularities, and we describe topological constraints on their creation and annihilation. Our findings have implications for the fields of non-Hermitian photonics, parity-time symmetric scattering systems, and dynamically controllable active metasurface pixels.