Effect of losses on the performance of very thin artificial magnetic conductors

Artificial magnetic conductors (AMCs) are utilized as in-phase reflectors (unlike ground planes made of good conductors) for improving the radiation performance of thin antennas. Periodically patterned resonant conductor geometries on top of grounded dielectric substrates, namely metasurfaces, is a suitable way to achieve the zero-degrees reflection phase on their surfaces upon plane-wave incidence. However, for extremely subwavelength AMC, losses play a significant role, and may completely destroy the required zero-degree reflection phase performance. For example, in millimeter-wave applications, the losses in conductors becomes important when the AMC is implemented on-chip and thus in a very subwavelength thickness. Under the effect of these losses, the zero-degree reflection phase is not guaranteed and the metasurface may not act as an AMC at the resonance frequency. In this study, we employ the transmission line formalism for plane waves impinging on a metasurface, which is modelled by a lumped circuit that accounts also for the losses. Then we determine a general threshold condition to quantify the emergence of AMC property for a resonant metasurface in terms of the lumped circuit model parameters. Finally we establish a couple of practical cases where we emphasize the impact of losses by reporting relevant circuit model parameters.