Cramér-Rao bounds for determination of electric and magnetic susceptibilities in metasurfaces.

Accurate and robust characterization of metasurfaces and metamaterials in terms of effective parameters is critical to the design of novel metadevices. We compute the Cramér-Rao lower bounds on the variance of any estimator for both the electric and magnetic surface susceptibilities of metasurfaces. We show that retrieval of such effective properties is inherently difficult around resonances, most notably for low-loss metasurfaces. We also put forth a least-squares estimator to mitigate this difficulty for the normal components of susceptibility tensors, which are observed to be the most ill-behaved. The present work is relevant to the development of loss-compensated metasurfaces for which noise has to be closely considered for accurate and robust device characterization.