Abstract: In this paper, we establish a novel unique continuation property (UCP) for the Maxwell system locally around a vertex corner. It is shown that if certain homogeneous conditions are imposed on the planes forming the vertex corner, the electric/magnetic field must vanish to a certain order. We derive the vanishing order and relate it to the polyhedral angles of the vertex corner. This extends the recent results in [21] where the UCP was considered associated with an edge corner. This type of UCP study originated from the study of a longstanding problem in inverse scattering theory. 

Key words: Maxwell system, Time-harmonic electromagnetic scattering, Unique continuation, Vanishing order, Vertex corner, Inverse scattering, A single far-field measurement