Abstract: An electromagnetic antenna includes a multiply connected surface, such as a toroidal surface; first and second insulated conductors; and first and second signal terminals. The first insulated conductor extends around and over the surface with a first pitch or winding sense from a first node to a second node. The second insulated conductor also extends around and over the surface with a second pitch or winding sense, which is opposite from the first pitch or winding sense, from a third node to a fourth node. The first and second insulated conductors are contrawound relative to each other around and over the surface. In one embodiment of the invention, at least one of the nodes is open. In other embodiments of the invention, the signal terminals are structured for connection to a cooperative antenna structure.