Abstract: An electromagnetic resonator has two or more non-intersecting, substantially overlapping surfaces of approximately similar size and shape separated from one another by a distance which is small in comparison to the physical extent of the surfaces. One or more substantially non-intersecting, electrically conductive paths cover substantial portions of each surface. The widths of the paths are substantially smaller than the physical extent of the surfaces. No path on any one of the surfaces is electrically connected to a path on any of the other surfaces. The conductive paths are oriented such that, for each of the surfaces, macroscopic current flows, with respect to the surfaces, in a direction other than the direction in which microscopic current flows in the paths.