Non-dipole interaction of helix inclusions in metamaterials with artificial permeability

An analytic approach to calculate induced permeability of metamaterial filled with helix inclusions is developed. For an electrically small coil, the dynamic magnetization is determined by lumped inductance, capacitance, and resistance that are calculated from the coil design. The susceptibility of a coil is shown to be close to that of diamagnetic ellipsoid of the same elongation. Contrary to permeable particles in a composite, the coils screen each other thus decreasing the magnetic response of metamaterial compared to total response of comprised coils. The filling effect on magnetic spectrum of metamaterial is analyzed and verified by measurements for the case of identical coaxially placed coreless coils. The critical filling where magnetic response of metamaterial is maximal depends on coil shape and resistance. The coil-filled metamaterials may find applications as permeable EMI suppressors or microwave absorbers free of Snoek or Acher limitations on the high-frequency permeability, as well as of Curie limitation on the high-temperature magnetic performance.