Magnetic polarizability of planar extremely subwavelength Mu-negative metamaterials

An planar extremely subwavelength Mu-negative metamaterials is presented at low frequencies, composed of periodically arranged lumped components and subwavelength distributed structures with the combination of double layer rectangular spiral unit structure. The magnetic polarizability is induced by the resonance of the dual-layer metamaterials excited by an alternating electromagnetic field. The equivalent value of the magnetic polarizability in the metamaterials is obtained with an integral treatment of the magnetic polarizability distribution.