We determine rigorously the effective permeability of magnetic metamaterialscomposed of passive particles exhibiting magnetic resonances. The effectivepermeability is expressed in terms of circuit parameters characteristic tothese particles (L, C, and R) and particle geometry. The derivation takes intoaccount the magnetic coupling between particles. We show that a biggerconcentration of particles leads to an improvement in the metamaterialperformances (such as bandwidth or loss tangent), but this effect saturates asthe particles are packed more tightly. The theory is validated throughnumerical simulations of physically realizable metamaterials.
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