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We present a theory of perfect absorption in a bilayer model composed of a mu-near-zero (MNZ) metamaterial (MM) absorbing layer on a metallic substrate. Our analytical solutions reveal that a MM layer with a large purely imaginary permeability and a moderate permittivity backed by a metallic plane has a zero reflection at normal incidence when the thickness is ultrathin. The impedance-mismatched metamaterial absorber (MA) can be 77.3% thinner than conventional impedance-matched MAs with the same material loss in order to get the same absorption. A microwave absorber using double-layered spiral MMs with a thickness of only about one percent of the operating wavelength is designed and realized. An absorption efficiency above 93% at 1.74 GHz is demonstrated experimentally at illumination angles up to 60 degrees. Our absorber is 98% lighter than traditional microwave absorbers made of natural …