New dual structures which are aperture-type Frequency Selective Surfaces (FSS) residing on a dual magnetic dielectric slab and patch-type FSS on an electric dielectric slab are proposed. The relative permittivity of electric dielectric is equal to the relative permeability of magnetic dielectric. The duality of aperture-type and patch-type FSS without any dielectric with an electric dielectric and with a dual magnetic dielectric are analyzed. The spectral Green's functions of arrays on different slabs are derived through spectral domain immittance approach. The affection of substrate on the reflection and transmission characteristics of rectangular FSS compared with the FSS in a free space is considered, and the effects are discussed through changing thickness and parameter of dielectric. It shows that the proposed structures are complementary around resonant frequency, but resonant frequency offset emerges, and the magnitude of resonant frequency offset has relations with the dielectric type, thickness and parameter.
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