Go itami * & osamu Sakai A metal plate array (MpA) which is a structure complimentary to a metal hole array (MHA), supports spoof surface plasmon polaritons (SSpp) as well as an MHA does. Babinet's principle attributes the phenomenon of duality to transmission characteristics of the complimentary impedance surfaces because of the symmetry of the behaviors of electric and magnetic fields. However, it is also a fact that the complimentary structures do not follow this principle if they have wavelength-size thickness, because electromagnetic waves do not treat such thick structures as a boundary surface but as propagation spaces with the specific boundaries such as a waveguide which shows SSPP modes. If the thickness is so small that it is negligible, Babinet's principle is still valid, while it has been uncertain how the layer thickness works to break the principle as it is increased. The unconfirmed transformation is revealed analytically and experimentally with the use of MpAs and MHAs of varying thicknesses. The behavior of electromagnetic waves interacting with objects is broadly classified into two cases. For wavelengths significantly larger than the object, the wave's electric fields are treated as near fields and electromagnetic behavior is expressed as a scattering phenomenon. For wavelengths much smaller than the object the wave's electric fields are treated as far fields and the electromagnetic behavior is expressed as propagating waves, either transmitted or reflected. However, when the wavelength is of the same order as the object size, the scattering phenomena become more complex. In this case, if such objects are perforated periodically, they can be provided an interesting medium with properties, otherwise not attainable with naturally occurring materials, such as a negative refractive index (NRI) 1-6. In general, these artificial structures are called metamaterials. In 2000, Pendry showed theoretically the concept of a perfect lens with a negative refractive index (NRI) medium 1 , and in 2001, Shelby et al. verified the possibility of an NRI experimentally by using the two artificial resonators for negative permeability and permittivity media 2. Their studies demonstrated the feasibility of metamaterials, and accelerated the advances in the field in recent years 1-3, 7-12. In such studies, a split ring resonator (SRR) is often used as a negative permeability medium for NRI realization. And the complementary split ring resonator (CSRR) is also known as the resonator for negative permittivity realization, based on Babinet's principle 12-16. In these two resonators, the essential difference in their resonance is based on the following electromagnetic radiation mechanisms: SRR radiates the topologically overlaid waves from the infinitesimal electric dipoles, and CSRR radiates them from the infinitesimal magnetic dipoles. Based on this principle, the SRR and CSRR show band-stop and band-pass characteristics if they are used as planar spatial filters. A frequency selective surface (FSS) is also a spatial f...