Fundamental properties of canonical soft and hard surfaces, perfect magnetic conductors and the newly introduced DB surface and their relation to different practical applications including cloaking

There exist different types of artificial surfaces that can be used to control wave propagation. Examples are soft and hard surfaces, high impedance surfaces and electromagnetic bandgap (EBG) surfaces. Ideal canonical representations of such surfaces are desirable for initial analysis and proof of concept in new applications, before starting detailed time-consuming numerical simulations and design. The soft and hard surfaces are well represented by an ideal canonical PEC/PMC strip grid, and the high impedance surface by a PMC. The EBG surface has no ideal canonical form, but in the present paper it is argued that the newly introduced DB surface (with boundary condition D_n = B_n = 0) can be considered an ideal canonical representation of an EBG surface, or in other words an isotropic soft surface. There exists also a theoretical D´B´ surface (with boundary condition partdD_n/partn = partB_n/partn = 0), but this has no known realization. It is argued that if the latter could be realized, it will be very suitable for cloaking.