An artificial surface demonstrating angular and polarization dependency to the polarization of the applied field is introduced. This artificial surface consists of a periodic strip grating on a grounded dielectric slab. A method based on Floquet's modal expansion is presented to solve the scattering problem of such surfaces. A code based on method of moments (MoM) is also developed to analyze and design these artificial surfaces. The obtained results using these methods are compared against each other. The extracted reflection parameters are then employed to characterize the surface impedance of the artificial surface for different incident angles and both TE and TM polarizations. This artificial surface is used as the ground plane of cavity resonance antennas. Next, a highly reflective frequency selective surface (FSS) is designed to show high reflectivity at two different frequencies. This FSS is to be used as the superstrate layer of the cavity resonance antenna. The impedance surface of the artificial ground plane and the equivalent admittance of the designed FSS are employed in the transverse equivalent network (TEN) model to obtain radiation properties of such antennas. Finally, compact high-gain dual-band dual-orthogonally polarized antennas are designed based on the aforementioned analyses.