One-periodic planar arrays of straight wires or metal strips have a long history of applications as quasioptical polarizing devices and partially transparent mirrors. Their properties are well known. Planar double-periodic structures have been used in the microwave, terahertz and optical frequency ranges because of their remarkable electromagnetic properties and manufacturing simplicity. In microwaves, these structures are used as absorbing and scattering covers, frequency-selective and polarization-selective surfaces. Planar periodic structures of complex-shaped metal strips have a feature of resonance transmission and reflection of incident waves without any high diffraction orders forming. Thus, they are the basis for a series of artificial materials including metamaterials. But a quality factor of resonances of these structures is usually of the order of unity.