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In this paper we present some recent results of our theoretical investigations of electromagnetically controllable surfaces. These surfaces are designed on the basis of periodic arrays made of metallic inclusions of special form which are placed on a thin substrate of active material (magnetized ferrite or optically active semiconductor). The main peculiarity of the studied structures is their capability to support the trapped-mode resonance which is a result of the antiphase current oscillations in the elements of a periodic cell. Several effects, namely: tuning the position of passband and the linear and nonlinear (bistable) transmission switching are considered when an external static magnetic field or optical excitation are applied. Our numerical calculations are fulfilled in both microwave and optical regions.
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