  We theoretically study the interactions between plasmonic and photonic modes
within a structure that is composed of two thin corrugated metallic plates,
embedded in air. We show that the interactions depend upon the symmetry of the
interacting modes. This observation is explained by the phase difference
between the Fourier components of the two gratings. The phase can be controlled
by laterally shifting one grating with respect to the other. Therefore, this
relative shift provides an efficient "knob" that allows to control the
interaction between the various modes, resulting in an efficient modulation of
light transmission and reflection in the proposed structure. Based on this
concept we show that the investigated structure can be used as tunable
plasmonic filter.
