We simulate the s-polarized electromagnetic field diffracted by a truncated two-dimensional lattice. We observe strong decay of the transmittivity for frequencies lying in the gaps displayed by the dispersion relation of the infinite crystal and find regular oscillations outside these gaps. The structure of the field in the lattice is explained in terms of modes of its infinite counterpart. In particular, the oscillations are related to the resonance in the layer of propagating Bloch waves, just as in a Fabry–Perot interferometer. This interpretation enables us to retrieve the dispersion relation. Finally, we study the symmetry properties of the modes and show that for certain frequencies the transmissivity of the system is null under symmetric illumination but nonzero under antisymmetric lighting or vice versa.
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