We report that directional asymmetry of transmission of circularly polarized waves, which previously had only been observed in two-dimensional arrays of planar chiral particles, may occur in a much larger class of planar periodic structures. If the particles constituting such periodic arrays are not chiral, asymmetric transmission can still be observed if planar enantiomorphism is imposed on the structural level, by a particular arrangement of particles in the array. Moreover, in order to see asymmetric transmission at oblique incidence planar enantiomorphism is required not for the structure itself, but only for the projection of the structure onto the plane normal to the incident beam. Our findings confirmed by a series of model microwave experiments show that asymmetric transmission may occur in highly symmetric structures such as arrays of spherical semiconductor quantum dots at oblique incidence or in two-dimensional arrays of oriented elliptical plasmonic metal particles at normal incidence
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