Abstract
In this article, we demonstrate how twist symmetries can be employed in the design of flat lenses. A lens design is proposed, consisting of 13 perforated metallic sheets separated by an air gap. The perforation in the metal is a two-dimensional array of complementary split-ring resonators. In this specific design, the twist symmetry is local, as it is only applied to the unit cell of the array. Moreover, the twist symmetry is an approximation, as it is only applied to part of the unit cell. First, we demonstrate that, by varying the order of twist symmetry, the phase delay experienced by a wave propagating through the array can be accurately controlled. Secondly, a lens is designed by tailoring the unit cells throughout the aperture of the lens in order to obtain the desired phase delay. Simulation and measurement results demonstrate that the lens successfully transforms a spherical wave emanating from the focal point into a plane wave at the opposite side of the lens. The demonstrated concepts find application in future wireless communication networks where fully-metallic directive antennas are desired.
Highlights
A periodic structure possesses a higher geometrical symmetry if it is invariant under a translation and one or more additional geometrical operations
The twist symmetry was local since only the unit cell was twist-symmetric, and not the full array of complementary split ring resonators (CSRRs)
A periodic structure with local twist symmetry was applied for the design of a fully-metallic lens
Summary
A periodic structure possesses a higher geometrical symmetry if it is invariant under a translation and one or more additional geometrical operations. A Cartesian glide symmetry is obtained if the additional geometrical operation, which is applied jointly with the translation, is a mirroring with respect to a plane. A structure possesses Cartesian glide symmetry if its unit cell consists of two sub-unit cells that are displaced a distance p/2 and mirrored with respect to a plane, where p is the period of the full unit cell. A structure possesses an m-fold twist symmetry (m being an integer) if its unit cell consists of m sub-unit cells, which are displaced a distance p/m and rotated 2π/m with respect to the adjacent sub-unit cells. A two-fold twist-symmetric structure possesses glide symmetry if the sub-unit cell is mirror-symmetric with respect to one plane that includes the periodicity axis. In [1,2,3,4], it was shown that there were no stop-bands between the m first modes in Symmetry 2019, 11, 581; doi:10.3390/sym11040581 www.mdpi.com/journal/symmetry
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