Abstract
A systematically theoretical study on how to form two-dimensional photonic lattices with various plane groups by three elliptically polarized beams is presented. It is shown that nine plane groups can be formed in the photonic lattices by use of an intuitionistic intensity pattern-superposition method; however, we demonstrate that the other eight plane groups cannot be constructed. A phase shift associated with the interference intensity and the elliptic polarization is derived, and a relevant formula for interference intensity is deduced. The phase shift can be used to obtain the lower symmetries in some wallpaper groups such as p1, pm, cm, and p3m1 without introducing additional undesired symmetries. This analysis may lay the foundation for the study of space groups in holographic three-dimensional photonic crystals and multidimensional photonic quasicrystals.
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