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.

© 2005 Optical Society of America

Formation principles of two-dimensional compound photonic lattices by one-step holographic lithography

W. D. Mao, J. W. Dong, Y. C. Zhong, G. Q. Liang, and H. Z. Wang
Opt. Express 13(8) 2994-2999 (2005)

Theoretical bandgap modeling of two-dimensional triangular photonic crystals formed by interference technique of three noncoplanar beams

X. L. Yang, L. Z. Cai, and Q. Liu
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Theoretical bandgap modeling of two-dimensional square photonic crystals fabricated by the interference of three noncoplanar laser beams

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All fourteen Bravais lattices can be formed by interference of four noncoplanar beams

L. Z. Cai, X. L. Yang, and Y. R. Wang
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Formation of three-dimensional periodic microstructures by interference of four noncoplanar beams

L. Z. Cai, X. L. Yang, and Y. R. Wang
J. Opt. Soc. Am. A 19(11) 2238-2244 (2002)