Abstract
A mathematical scheme capable of describing the features of the photolithographic multi-beam–multi-shot approach is introduced here. We will show in detail how such a technique can reproduce any of the fourteen three-dimensional Bravais lattices. Furthermore, we will mathematically show the independence of the lattice constant of the structure from the laser wavelength. Finally, we will compare the four-beams–one-shot and the three-beams–three-shots techniques by means of simulations reproducing opal and connected FCC-like lattices.
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V.P. Bykov, Sov. J. Quantum Electron. 4, 861 (1975)
E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1989)
S. John, Phys. Rev. Lett. 58, 2486 (1987)
S. John, T. Quang, Phys. Rev. A 50, 1764 (1994)
S.Y. Zhu, H. Chen, H. Huang, Phys. Rev. Lett. 79, 205 (1997)
T. Baba, M. Nakamura, IEEE J. Quantum Electron. 38, 909 (2002)
H.T. Chien, C.C. Chen, P.G. Luan, Opt. Commun. 259, 873 (2006)
S. Shoji, S. Kawata, Appl. Phys. Lett. 76, 2668 (2000)
M. Campbell, D.N. Sharp, M.T. Harrison, R.G. Denning, A.J. Turberfield, Nature 404, 53 (2000)
M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, C.M. Soukoulis, Nature Mater. 3, 444 (2004)
D.C. Meisel, M. Wegener, K. Busch, Phys. Rev. B 70, 165104 (2003)
D.N. Sharp, A.J. Turbefield, R.G. Denning, Phys. Rev. B 68, 205102 (2003)
L.Z. Cai, X.L. Yang, Y.R. Wang, Opt. Lett. 27, 900 (2002)
L. Yuan, G.P. Wang, X. Huang, Opt. Lett. 28, 1769 (2003)
S. Shoji, R. Proietti Zaccaria, H.B. Sun, S. Kawata, Opt. Express 14, 2309 (2006)
F.C. Phillips, An Introduction to Crystallography (Oliver & Boyd, Edinburgh)
J.F. Nye, Physical Properties of Crystals (Oxford University Press, London)
J.F. Cornwell, Group Theory in Physics: An Introduction (Academic Press, San Diego, 1997)
K.M. Ho, C.T. Chan, C.M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990)
E. Yablonovitch, T.J. Gmitter, K.M. Leung, Phys. Rev. Lett. 67, 2295 (1991)
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Proietti Zaccaria, R., Shoji, S., Sun, HB. et al. Multi-shot interference approach for any kind of Bravais lattice. Appl. Phys. B 93, 251–256 (2008). https://doi.org/10.1007/s00340-008-3158-4
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DOI: https://doi.org/10.1007/s00340-008-3158-4