Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs

[EN] We discuss the simultaneous existence of phononic and photonic band gaps in a periodic array of holes drilled in a Si membrane. We investigate in detail both the centered square lattice and the boron nitride (BN) lattice with two atoms per unit cell which include the simple square, triangular and honeycomb lattices as particular cases. We show that complete phononic and photonic band gaps can be obtained from the honeycomb lattice as well as BN lattices close to honeycomb. Otherwise, all investigated structures present the possibility of a complete phononic gap together with a photonic band gap of a given symmetry, odd or even, depending on the geometrical parameters. (C) 2010 Optical Society of AmericaThis work is supported in part by the European Commission Seventh Framework Programme (FP7) under the FET-Open project TAILPHOX No 233833 and by Ministry of Higher Education and Research, Nord-Pas de Calais Regional Council and FEDER through the 'Contrat de Projets Etat Region (CPER) 2007-2013'.Pennec, Y.; Rouhani, BD.; El Boudouti. E. H.; Li, C.; El Hassouani, Y.; Vasseur, JO.; Papanikolaou, N.... (2010). Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs. Optics Express. 18(13):14301-14310. https://doi.org/10.1364/OE.18.01430114301143101813Kushwaha, M. S., Halevi, P., Dobrzynski, L., & Djafari-Rouhani, B. (1993). Acoustic band structure of periodic elastic composites. Physical Review Letters, 71(13), 2022-2025. doi:10.1103/physrevlett.71.2022Sigalas, M., & Economou, E. N. (1993). Band structure of elastic waves in two dimensional systems. 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