Eur. Phys. J. B 68, 47-58 (2009)
https://doi.org/10.1140/epjb/e2009-00061-3

Surface loving and surface avoiding modes

¹ CNRS, BP 94347, CEMES (Centre d'Élaboration des Matériaux et d'Études Structurales), 31055 Toulouse, France
² Université de Toulouse, UPS, 31055 Toulouse, France
³ Groupe d'Étude des Semiconducteurs, UMR 5650 CNRS-Université Montpellier II, Bât. 21, CC074, Place Eugène Bataillon, 34095 Montpellier Cedex 05, France

Corresponding author: ^a combe@cemes.fr

Received: 5 January 2009
Published online: 21 February 2009

Abstract

We theoretically study the propagation of sound waves in GaAs/AlAs superlattices focusing on periodic modes in the vicinity of the band gaps. Based on analytical and numerical calculations, we show that these modes are the product of a quickly oscillating function times a slowly varying envelope function. We carefully study the phase of the envelope function compared to the surface of a semi-infinite superlattice. Especially, the dephasing of the superlattice compared to its surface is a key parameter. We exhibit two kind of modes: Surface Avoiding and Surface Loving Modes whose envelope functions have their minima and respectively maxima in the vicinity of the surface. We finally consider the observability of such modes. While Surface Avoiding Modes have experimentally been observed [Phys. Rev. Lett. 97, 1224301 (2006)], we show that Surface Loving Modes are likely to be observable and we discuss the achievement of such experiments. The proposed approach could be easily transposed to other types of wave propagation in unidimensional semi-infinite periodic structures as photonic Bragg mirror.