Surface loving and surface avoiding modes

Abstract

We theoretically study the propagation of sound waves in GaAs/AlAs superlattices focussing 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.

Defect-Controlled Hypersound Propagation in Hybrid Superlattices

“…Moreover, the envelope function of the displacement field for mode e 2 almost vanishes at the surface. The latter can therefore be qualified as a surface avoiding mode (SAM) recently reported for semiconductor SLs [15,35]. Additional evidence of the surface mode is its 164301-2 dependence on the top layer thickness [7,36].…”

The inverted pendulum, interface phonons and optic Tamm states

“…As exploited recently [8], the physic of the parametric oscillator is equivalent to that of the propagations of waves in a lossless unidimensional infinite periodic (LUIP) medium. In this manuscript, we transpose the striking possibility for an oscillator to oscillate in the vicinity of an unstable equilibrium position using a parametric excitation (in the inverted pendulum experiment, for instance) to the case of waves in LUIP media.…”