Fano line shapes of leaky surface acoustic waves extending from supersonic surface wave points

This paper highlights the close connection between two issues that are attracting considerable attention in diverse areas of physics including photonics, acoustics, fluid dynamics and the dynamical properties of periodic structures, namely bound states in a continuum (BIC), and asymmetric Fano resonance line shapes. The discussion is framed in the context of solid state acoustics, with supersonic surface acoustic waves (supersonic-SAW) taken as representative examples of BIC. One of these pertains to the surface of an anisotropic solid and the other to an isotropic layer on an isotropic substrate. These are surface modes lying within a continuum of bulk radiating states, which at isolated values of the system parameters become uncoupled from these states. We demonstrate how for generic non-symmetry-protected supersonic-SAW, varying these parameters leads to the unfolding of this mode into a leaky pseudo-SAW, with the resonance line shape conforming accurately to the Fano expression. With passage through the SSAW point in parameter space, the Fano q parameter diverges and changes sign. It is anticipated that this is a fairly general feature of the unfolding of BIC with variation of relevant control parameters.