propagation in two parallel linear defects for frequencies in which both S and A supermodes exist. Nevertheless, from Figs. \[sc\_fig2\](a) and (b) it is clear that there are frequencies in which only one of the supermodes can propagate. In particular, marked with a gray (red in the online version) shadow in Figs. \[sc\_fig2\](a) and (b), there is a quite broad range of frequencies where only the A supermode is present. For these frequencies it is not possible to use the coupled-mode theory since only one supermode is available. However, it is still possible to adiabatically modify and follow the A supermode of the system by smoothly modifying the radius size of the defects along the propagation direction. In fact, the absence of the S supermode significantly relaxes the smoothness condition for the change in radii size of the linear defects along the propagation direction. Therefore, in this range of frequencies it is possible to design much shorter SC structures for applications that only require the following of a single supermode.

![(Color online) (a) Numerical simulation of the intensity of a harmonic sound wave propagating with a frequency of $2.08\times 10^5\,\rm{Hz}$ along the SC with two linear defects for the coherent 