k}$, as shown in [Eq. [(\[sc\_mixing\])]{}]{}. This ratio, and therefore the supermode transverse profiles, can be controlled by modifying the radii of the defects. Thus, the coupled-mode equations (\[sc\_coupled\]) allow us to easily confirm that, as we have discussed in Section \[sc\_sectionSC\], by smoothly changing the radii of the linear defects it is possible to modify and follow the S and A supermodes of the system and control the sound propagation. Calculating the projected band diagrams for a single defect with [Eq. [(\[sc\_eigenvalue\])]{}]{}, [Eq. [(\[sc\_coeff1\])]{}]{} and [Eq. [(\[sc\_coeff2\_a\])]{}]{} it is straightforward to check that the value of $|\Delta k|=|k_L-k_U|$ increases by making the defect radii progressively different between them (see Figs. \[sc\_fig2\](c) and (d)). In the case in which the defects are equal, $r_{dU}=r_{dL}$, then $\Delta k=0$. The values of the couplings $\sqrt{\Omega_{UL}\Omega_{LU}}$ can be found by using [Eq. [(\[sc\_kmodes\])]{}]{}, since $k_\pm$ can be obtained from the band diagrams with two defects in the SC. Thus, it can be checked that when the radii of the defects are equal, $|\Delta k|\ll\sqrt{\Omega_{UL}\Omega_{LU}}$ and $\theta=\pi/4$. Whereas when $|r_{dL} - r_{dU}|\gg0$, the condition $|\Delta k|\gg\sqrt{\Omega_{UL}\Omega_{LU}}$ is fulfilled and $\theta$ is equal to either $0$ or $\pi/2$, depending on the sign of $\Delta k$. 