linear defects are of equal radius), and one represented as a black solid line (red in the online version) which we will call A (as it corresponds to an antisymmetric supermode when both defects are equal). It is worth to note that in [Fig. \[sc\_fig2\]]{}(b) there is another band (light gray solid line or orange color in the online version) which significantly overlaps in frequencies with the A band. This band corresponds to a higher order supermode of the system with an antisymmetric transverse profile within one waveguide (see [Fig. \[sc\_fig2\]]{}(b)). Thus, this supermode will not be excited by the sound source that will be used, which has a symmetric transverse profile centered at the linear defect (a Gaussian transverse pressure profile). Figs. \[sc\_fig2\](c) and (d) allow for the comparison of both, the projected band diagrams and the supermodes, for a single and a two linear defect case. We have plotted one of the bands as a dark gray solid line (green in the online version) in [Fig. \[sc\_fig2\]]{}(c) and one as a black solid line (red in the online version) in [Fig. \[sc\_fig2\]]{}(d), similarly as in Figs. \[sc\_fig2\](a) and (b).

Let’s continue now with the two linear defect case. 