adiabatically followed, for example because of a too sudden change of the radius of the defect, the A supermode (or even some other higher supermodes) would be excited, limiting the efficiency of the splitting. As long as the adiabaticity condition is fulfilled, the length of the device is not a critical parameter in order to maintain an equal splitting. For longer devices as compared to the one here proposed, the adiabaticity of the process will also be successfully fulfilled and the splitting will be efficient for all the range of frequencies of the S supermode. However, for shorter devices, some oscillations in the splitting efficiency might start appearing as a result of the impossibility to adiabatically follow the S supermode.

Phase difference analyzer {#sc_PDA}
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![image](fig6.pdf){width="0.66\linewidth"}

A structure similar to the one described in Section \[sc\_CMAS\] can be designed in order to measure the phase difference between two sound beams. In this case, at the input the two defects are empty of cylinders, being $\theta=\pi/4$ and both the S and the A supermodes spread equally into the two defects, see [Fig. \[sc\_fig2\]]{}(a). Along the propagation direction, the defect radius of the lower linear defect smoothly increases its size up to 