In this way, by changing the difference between the radii of the linear defects, it is possible to modify the mixing angle $\theta$ from either $0$ or $\pi/2$, corresponding to the S and A supermodes localized in only one of the defects, to $\pi/4$, where the S and A supermodes are equally spread between the two linear defects. This is in agreement with the results shown in Figs. \[sc\_fig2\](a) and (b).

Additionally, the coupled-mode equations provide a useful analogy between propagation of waves along two coupled waveguide systems and the time evolution of the population in two-level atomic systems interacting with a laser beam. In fact, the protocol to modify and follow the S and A supermodes presented here resembles the well-known quantum-optical rapid adiabatic passage (RAP) technique,[@leslie_allen_optical_1987; @shore_theory_1990] which allows for a coherent control of atomic population in a system of two internal atomic states interacting with a chirped laser pulse.

Coherent multifrequency adiabatic splitter {#sc_CMAS}
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In this section we will apply the previous ideas coming from the coupled-mode theory in order to obtain a robust $50\%$ coherent superposition of sound waves at the output of a SC with two coupled linear defects. To this aim, we need 