phase difference to every measured value.

![(Color online) (a) Numerically calculated intensity in each waveguide output as a function of the phase difference between the input sources. The results follow those expected from [Eq. [(\[sc\_Ip\])]{}]{} and [Eq. [(\[sc\_Im\])]{}]{}, represented with a dashed black curve. (b) The solid line represents the measured phase difference from the numerical simulations using [Eq. [(\[sc\_def\])]{}]{} as a function of the known phase difference between the sources. The black dashed curve corresponds to the ideal measurement given by [Eq. [(\[sc\_def\])]{}]{} together with [Eq. [(\[sc\_Ip\])]{}]{} and [Eq. [(\[sc\_Im\])]{}]{}.[]{data-label="sc_figfase2"}](fig8.pdf){width="1\linewidth"}

The results shown above correspond to a frequency of $1.9\times 10^5\,\rm{Hz}$, which is approximately in the middle of the frequency range where both S and A supermodes coexist, see Figs. \[sc\_fig2\](a) and (b). For this reason, both supermodes are excited with similar intensities. However, for other frequencies surrounding that frequency, one of the supermodes will be excited with slightly more intensity than the other one. Nevertheless, the system can still be used for the measurement of the phase difference between two beams by adjusting the normalization in [Eq. [(\[sc\_simin\])]{}]{} and [Eq. [(\[sc\_antisimin\])]{}]{}, and also calibrating the obtained outputs.

One-supermode case {#sc_onesmode}
==================

Up to now we have studied sound 