the field intensity in the upper and lower defects.[]{data-label="sc_migrap"}](fig3.pdf){width="1\linewidth"}

  ------------------------ ------------------ -------------------------- ---------------
        **Sign of**          **Injection**         **Mixing angle**       **Followed**
   **$\Delta k=k_L-k_U$**                           **evolution**         **supermode**
            $+$             $C_U=1$, $C_D=0$     $0\Rightarrow \pi/4$       $p_+(z)$
            $+$             $C_U=0$, $C_D=1$     $0\Rightarrow \pi/4$       $p_-(z)$
            $-$             $C_U=1$, $C_D=0$   $\pi/2\Rightarrow \pi/4$     $p_-(z)$
            $-$             $C_U=0$, $C_D=1$   $\pi/2\Rightarrow \pi/4$     $p_+(z)$
  ------------------------ ------------------ -------------------------- ---------------

  : Four possible situations for which, at the output of the device, the field injected in one of the linear defects ends up in a $50\%$ superposition between the two parallel coupled linear defects.[]{data-label="sc_taula2"}

![image](fig4.pdf){width="\linewidth"}

![(Color online) (a) Normalized power at the upper $\tilde{P}_{U,out}$ (red dots) and lower $\tilde{P}_{L,out}$ (blue squares) outputs, and (b) normalized total power reaching the outputs, $\tilde{P}_{out}$, as a function of the frequency.[]{data-label="sc_figsplitrange"}](fig5.pdf){width="0.7\linewidth"}

We have designed a structure following the example above described (corresponding to the first row of table \[sc\_taula2\]) and performed numerical simulations by integrating [Eq. [(\[sc\_linearized\])]{}]{} with the Finite Element method in order to confirm the predictions of the coupled-mode equations for the $50\%$ splitting. [Fig. \[sc\_figsplit\]]{} shows the results of the numerical simulation of sound waves of frequency $1.9\times 10^5\,\rm{Hz}$ propagating through the designed structure. We can see how the initial input beam injected in the upper defect is equally split 