to modify the mixing angle $\theta$ from either $0$ or $\pi/2$ to $\pi/4$. For example: if we consider that at the input of the system only the upper linear defect is excited ($C_U=1$ and $C_L=0$) and the radii are different enough so $\Delta k$ is large compared to $\sqrt{\Omega_{UL}\Omega_{LU}}$, then $\theta=0$ and only the S supermode $p_+(z_{\rm{initial}})$ is excited. Thus, if along the $z$ propagation direction the defect radii become progressively more similar (reaching equal values at the output of the system), $\Delta k$ decreases making $\sqrt{\Omega_{UL}\Omega_{LU}}$ large compared to $\Delta k$, and $\theta$ evolves adiabatically from $0$ up to $\pi/4$. At the output of the system, where the linear defects are equal and $\theta=\pi/4$, the followed S supermode $p_+(z_{final})$ in [Eq. [(\[sc\_antisim\])]{}]{} corresponds to have $50\%$ of the field in each of the two linear defects. [Fig. \[sc\_migrap\]]{} schematically represents the evolution of the mixing angle $\theta$ and the amplitude in each linear defect provided by the coupled-mode equations. As summarized in table \[sc\_taula2\], there are four possible ways to achieve the $50\%$ power superposition at the output of the two coupled linear defects.

![(Color online) Schematic representation of the evolution of (a) the mixing angle $\theta$ and (b) 