range with only one supermode, for which we will design spatial adiabatic passage processes that will make the system behave as a coherent multifrequency adiabatic splitter and as a coupler. Finally, in Section \[sc\_CONC\], we will present the conclusions.

Physical system {#sc_sectionSC}
===============

We consider a two-dimensional square lattice SC made of steel cylinders (filling medium) immersed in water (host medium) containing linear defects. In the following, we will assume that the steel cylinders are a rigid material, disregarding transversal waves in the cylinders. This approximation, although it can slightly shift the bands in frequency,[@li_bandgap_2011] it is commonly used to describe the qualitative behavior of those processes which do not critically depend on a particular set of parameter values, and/or to show the existence of new physical phenomena.[@espinosa_subdiffractive_2007; @soliveres_self_2009] In this context, the propagation of sonic waves in SCs consisting of two different materials can be described by the following linear equations:[@perez-arjona_theoretical_2007]

$$\begin{aligned}
\rho\frac{\partial \mathbf{v}}{\partial t}&=-\nabla p,\\
\frac{\partial p}{\partial t}&=-B\mathbf{\nabla\cdot v},\end{aligned}$$

\[sc\_linearized\]

where $B(\mathbf{r})$ is the bulk modulus, $\rho(\mathbf{r})$ is the density, $p(\mathbf{r},t)$ is the pressure field and $\mathbf{v}(\mathbf{r},t)$ is the velocity vector field. Merging Eqs. (\[sc\_linearized\]a) and (\[sc\_linearized\]b) it is possible to obtain the wave equation for the pressure 