Propagating and evanescent properties of double-point defects in Sonic   Crystals
  Complex Band Structures and Multiple Scattering Theory have been used in this paper to analyze the overlapping of the evanescent waves localized in point defects in Sonic Crystals. The Extended Plane Wave Expansion (EPWE) with supercell approximation gives the imaginary part of the Bloch vectors that produces the decay of the localized modes inside the periodic system. Double-cavities can present a coupling between the evanescent modes localized in the defect, showing a symmetric or antisymmetric modes. When point defects are close, the complex band structures reveal a splitting of the frequencies of the localized modes. Both the real part and the imaginary values of wave vector of the localized modes in the cavities present different values for each localized mode, which gives different properties for each mode. Novel measurements, in very good agreement with analytical data, show the experimental evidences of the symmetric and antisymmetric localized modes for a double-point defect in Sonic Crystals (SC). The investigation on the localization phenomena and the coupling between defects in periodic systems has a fundamental importance both in pure and in applied physics. 
V. Romero-Garc\'ia and J.V. S\'anchez-P\'erez and and L.M.   Garcia-Raffi
cond-mat.mtrl-sci