  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.
