Bloch waves in periodic multi-layered acoustic waveguides

Abstract

The band spectrum and associated Floquet–Bloch eigensolutions, arising in acoustic and electromagnetic waveguides, which have periodic structure along the guide while remaining of finite width, are found. Homogeneous Dirichlet or Neumann conditions along the guide walls, or an alternation of them, are taken. Importantly, in some cases, a total stop band at zero frequency is identified providing space for low-frequency localized modes; geometric defects in the structured waveguide also create these modes. Numerical and asymptotic techniques identify dispersion curves and trapped modes. Some cases demonstrate maxima and minima of the spectral edges within the Brillouin zone and also allow for ultraslow light or sound. Imaging applications using anomalous dispersion to generate subwavelength resolution are possible and are demonstrated.