Abstract
The properties of sonic crystals (SC) are theoretically investigated in this work by solving the inverse problem k(ω) using the extended plane wave expansion (EPWE). The solution of the resulting eigenvalue problem gives the complex band structure which takes into account both the propagating and the evanescent modes. In this work we show the complete mathematical formulation of the EPWE for SC and the supercell approximation for its use in both a complete SC and a SC with defects. As an example we show a novel interpretation of the deaf bands in a complete SC in good agreement with multiple scattering simulations.
Highlights
Exploitation of wave propagation properties of periodic materials has showed in the last decades an increasing number of application in condensed matter physics, specially in photonics[1,2] and phononics.[3,4,5] The particular dispersion relation of these systems, known as the band structure, reveals several properties depending on the frequency
The extended plane wave expansion (EPWE) shows that the called deaf bands are ranges of frequencies where evanescent waves with the correct symmetry are excited in the system
The complex band structure obtained using the EPWE takes into account these waves and shows additional bands never predicted by the classical methods ω(k)
Summary
Exploitation of wave propagation properties of periodic materials has showed in the last decades an increasing number of application in condensed matter physics, specially in photonics[1,2] and phononics.[3,4,5] The particular dispersion relation of these systems, known as the band structure, reveals several properties depending on the frequency. Recent works[18,19] develop an extended plane wave expansion (EPWE) method to solve the inverse problem k(ω) taking into account both the propagating and the evanescent properties of the system. This method provides a more complete picture of the physical properties of the system than the classical ω(k) procedures as well as novel interpretation of the existing phenomena.
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