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RESEARCH PRODUCT

Notice of Removal: Stochastic generation of the phononic band structure of lossy and infinite crystals

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The concept of the band structure is central to the field of phononic crystals. Indeed, capturing the dispersion of Bloch waves — the eigenmodes of propagation in periodic media — gives invaluable information on allowed propagation modes, their phase and group velocities, local resonances, and band gaps. Band structures are usually obtained by solving an eigenvalue problem defined on a closed and bounded domain, which results in a discrete spectrum. There are at least two cases, however, that cannot be reduced to a simple eigenvalue problem: first, when materials showing dispersive loss are present and second, when the unit-cell extends beyond any bound, as in the case of phononic crystal of holes or pillars on a semi-infinite substrate.