Stochastic generation of the phononic band structure of lossy and infinite crystals
Résumé
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.