Nonlocality-enabled inverse design of Dirac-type and higher-order degeneracies for traveling and evanescent waves in phononic crystals

We propose complete tailoring procedures with analytical precision for band degeneracies in one-dimensional (1D) nonlocal phononic crystals, focusing on the role of beyond-nearest-neighbor (BNN) interactions. Unlike trivial Dirac cones at either the center or boundary of Brillouin zone (BZ), we demonstrate non-trivial Dirac-type and higher-order band crossings at any desirable wave number within the BZ by tuning BNN interactions. Our analyses show that odd-indexed BNN interactions determine the quantity and wave number of degeneracy points, while even-indexed BNN interactions primarily affect the frequency. Moreover, we discover new evanescent wave modes and associated degeneracies in the complex-valued wave number. In addition, we study a varieties of spatial-temporal response patterns in time-domain simulations for the interplay between traveling and localized modes at the propagating and evanescent degeneracies.