Brillouin scattering-like effect and non-reciprocal propagation of elastic waves due to spatio-temporal modulation of electrical boundary conditions in piezoelectric media

Abstract

The properties of a one-dimensional phononic crystal made of identical piezoelectric elements separated by thin metallic electrodes connected to the ground are studied theoretically for cases where the locations of the electrical connections change as a function of time with a specific speed. This spatiotemporal modulation of the electrical boundary conditions results in significant non-linear effects that are evidenced numerically. The interaction between an incident harmonic longitudinal wave and the time-dependent phononic crystal is shown to lead to frequency splitting analogous to Brillouin scattering. Moreover, the boundaries of the Bragg bandgaps are strongly affected, and for some specific modulation speed, one-way wave propagation can be achieved. Published by AIP Publishing.

Tailoring phonon band structures with broken symmetry by shaping spatiotemporal modulations of stiffness in a one-dimensional elastic waveguide

“…While observation of gaps of type A and A' had already been reported in Ref. [10], the primary result of this study is the observation of hybridization between second harmonics (n = 2) and the second and third zeroth-order static bands which produces the gaps labeled B and B . Similarly to the A and A gaps, the gaps B and B form only on one side of the Brillouin zone and in particular on its negative side.…”

“…We have shown previously that the interaction between elastic waves with frequency ν 0 and a spatiotemporal modulation of the elastic constants leads to a frequency splitting that resembles Brillouin scattering [10]. As will be demonstrated in the following theoretical analysis, the frequency of the Brillouin modes contains harmonics of the frequency associated with the moving modulation: υ n = υ 0 ± nF , where…”

“…In contrast, energy can be added extrinsically to break symmetry. In this case, symmetry of elastic waves can be broken by moving fluids [6,7], gyroscopic inclusions [8], or directed and externally driven spatiotemporal modulations of the elastic properties of the medium [9][10][11][12][13]. For the sake of completeness, one may note that investigation of nonreciprocity in the propagation of electromagnetic waves [14][15][16][17][18][19] has preceded their elastic counterparts.…”

“…Previous studies [9][10][11][12][13] have theoretically and computationally demonstrated that time-reversal symmetry can be broken by creating a moving-superlattice-like spatial modulation of the elastic constants in a one-dimensional elastic medium. The symmetry breaking, in a time-dependent superlattice leads to bulk phonon modes with nonconventional topology, which do not possess the conventional mirror symmetry in momentum space [9][10][11][12][13].…”

“…The symmetry breaking, in a time-dependent superlattice leads to bulk phonon modes with nonconventional topology, which do not possess the conventional mirror symmetry in momentum space [9][10][11][12][13]. In all cases, the spatiotemporal modulation results in effects such as frequency splitting of a monochromatic incident signal that is analogous to Brillouin scattering [10].…”