Willis Metamaterial on a Structured Beam

Abstract

Bianisotropy is common in electromagnetics whenever a cross-coupling between electric and magnetic responses exists. However, the analogous concept for elastic waves in solids, termed as Willis coupling, is more challenging to observe. It requires coupling between stress and velocity or momentum and strain fields, which is difficult to induce in non-negligible levels, even when using metamaterial structures. Here, we report the experimental realization of a Willis metamaterial for flexural waves. Based on a cantilever bending resonance, we demonstrate asymmetric reflection amplitudes and phases due to Willis coupling. We also show that, by introducing loss in the metamaterial, the asymmetric amplitudes can be controlled and can be used to approach an exceptional point of the non-Hermitian system, at which unidirectional zero reflection occurs. The present work extends conventional propagation theory in plates and beams to include Willis coupling, and provides new avenues to tailor flexural waves using artificial structures.

Symmetry breaking creates electro-momentum coupling in piezoelectric metamaterials

“…Therefore, they capture a new mechanism that can be employed for rectifying mechanical waves by modulation of external stimuli. We expect that future studies will show that extraordinary wave response such as asymmetric reflections and unidirectional transmission are modeled by the new couplings [42], analogously to Willis coupling [28,[32][33][34]. These kind of results are to be guided by theoretical analyses based upon proper homogenization schemes [25].…”

“…A series of theoretical studies were carried out to characterize Willis coupling and understand its physical origins [18][19][20][21][22][23][24][25][26]. Guided by accompanying predictions that Willis coupling is connected with unusual phenomena such as asymmetric reflections and unidirectional transmission, recent experimental realizations of Willis metamaterials that demonstrate these phenomena were reported [27][28][29][30][31][32][33][34][35]. To date, these investigations were limited to metamaterials that are deformable only by mechanical forces.…”

Static chiral Willis continuum mechanics for three-dimensional chiral mechanical metamaterials

“…Willis elasticity has been around for many years [16,17]. The Willis continuum-mechanics equations have mostly been used in the context of dynamic effects (or elastic waves) [16][17][18][19][20][21][22][23][24][25][26][27][28]. We will use them in the static regime.…”

Enhanced Low‐Frequency Monopole and Dipole Acoustic Antennas Based on a Subwavelength Bianisotropic Structure

“…We consider a monopole source with maximum pressure and null velocity placed at the center of a Mie resonantor, as shown in Figure 1d. It is known the monopole and dipole moments are dominant in the scattered fields for subwavelength scatters . For SMR or TMR, the monopole and dipole moments are proportional to the local pressure field and local velocity, respectively .…”

“…The acoustic BM is commonly implemented by asymmetric structural units where the constitutive relations are coupled . The field coupling in the acoustic BM is referred as Willis coupling that includes the strain‐velocity coupling in elasticity or the pressure‐velocity coupling in acoustics . The Willis coupling offers a new freedom for acoustic wave manipulation and has produced many fascinating applications .…”