Buckling-induced transmission switching in phononic waveguidesa)

On-chip phononic circuits tailor the transmission of elastic waves and couple to electronics and photonics to enable new signal manipulation capabilities. Phononic circuits rely on waveguides that transmit elastic waves within desired frequency passbands, which are typically designed based on the Bloch modes of the constitutive unit cell of the waveguide, assuming periodicity. Acoustic microelectromechanical system waveguides composed of coupled drumhead resonators offer megahertz operation frequencies for applications in acoustic switching. Here, we construct a reduced-order model (ROM) to demonstrate the mechanism of transmission switching in coupled drumhead-resonator waveguides. The ROM considers the mechanics of buckling under the effect of temperature variation. Each unit cell has two degrees of freedom: translation to capture the symmetric bending modes and angular motion to capture the asymmetric bending modes of the membranes. We show that thermoelastic buckling induces a phase transition triggered by temperature variation, causing the localization of the first-passband modes, similar to Anderson localization caused by disorders. The proposed ROM is essential to understanding these phenomena since Bloch mode analysis fails for weakly disordered (<5%) finite waveguides due to the disorder amplification caused by the thermoelastic buckling. The illustrated transmission control can be extended to two-dimensional circuits in the future.