Tetramode Metamaterials as Phonon Polarizers

In classical Cauchy elasticity, 3D materials exhibit six eigenmodes of deformation. Following the 1995 work of Milton and Cherkaev, extremal elastic materials can be classified by the number of eigenmodes, N, out of these six that are “easy”. Using Greek number words, this leads to hexamode (N = 6), pentamode (N = 5), tetramode (N = 4), trimode (N = 3), dimode (N = 2), and monomode (N = 1) materials. While hexamode materials are unstable in all regards, the possibility of pentamode metamaterials (“meta‐fluids”) has attracted considerable attention throughout the last decade. Here, inspired by the 2021 theoretical work of Wei, Liu, and Hu, microstructured 3D polymer‐based tetramode metamaterials are designed and characterized by numerical band‐structure calculations, fabricated by laser printing, characterized by ultrasound experiments, and compared to the theoretical ideal. An application in terms of a compact and broadband polarizer for acoustical phonons at ultrasound frequencies is demonstrated. An experimental realization and application of a tetramode material are presented. According to Cauchy elasticity, four out of the six deformation modes of such materials are considered “easy”. A property that can be exploited as a compact broadband polarizer for transverse phonons. This is demonstrated experimentally with a 3D metamaterial structure fabricated using direct laser writing.