Metamaterials whose momentum is constitutively coupled with their strain show promise in wave manipulation for engineering purposes and are called Willis materials. They were discovered using an effective medium theory which shows that their response is non-local in space and time. Recently, we generalized this theory to account for piezoelectricity and demonstrated that the effective momentum can depend constitutively on the electric field, thereby enlarging the design space for metamaterials. Here, we develop the mathematical restrictions on the effective properties of such generalized Willis materials, owing to passivity, reciprocity, and causality. Establishing these restrictions is of fundamental significance, as they test the validity of theoretical and experimental results and applicational importance since they provide elementary bounds for the maximal response that potential devices may achieve.
Photonics Initiative, Advanced Science Research Center, City University of New York（纽约市立大学高级科学研究中心光子学倡议）；Gulliver, CNRS, ESPCI Paris, Université PSL（巴黎高等物理化工国立学院CNRS Gulliver实验室）；Laboratory of Wave Engineering, EPFL（洛桑联邦理工学院波工程实验室）；Faculty of Mechanical Engineering, Technion–Israel Institute of Technology（以色列理工学院机械工程学院）；University of Chicago, James Franck Institute（芝加哥大学詹姆斯·弗兰克研究所）；University of Chicago, Kadanoff Center for Theoretical Physics（芝加哥大学卡达诺夫理论物理中心）；Walker Department of Mechanical Engineering, The University of Texas at Austin（德克萨斯大学奥斯汀分校沃克机械工程系）；Physics Program, Graduate Center, City University of New York（纽约市立大学研究生院物理学项目）
