Optimization of an acoustic leaky-wave antenna based on acoustic metamaterial

In recent years, an increasing number of pioneering studies have been carried out in the field of acoustic metamaterials, following the path of electromagnetic metamaterials. These artificial engineered materials are designed in such a way so as to achieve new macroscopic properties, like negative refraction, that are not readily present in nature. While the design and the fabrication of these artificial materials is a hot topic among scientists in different fields of physics such as photonic, electromagnetic, acoustic and recently mechanic, an important part of the scientific research is now oriented towards the identification of actual applications for these structures. As the novel idea of metamaterial was first developed in the electromagnetic realm and for the microwave frequency range, it is somehow more mature in these fields than in acoustics. Metamaterial applications are now widely developed in electromagnetics especially for the design of new antenna. Among other examples, metamaterial concepts are aiming at reducing the coupling between two adjacent radiating elements of the array and increasing the operating bandwidth of radiating elements. It is also used for phase compensation in microwave transistors, and many more applications are rising in the recent literature. In year 2009, in analogy with electromagnetic transmission line metamaterial, our group proposed a concept of acoustic transmission line metamaterial, consisting of a waveguide periodically loaded with membranes along the duct, and transverse open channels (denoted “stubs”). Based on our proposed structure and in analogy with applications of transmission line electromagnetic metamaterials, researchers proposed the idea of an acoustic counterpart to the “backward wave antenna”. These antennas or radiating devices have a very special property such that the radiation angle or the directivity changes with the frequency. In this article, a comprehensive, step by step, design methodology for acoustic backward wave antenna is presented. For this purpose we use the model proposed in our 2009 publication for acoustic transmission line metamaterial, but we focus the discussion on the optimization of the antenna performance. We also propose some closed form formulas for the practical design of such devices, and a formal validation of the structure is proposed using Comsol Multiphysics.