Beam path and focusing of flexural Lamb waves within phononic crystal-based acoustic lenses

Abstract

We describe an analytical approach that allows calculating the trajectories of an elastic beam within a two-dimensional phononic crystal-based gradient index medium. The formalism takes into account the anisotropy along the lines of inclusions where the equi-frequency contours may depart from a circle. We then report on a numerical and experimental study of the focusing of flexural Lamb waves in gradient-indexed phononic crystals. The silicon/air heterostructures that we considered for this work features an index that is obtained through the modulation along one axis of either the diameter of the air inclusions or their spacing. In both cases, numerical and experimental results agree very well. The formalism that we have developed explains well the location, shape and size of the focus in either system.

Keywords

• phononic crystal
• focusing
• ray trajectory
• Lamb waves
• anisotropy
• 43.20+g