Parameterization of localized states of liquid surface waves in non-Bragg structures

Abstract

Localized defect states of liquid surface waves in non-Bragg periodic structures are investigated experimentally and validated numerically using the finite element method. Two parameters are considered, one is the position of the defect along the full length of the structure and the other is the filling fraction achieved by calibrating the length of the structures as a factor of the periodic length. It is well known that defects in periodic structures always cause the transparency modes inside the stopbands and may localize the wave energy in the nearfield of the defect element. Here, we examine the interplay between the structure transmission in the defect mode and the localization around the defect element. The experimental and numerical results show that the magnitude of the transmission coefficient of the defect mode can be affected by the position of the defect in the overall structure. However, the frequency of the defect mode is found to be independent of the defect location. It is further established that the mode frequency can be controlled via the manipulation of the effective filling fraction of the periodic structures with a positive gradient. These findings enrich our knowledge of defect mode parameters for liquid surface waves and due to the universal nature of wave phenomena, the findings would open new avenues of wave energy control and manipulation applications.