Acoustic band structures and time reversal of elastic waves in two- and three-dimensional phononic crystals

The present study aims to investigate experimentally the acoustic band structures of elastic waves in two-dimensional (2D) and three-dimensional (3D) phononic crystals (PCs) consisting of periodic square arrays of cylindrical air holes in a solid matrix made of cubic polyoxymethylene. In the 2D PC, the first band gap appeared at frequencies between 0.50 and 0.77 MHz, and the second pass band at frequencies between 0.77 and 1.17 MHz. On the other hand, the 3D PC exhibited a wider band gap extending from a frequency of 0.44 MHz with noise level transmission at a frequency around 0.93 MHz. The time compressions of the time-reversed waves through the 2D and the 3D PCs were also obtained by using a time reversal process. The 2D PC exhibited better time compression than the 3D PC in the time-reversed waves, consistent with the fact that the time compression achieved by time reversal is sensitive to the number of frequency information grains.