Enhancement of acoustic rainbow trapping based on coupled-mode theory

Acoustic rainbow trapping, in which acoustic waves with distinct frequencies are separated and trapped at different positions, was given high consideration in frequency filtering, energy acquisition, and acoustic wave manipulation. However, due to inherent attenuation, acoustic waves trapped far from the acoustic source suffer from large losses and small amplitudes. Thus, we introduce coupled-mode theory in acoustic rainbow trapping to enhance trapped acoustic fields. First, we design a two-dimensional network composed of annular units with cross-shaped connections to adjacent units. By setting gradient coupling strengths between units, seven flatbands with distinct frequencies are achieved, which produce acoustic rainbow trapping in different units. Furthermore, the coupling strengths are adjusted according to coupled-mode theory, making the flatband frequencies of adjacent units approach each other. Simulations and experiments demonstrate that the amplitudes of the trapped acoustic waves are considerably increased, which enhance the acoustic rainbow trapping in the structure.