Enhancement of sound by soft reflections in exponentially chirped crystals

The enhancement of sound inside a two dimensional exponentially chirped crystal during the soft reflections of waves is experimentally and theoretically explored in this work. The control of this enhancement is achieved by a gradual variation of the dispersion in the system by means of a chirp of the lattice constant. The sound enhancement is produced at some planes of the crystal in which the wave is softly reflected due to a progressive slowing down of the sound wave. We find that the character of the sound enhancement depends on the function of the variation of dispersion, i.e., on the function of the chirp. A simple coupled mode theory is proposed to find the analytical solutions of the sound wave enhancement in the exponentially chirped crystal. Harmonic and time domain numerical simulations are performed to interpret the concept of the soft reflections, and to check the analytically calculated field distributions both in good agreement with experiments. Specially we obtain stronger sound enhancement than in linearly chirped crystals. This sound enhancement could motivate applications in energy harvesting, e.g., to increase the efficiency of detectors and absorbers.