Shaping acoustic discrete Talbot pattern in aperiodic waveguide arrays

In this work, we propose an aperiodic acoustic waveguide array by slow-varying the waveguide widths to construct parabolic refractive-index distribution; the discrete Talbot pattern supported by the acoustic waveguide arrays for periodically inputting can be shaped by focusing trajectories due to gradient potential. Theoretically, we predict the focusing length and propagating trace of the spoof acoustic waves based on the Hamiltonian acoustic method and the Talbot distance with the coupled mode theory. The simulation and experiment results demonstrate the shaping Talbot effect that the Talbot pattern is tailored by the envelope in aperiodic waveguide arrays. In particular, the shaped Talbot pattern can be freely tuned by changing the refractive-index gradient and incident angle. This work provides a method of tailoring the Talbot pattern of wave acoustics by using the focusing envelope of ray acoustics, which may open a door for a variety of new applications in imaging technologies of integrated on-chip acoustics.