Frequency-dependent focal length of a plano-spherical convex subsonic index lens

This study aims to investigate the frequency-dependent characteristics of the focal length of an acoustic lens made of a material with a frequency-dependent acoustic refractive index (ARI). For this purpose, an exchangeable plano-spherical convex subsonic index lens (PSCSIL) was fabricated using a polydimethylsiloxane (PDMS) material. The ARI of the lens material was evaluated via the tone-burst through-transmission method over the frequency range of 1–10 MHz. The frequency dependence of the focal length of the fabricated PSCSIL was evaluated through graphical analysis of the acoustic field scanned by a hydrophone as well as of that simulated using the finite element method. The measured ARI and focal length were observed to be dependent on frequency. The simulated and measured focal lengths of the PSCSIL exhibited a great discrepancy with their respective values predicted using the conventional focal length equation. This discrepancy was further studied using the ray-tracing method and is described in the discussion section. In conclusion, the spherical curvature of PSCSIL does not induce the convergence of rays to meet in a point. The ray tracing method does not take into account the phase complexity of the near-field region inside the lens. This causes the actual focal length to be shorter than the predicted one.