Numerical and experimental analysis of a focused reflected wave in a multi-layered material based on a ray model.

•Using a reflective focal probe for simultaneous sound-velocity and thickness measurements of a multi-layered material.•We study the multi-mode wave focus to identify the focused longitudinal waves.•Proposing the ‘bottom left’ principle to identify longitudinal-wave focus.•A phase differentiation theory is proposed to find the incident angle for the focus of the tilted rays.