Acoustic carpet invisibility cloak with two open windows using multilayered homogeneous isotropic material

We present a method for designing an open acoustic cloak that can conceal a perturbation on flat ground and simultaneously meet the requirement of communication and matter interchange between the inside and the outside of the cloak. This cloak can be constructed with a multilayered structure and each layer is an isotropic and homogeneous medium. The design scheme consists of two steps: firstly, we apply a conformal coordinate transformation to obtain a quasi-perfect cloak with heterogeneous isotropic material; then, according to the profile of the material distribution, we degenerate this cloak into a multilayered-homogeneous isotropic cloak, which has two open windows with negligible disturbance on its invisibility performance. This may greatly facilitate the fabrication and enhance the applicability of such a carpet-type cloak. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)