Revisit the carpet cloak from optical conformal mapping

The original carpet cloak [Phys. Rev. Lett. 101, 203901 (2008)] was designed by a numerical method, the quasi-conformal mapping. Therefore its refractive index profile was obtained numerically. In this letter, we propose a new carpet cloak based on the optical conformal mapping, with an analytical form of a refractive index profile, thereby facilitating future experimental designs.