A Cartesian model for perfect cloaks that lead the incident electromagnetic wave around the cloaked object, has been introduced. A structure of layered slabs made from gradually electromagnetically sparser materials is excited by a line source located in the vicinity of the front surface of the device. The propagation directions of the incident rays are shifted, as dictated by the Snell's law, to be almost tangentially oriented to the rear boundary of the slab cluster. In this sense, the incident power is distributed along a much more extended region compared to the case of free space, which makes any kind of electromagnetic entity to interact weakly with the electromagnetic field. At the same time, the reflections back to the source are not significant due to the matched impedance and the smooth material change of the layered structure. Therefore, this new model uncovers a principle of operation, which demonstrates substantial qualities in functioning as cloak.