A non-reflecting metamaterial slab under the finite-embedded coordinate transformation

Under the restrictions that the mapping functions of transformation are defined in extended two-dimensional (2D) forms and the incident waves are 2D propagating fields, the conditions for non-reflecting boundaries in a finite-embedded coordinate transformation metamaterial slab are derived. By exploring several examples, including some reported in the literatures and some novel ones developed in this study, we show that our approach can be efficiently used to determine the condition for a finite-embedded coordinate transformed metamaterial slab to be non-reflecting.