An exact mathematical proof for the condition of zero reflection by multilayered metamaterial media

The planar multilayered media composed of a combination of common materials and metamaterials are analyzed by a full-wave matrix method for determining the conditions of zero reflection under normal plane wave incidence. Although the exact mathematical analysis is performed at a single frequency, but it may be carried out for a frequency spectrum to design the structure for a specified band width. Consequently, it is observed that the conditions of zero reflection by multilayered media may be achieved by various combinations of common materials and metamaterials.