Analysis of anisotropic epsilon-near-zero hetero-junction lens for concentration and beam splitting

In this Letter, we analyze a recently reported hetero-junction lens of two anisotropic epsilon-near-zero (ENZ) media for its concentration and beam splitting properties. The equivalent lensmakers' equation of the concentrating mechanism is first derived using geometrical optics and dispersion relations; and aberrations are discussed. It is shown that the light concentrator's focal distance is directly proportional to the thickness of the lens, opposite to conventional dielectric lenses. It is then shown that the same hetero-junction structure can be used as a near-field beam-splitter when illuminated from the back, in addition to its concentration property. Equal and unequal beam splitting, as well as beam shifting can be achieved using a very thin device.