  Negative refraction through a triangular prism may be explained without
assigning a negative refractive index to the prism by using array theory. For
the case of a beam incident upon the wedge, the array theory accurately
predicts the beam transmission angle through the prism and provides an estimate
of the frequency interval at which negative refraction occurs. Negative
refraction effects not only occur in prisms made of traditional metamaterial
unit cells, such as magneto-dielectric spheres, but also in solid prisms made
of completely filled, homogenous unit cells. In both prisms, the hypotenuse has
a staircase shape because they are built of cubic unit cells. The large phase
delay imparted by each unit cell, combined with the staircase shape of the
hypotenuse, creates the necessary conditions for negative refraction. Full wave
simulations using the finite-difference time-domain method show that array
theory accurately predicts the beam transmission angle for both solid prisms
and prisms made of magneto-dielectric spheres.
