Explaining negative refraction without negative refractive indices

摘要

Negative refraction through a triangular prism may be explained withoutassigning a negative refractive index to the prism by using array theory. Forthe case of a beam incident upon the wedge, the array theory accuratelypredicts the beam transmission angle through the prism and provides an estimateof the frequency interval at which negative refraction occurs. Negativerefraction effects not only occur in prisms made of traditional metamaterialunit cells, such as magneto-dielectric spheres, but also in solid prisms madeof completely filled, homogenous unit cells. In both prisms, the hypotenuse hasa staircase shape because they are built of cubic unit cells. The large phasedelay imparted by each unit cell, combined with the staircase shape of thehypotenuse, creates the necessary conditions for negative refraction. Full wavesimulations using the finite-difference time-domain method show that arraytheory accurately predicts the beam transmission angle for both solid prismsand prisms made of magneto-dielectric spheres.