Explaining negative refraction without negative refractive indices

TL;DR

This paper demonstrates that negative refraction can be explained using array theory without negative refractive indices, accurately predicting beam behavior in various prism structures through simulations.

Contribution

It introduces a new array theory approach to explain negative refraction, avoiding the need for negative refractive index assumptions, and validates it with full wave simulations.

Findings

Array theory accurately predicts beam transmission angles.

Negative refraction occurs in both metamaterial and homogeneous prisms.

Staircase hypotenuse shape is key to negative refraction.

Abstract

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.