II. Wissenschaftliche Vorträge

Robert l/IZ. Boyd
„How Light Behaves when the Refractive Index Vanishes"
Sitzung der Mathematisch-naturwissenschaftlichen Klasse am 25. Oktober
2019

The refractive index derives its name from the fact that it determines how much a
beam of light bends (or refracts) when it passes from one material to another. This
relationship is expressed by Snell’s law, which has the form
»i sin 0] = n2 sin 02
and is illustrated in part (a) of Fig. 1. From the form of Snell’s law, we see that if
«i is equal to zero, then for any angle of incidence 0i the angle of refraction 02 will
be equal to zero, as illustrated in part (b) of the figure. As a consequence, light can
leave a zero-index material (ZIM) only in a direction perpendicular to the surface
of the material. A basic law of physics States that light rays are reversible. For exam-
ple, if a light ray can travel from medium 1 to medium 2 along a certain path, it can
travel from medium 2 to medium 1 along the same path, but with the directions
reversed. We thus see that light can enter a ZIM only from a direction perpendic-
ular to the surface of the material.


Fig. 1. (a) General form of Snell’s law. (b) For the special case in which the refractive index of medium 1 van-
ishes, light always leaves perpendicular to the inteiface.

Most common materials have refractive Indices that lie in the ränge from
n = 1 (the value for air) to n = 4 (for germanium). However, refractive Indices
smaller than n = 1 can be obtained under special situations, such as close to and
slightly above the frequency of an atomic absorption line. To obtain materials with
ti = 0, two approachcs are generally used. One approach is to use a metamaterial,
that is a material that has been designed at a subwavelength level to possess a van-
ishing refractive index. The other approach is to make use a material with a sig-
nificant population of free electrons residing in a conduction band. The dielectric
permittivity e(o)) (which is simply the square of the complex index of refraction) of
such a material is given by
2
£(w)= £oo- o ’
o) - Zicoy

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