Robert W. Boyd

where £«,, cop, and y are parameters that describe the optical properties of the mate-
rial. We can see by inspection that the real part of c(ci?) will vanish at the frequency
0) = ü)p/y[€^. This frequency, known as the shielded plasma frequency, can corre-
spond to infrared, visible, or ultraviolet radiation depending on the optical proper-
ties of the material.
Zero-index materials possess many other properties that are both intellec-
tually intriguing and important for applications in modern optical technology
[3]. One such property is that fundamental radiative processes become modified
in a ZIM. We recall that the Einstein A coefficient gives the rate of spontaneous
emission of an atomic System, and the Einstein B coefficient is proportional to
the rate of stimulated emission [1], It can be shown [2] that these quantities are
modified for the case of an atom in a medium of background refractive index n,
and are given by
A = nAV3C
and
B-*-*vac
“ 2~ *
n
We see from the first of these equations that spontaneous emission can be
entirely suppressed for the limiting case of n = 0. The vanishing of spontaneous
emission can have enormous technological implications; for example, it can be
used to construct a threshold-less (and thus highly energy-efficient) laser. At first
sight, it might appear stränge that spontaneous emission can be suppressed in this
way, in that spontaneous emission is often ascribed to bc a consequence of vacuum
fluctuations, which would not be suppressed in a ZIM. In fact, the origin of the
suppression is that the density of States of the electromagnetic field vanishes for
n = 0; thus, spontaneous emission is suppressed for the simple reason that there is
no field mode into which the atom can radiate.
The author’s own research in ZIMs has been in the study of their nonline-
ar optical properties. Nonlinear optical properties are technologically important
because they can be utilized for the constructions of photonic devices such as
switches. For rather technical reasons [4], ZIMs tend to possess extremely large
nonlinear optical responses. For the particular case of the doped semiconductor
indium-tin-oxide (ITO), we measured a nonlinear n2 coefficient 106 times larger
than that of fused silica. In subsequent work, we fabricated a metasurface con-
sisting of gold nanorods deposited onto an ITO Substrate, and we found that the
nonlinear coefficient is further enhanced and can be controlled in both magnitude
and sign [5],

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