Biomedical Engineering Reference
In-Depth Information
open one, that is, hyperboloid as shown in Fig. 8.6c [45, 53-
58]. This topological transition from an ordinary to a so-called
hyperbolic photonic metamaterial (HMM) is an analog of the
Lifshitz topological transition in superconductors [59] when their
Fermi surfaces undergo transformation under the influence of
external factors such as pressure or magnetic fields. In the same
manner that the Lifshitz transition leads to dramatic changes in
the electron transport in metals [60, 61], the topological transition
of the photonic metamaterial has a dramatic effect on its DOS and
photontransportcharacteristics.Thisenablesdevelopmentofnovel
deviceswithenhancedopticalpropertiesincludingsuper-resolution
imaging, optical cloaking, and enhanced radiative heat transfer [45,
53-58]. The spectral region that includes the high-energy branches
of the dispersion corresponds to the metamaterial transformation
into a type I hyperbolic regime. The type I HMM is characterized
by a single negative component of the dielectric tensor, which is
perpendicular to the interface. A type II HMM (corresponding to
the spectral region overlapping low-energy dispersion branches)
features two negativein-planecomponents of thedielectric tensor.
In the following, we will reveal that the global topological
transition of the multilayered metamaterial into the hyperbolic
regime is driven by the collective dynamics of local topological
features in the electromagnetic field such as nucleation, migration,
and annihilation of nanoscale optical vortices. It has been already
shown both theoretically and experimentally that the high DOS in
the hyperbolic metamaterial strongly modifies radiative rates of
quantum emitters such as quantum dots positioned either inside or
close to the HMM [53, 55, 56]. To reveal the local electromagnetic
field topology underlying this process, we consider radiation of a
classical electric dipole located in air just outside the HMM slab (as
shownFigs.8.6-8.9).Thedipoleisseparatedfromthemetamaterial
slab by a 10 nm thick TiO
2
spacer layer, which is a typical
configuration in the experiment that helps to avoid quenching of
quantum emitters such as quantum dots via non-radiative energy
transfer to the metamaterial slab [53, 55, 56].
Figures 8.7 and 8.8 demonstrate how the metamaterial in the
type I and type II hyperbolic regimes modifies radiation and
transport of photons emitted by a dipole source. The availability
