The resulting destructive interference of quantum probability amplitudes
inhibits absorption and leads to a narrow transparency window in the spectrum of the otherwise opaque atomic
medium. As a result, the probe beam
can propagate without losses. This resonant transmission peak is accompanied
by sharp normal dispersion, which can
lead to a dramatic reduction in group
velocity and a significant enhancement
of nonlinear interactions.
However, scientists’ observations of
EIT in atomic gases were restricted to
the available atomic resonances, and
the work necessitated optical pumping
and often cryogenic temperatures. Such
requirements severely hinder practical
applications, particularly with respect to
integration. These obstacles were soon
overcome by the realization that the
essential physics behind EIT are actually
classical, and similar behavior can be
observed in very simple systems, such as
coupled spring-mass oscillators.
This insight led to the implementation of induced transparency effects in
classical optical systems—for example,
coupled optical resonators, photonic
bandgap crystals and photonic crystal
waveguides—that are robust and do not
require special experimental conditions.
The operation frequency is directly
related to the geometry of the structure
and can be varied in a wide spectral
range through scaling. Nevertheless,
in all approaches to classical EIT, the
structure extends along the propagation
direction of the incident wave, which
imposes restrictions on the minimum
dimensions of the medium.
Excited state
Pump
Probe
Meta-stable
state
Ground state
Typical three-level atomic system
used in demonstrations of EIT.
The ground state is coupled to the
excited state, where absorption
occurs via a probe beam. A pump
beam couples the metastable state
to the excited state, while transitions
from the metastable to the ground
state are not allowed. Interference
between the two transitions leads to
a vanishing probability for the atoms
to be found in the excited state; con-
sequently, absorption is minimized.
Transparency window
Absorption
Pump on
Frequency
Pump off
Refractive index
Pump on
Pump off
Frequency
(Left) A characteristic probe absorption spectrum of an atomic medium under EIT conditions. The broad absorption peak experienced by the probe beam is split in two by a narrow dip when the pump is applied. (Right) This results in a very sharp variation of the
refractive index, which is responsible for long pulse delays and slow-light behavior.
F
Mechanical analog of an atomic EIT system. The first oscillator is subject to friction
and corresponds to the atom under the influence of the probe beam (external force
F), while the second stands for the coupling to the pump beam. Under certain conditions, the first oscillator remains still, thus eliminating dissipation in the system.
Metamaterial-induced
transparency
In the case of metamaterials, we used
Fano resonances in a planar array
of asymmetrically split-ring “meta-
molecules” that consist of two arcs with
different lengths in order to minimize
scattering losses and achieve high-
quality resonances. Indeed, breaking
the symmetry of the split-ring leads to
two closely spaced resonances, each of
which corresponds to strong excitation
of one of the two arcs. When excited by
an incident electromagnetic wave, the
two arcs support currents oscillating
in-phase, apart from a narrow frequency
range, where an anti-symmetric current
configuration is established due to the
coupling of the two resonances.
As a consequence, these anti-symmetric
currents radiate fields that interfere
destructively, allowing the incident wave
to propagate without losses, as signified by a narrow transparency window
in the transmission spectrum of the
metamaterial. This resonant mode has a
long lifetime due to its weak coupling to
free-space radiation and therefore appears
to be “trapped” in the vicinity of the
metamaterial surface—hence the term
“trapped mode.” An important consequence of causality restrictions is that, at
the metamaterial resonance, the transmission band is accompanied by steep
normal dispersion, providing for low
group velocities and slow light behavior.
In fact, we showed in a recent study
that similar resonances can also be
observed experimentally in a bi-layered
structure. In this case, the two metamaterial layers can be either identical
or very similar, and they are separated
by a small sub-wavelength distance
along the propagation direction. This
displacement allows the two layers to be
excited with opposite phases at a specific
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