11 Plasmonic Functionalities Based on Detuned Electrical Dipoles
405
An increase in the group index can thereby be traced to the dispersion of the real part
of cell polarizability, resulting in [see Eq. (11.2)]
d[Re(λ 1 + λ 2 )]
dε
ε 0
∼ 4 Aε 0
4π 2 − ω 2
(4π 2 + ω 2 ) 2 .
(11.5)
It should be borne in mind that the group velocity is generally not a useful concept in
regions of anomalous dispersion [23] and that the above relation should therefore be
considered only for relatively large detuning: π > 0.5ω . In the case of normal dispersion at the probe frequency, one can show that the group refractive index exhibits a
broad maximum at π opt =
∝
0.75ω . A similar condition of the detuning to be close
to the broadening of two resonances is also found in the dressed-state picture of the
EIT for atomic media [7, 8]. Finally, the above condition [Eq. (11.5)] being obtained
in the approximation of non-interacting dipolar scatterers should be considered only
as an estimate of the optimum DED detuning, with a careful optimization yet to be
conducted for a given DED configuration designed to operate in a given frequency
range. In the following, we therefore study a realistic DED configuration consisting
of two differently-sized and weakly-interacting gold nanorod antennas numerically,
and address the intriguing phenomena of optical transparency and slow light.
11.2.1 The Two-Nanorod System
The DED concept deals, in principle, with any imaginable configuration that displays
scattering suppression in between the detuned resonances. In this section, however,
the concept will be further elucidated by considering the simplest DED configuration:
two detuned nanorods (Fig. 11.1a). At first, the optical properties of a single twonanorod configuration will be discussed with emphasis on the electric and magnetic
responses, followed by a discussion of two-nanorod metamaterials and its ability to
slow down light near the central frequency.
In the following we consider gold nanorods with cross-sections of w × w =
25 × 25 nm 2 , lengths (i) L 1 and (ii) L 2 = 150 nm, respectively, and a center-tocenter distance d. The surrounding medium is assumed to be glass with refractive
index 1.45. It should be emphasized that when d and L 1 are not explicitly mentioned
in this section, the configuration is considered with nominal values d = 120 nm and
L 1 = 125 nm. All modeling results presented throughout this chapter are conducted
with the finite-element method implemented in the commercial software Comsol
Multiphysics in which the dielectric function of gold is described by interpolation of
tabular values [25]. In the simulations, all corners of the nanorods are rounded with
a radius of 3 nm for numerical as well as physical reasons.
If a z-propagating x-polarized incident wave is considered, the individual nanorods
[(i) and (ii)] exhibit fundamental plasmonic resonances at ϕ ∼ 1065 nm and ϕ ∼
1190 nm, respectively (Fig. 11.1b). These resonances are related to standing waves
of short-range surface plasmon polaritons (SR-SPPs) [21] making it easy to control
405
An increase in the group index can thereby be traced to the dispersion of the real part
of cell polarizability, resulting in [see Eq. (11.2)]
d[Re(λ 1 + λ 2 )]
dε
ε 0
∼ 4 Aε 0
4π 2 − ω 2
(4π 2 + ω 2 ) 2 .
(11.5)
It should be borne in mind that the group velocity is generally not a useful concept in
regions of anomalous dispersion [23] and that the above relation should therefore be
considered only for relatively large detuning: π > 0.5ω . In the case of normal dispersion at the probe frequency, one can show that the group refractive index exhibits a
broad maximum at π opt =
∝
0.75ω . A similar condition of the detuning to be close
to the broadening of two resonances is also found in the dressed-state picture of the
EIT for atomic media [7, 8]. Finally, the above condition [Eq. (11.5)] being obtained
in the approximation of non-interacting dipolar scatterers should be considered only
as an estimate of the optimum DED detuning, with a careful optimization yet to be
conducted for a given DED configuration designed to operate in a given frequency
range. In the following, we therefore study a realistic DED configuration consisting
of two differently-sized and weakly-interacting gold nanorod antennas numerically,
and address the intriguing phenomena of optical transparency and slow light.
11.2.1 The Two-Nanorod System
The DED concept deals, in principle, with any imaginable configuration that displays
scattering suppression in between the detuned resonances. In this section, however,
the concept will be further elucidated by considering the simplest DED configuration:
two detuned nanorods (Fig. 11.1a). At first, the optical properties of a single twonanorod configuration will be discussed with emphasis on the electric and magnetic
responses, followed by a discussion of two-nanorod metamaterials and its ability to
slow down light near the central frequency.
In the following we consider gold nanorods with cross-sections of w × w =
25 × 25 nm 2 , lengths (i) L 1 and (ii) L 2 = 150 nm, respectively, and a center-tocenter distance d. The surrounding medium is assumed to be glass with refractive
index 1.45. It should be emphasized that when d and L 1 are not explicitly mentioned
in this section, the configuration is considered with nominal values d = 120 nm and
L 1 = 125 nm. All modeling results presented throughout this chapter are conducted
with the finite-element method implemented in the commercial software Comsol
Multiphysics in which the dielectric function of gold is described by interpolation of
tabular values [25]. In the simulations, all corners of the nanorods are rounded with
a radius of 3 nm for numerical as well as physical reasons.
If a z-propagating x-polarized incident wave is considered, the individual nanorods
[(i) and (ii)] exhibit fundamental plasmonic resonances at ϕ ∼ 1065 nm and ϕ ∼
1190 nm, respectively (Fig. 11.1b). These resonances are related to standing waves
of short-range surface plasmon polaritons (SR-SPPs) [21] making it easy to control