410
A. Pors et al.
BDP = δ α f =
αϕL(n g − n d )
ϕ 2
.
(11.8)
For the two-nanorod configuration (Fig. 11.4) we obtained αϕ ∼70 nm centered at the
wavelength ϕ ∼ 1150 nm and L ∼ 0.55 µm, which results in BDP ∼ 0.25. It should
be noted that a comparison of the main characteristics of the two plasmonic EIT
realizations has been conducted in [13], demonstrating a fundamental equivalence
between the two approaches, even though they are very different with respect to the
fabrication tolerances required.
11.2.2 The Three-Nanorod System
The DED configuration considered above consists of two nanorods of different length
and, consequently, polarizabilities of different strength. At the same time, as follows
from the qualitative arguments in Sect. 11.2 [Eq. (11.2)], a prominent EIT effect
depends on the cancellation of at least the real part of the total polarizability of the unit
cell. This criteria might be easier to achieve by using two small nanorods resonating
at a shorter wavelength being placed on both sides of the large nanorod resonating at a
longer wavelength. The resulting structure is termed the three-nanorod configuration
(Fig. 11.5a), and the EIT characteristics of the corresponding metamaterial is the
subject of this section. The configuration is also included to illustrate the versatility
of the DED concept. The configuration under study is made of two smaller gold
nanorods of size 105 × 40 × 50 nm 3 separated by a distance d = 100 nm to the
larger gold nanorod of size 150 × 60 × 50 nm 3 (Fig. 11.5a). It should be noted
that, to balance the scattering strengths of the longer nanorod and the two shorter
nanorods, the latter was designed to be narrower. Also, the induced currents in the
three-nanorod configuration do not induce a magnetic dipole at the central frequency,
which suggests a relatively weak dependence of the transmission properties on the
angle of incidence [10].
The EIT-properties of the three-nanorod DED metamaterial will be considered
for x-polarized light propagating along the z-axis and a parallelepiped unit cell of
size 300 × 300 × 150 nm 3 . In contrast to the previous section, the effective refractive
index will be computed using the S-parameter method for which the retrieval procedure is based on transmission and reflection coefficients [33]. Figure 11.5b shows
transmission and reflection spectra calculated for one layer of unit cell, exhibiting
the EIT-like transmission spectra with window of transparency at ∼870 nm and a
quite strong reflection away from the central wavelength, at which it is strongly suppressed. The fact that the reflection suppression is virtually complete at the central
wavelength while the transparency is not agrees well with our general consideration
of EIT realization with plasmonic nanostructures.
The transmission and reflection spectra calculated for three layers of unit cells
were used to determine the dispersion of the corresponding metamaterial effective
refractive index (Fig. 11.5c). Note the similarity of the dispersion of real and imaginary parts of the effective index to that obtained for the metamaterial using two
A. Pors et al.
BDP = δ α f =
αϕL(n g − n d )
ϕ 2
.
(11.8)
For the two-nanorod configuration (Fig. 11.4) we obtained αϕ ∼70 nm centered at the
wavelength ϕ ∼ 1150 nm and L ∼ 0.55 µm, which results in BDP ∼ 0.25. It should
be noted that a comparison of the main characteristics of the two plasmonic EIT
realizations has been conducted in [13], demonstrating a fundamental equivalence
between the two approaches, even though they are very different with respect to the
fabrication tolerances required.
11.2.2 The Three-Nanorod System
The DED configuration considered above consists of two nanorods of different length
and, consequently, polarizabilities of different strength. At the same time, as follows
from the qualitative arguments in Sect. 11.2 [Eq. (11.2)], a prominent EIT effect
depends on the cancellation of at least the real part of the total polarizability of the unit
cell. This criteria might be easier to achieve by using two small nanorods resonating
at a shorter wavelength being placed on both sides of the large nanorod resonating at a
longer wavelength. The resulting structure is termed the three-nanorod configuration
(Fig. 11.5a), and the EIT characteristics of the corresponding metamaterial is the
subject of this section. The configuration is also included to illustrate the versatility
of the DED concept. The configuration under study is made of two smaller gold
nanorods of size 105 × 40 × 50 nm 3 separated by a distance d = 100 nm to the
larger gold nanorod of size 150 × 60 × 50 nm 3 (Fig. 11.5a). It should be noted
that, to balance the scattering strengths of the longer nanorod and the two shorter
nanorods, the latter was designed to be narrower. Also, the induced currents in the
three-nanorod configuration do not induce a magnetic dipole at the central frequency,
which suggests a relatively weak dependence of the transmission properties on the
angle of incidence [10].
The EIT-properties of the three-nanorod DED metamaterial will be considered
for x-polarized light propagating along the z-axis and a parallelepiped unit cell of
size 300 × 300 × 150 nm 3 . In contrast to the previous section, the effective refractive
index will be computed using the S-parameter method for which the retrieval procedure is based on transmission and reflection coefficients [33]. Figure 11.5b shows
transmission and reflection spectra calculated for one layer of unit cell, exhibiting
the EIT-like transmission spectra with window of transparency at ∼870 nm and a
quite strong reflection away from the central wavelength, at which it is strongly suppressed. The fact that the reflection suppression is virtually complete at the central
wavelength while the transparency is not agrees well with our general consideration
of EIT realization with plasmonic nanostructures.
The transmission and reflection spectra calculated for three layers of unit cells
were used to determine the dispersion of the corresponding metamaterial effective
refractive index (Fig. 11.5c). Note the similarity of the dispersion of real and imaginary parts of the effective index to that obtained for the metamaterial using two