418
A. Pors et al.
(ϕ = 840 nm) one observes asymmetry in scattering due to interference between light
from the two detuned nanorods. However, at the central wavelength (ϕ = 941 nm)
the asymmetry is maximized with a vanishing amount of power scattered into the
−y-direction due to destructive interference.
For practical realization of environmental sensing, it is necessary to collect the
scattered light within a solid angle along the ±y-directions [see dashed circles in
Fig. 11.8b]. Figure 11.8c displays the amount of power scattered into a cone angle
of πσ = 22.5 ◦ in the +y-direction (τ +
sc ), −y-direction (τ −
sc ), and their ratio in the
neighborhood of the central wavelength. Clearly, the scattering ratio is an eminent
probe for environmental changes as it features a FWHM of ∼2 nm. At the same time,
the scattering ratio demonstrates a sensitivity of s ∼600 nm/RIU to the refractive
index of the surrounding medium (Fig. 11.8d), which results in a FOM as large as
∼300. Importantly, the configuration is quite robust towards fabrication tolerances.
As an example, if the separation d is changed to 90 nm the FWHM increases to
∼2.5 nm (not shown) which, of course, lowers the FOM but still keeps the value
remarkably high compared to conventional sensing techniques. It should be stressed
that it is possible to detect the scattered light from a single DED configuration. To
give an example, for the configuration in Fig. 11.8 (πσ = 22.5 ◦ ) illuminated with
the intensity of 1 mW/µm 2 , the scattered powers at the central wavelength would
amount to P + ∼ 6.5 µW and P − ∼ 2.3 nW that should be possible to reliably detect.
The scattered power available for the detection can be significantly increased if
the same idea is implemented using a periodic array of DED pairs. In this case, the
scattering directions with constructive and destructive interference can be chosen to
coincide with the directions of light diffraction into ±first orders. Considering noninteracting point dipoles again, the corresponding retardation phase should, in this
case, be considered in the direction of light diffraction determined by the array period
Θ y along the line connecting DED scatterers. The retardation phase k 0 n d d should
therefore be changed onto k 0 n d d sin σ 1 , where σ 1 is the diffraction angle given by
the grating equation: sin σ 1 = ϕ/(n d Θ y ). This modification results in the following
conditions required to extinguish one and maximize another diffraction order
d =
Θ y
4
, π =
ω
2
,
(11.12)
which are again strictly valid only for noninteracting scatterers. The periodicity in
the other direction, Θ x , should be as small as possible to increase the density of DED
pairs but large enough so as to not result in the strong coupling between the neighbor
DED pairs. In contrast, Θ y should be on the order of the wavelength so that the array
does not act as a metasurface with only zero-order diffraction.
The idea of using the ratio of scattering in the first diffraction orders as a
sensitive probe has been investigated experimentally as a proof-of-principle study.
In these experiments, we fabricated periodic (Θ x = 400 nm and Θ y = 750 nm)
arrays (50 × 50 µm 2 ) consisting of individual and double gold nanorods (of different
lengths) on a silica substrate using electron-beam lithography and lift-off applied to
a 50 nm thick gold film (Fig. 11.9a). Transmission spectra were measured using a
A. Pors et al.
(ϕ = 840 nm) one observes asymmetry in scattering due to interference between light
from the two detuned nanorods. However, at the central wavelength (ϕ = 941 nm)
the asymmetry is maximized with a vanishing amount of power scattered into the
−y-direction due to destructive interference.
For practical realization of environmental sensing, it is necessary to collect the
scattered light within a solid angle along the ±y-directions [see dashed circles in
Fig. 11.8b]. Figure 11.8c displays the amount of power scattered into a cone angle
of πσ = 22.5 ◦ in the +y-direction (τ +
sc ), −y-direction (τ −
sc ), and their ratio in the
neighborhood of the central wavelength. Clearly, the scattering ratio is an eminent
probe for environmental changes as it features a FWHM of ∼2 nm. At the same time,
the scattering ratio demonstrates a sensitivity of s ∼600 nm/RIU to the refractive
index of the surrounding medium (Fig. 11.8d), which results in a FOM as large as
∼300. Importantly, the configuration is quite robust towards fabrication tolerances.
As an example, if the separation d is changed to 90 nm the FWHM increases to
∼2.5 nm (not shown) which, of course, lowers the FOM but still keeps the value
remarkably high compared to conventional sensing techniques. It should be stressed
that it is possible to detect the scattered light from a single DED configuration. To
give an example, for the configuration in Fig. 11.8 (πσ = 22.5 ◦ ) illuminated with
the intensity of 1 mW/µm 2 , the scattered powers at the central wavelength would
amount to P + ∼ 6.5 µW and P − ∼ 2.3 nW that should be possible to reliably detect.
The scattered power available for the detection can be significantly increased if
the same idea is implemented using a periodic array of DED pairs. In this case, the
scattering directions with constructive and destructive interference can be chosen to
coincide with the directions of light diffraction into ±first orders. Considering noninteracting point dipoles again, the corresponding retardation phase should, in this
case, be considered in the direction of light diffraction determined by the array period
Θ y along the line connecting DED scatterers. The retardation phase k 0 n d d should
therefore be changed onto k 0 n d d sin σ 1 , where σ 1 is the diffraction angle given by
the grating equation: sin σ 1 = ϕ/(n d Θ y ). This modification results in the following
conditions required to extinguish one and maximize another diffraction order
d =
Θ y
4
, π =
ω
2
,
(11.12)
which are again strictly valid only for noninteracting scatterers. The periodicity in
the other direction, Θ x , should be as small as possible to increase the density of DED
pairs but large enough so as to not result in the strong coupling between the neighbor
DED pairs. In contrast, Θ y should be on the order of the wavelength so that the array
does not act as a metasurface with only zero-order diffraction.
The idea of using the ratio of scattering in the first diffraction orders as a
sensitive probe has been investigated experimentally as a proof-of-principle study.
In these experiments, we fabricated periodic (Θ x = 400 nm and Θ y = 750 nm)
arrays (50 × 50 µm 2 ) consisting of individual and double gold nanorods (of different
lengths) on a silica substrate using electron-beam lithography and lift-off applied to
a 50 nm thick gold film (Fig. 11.9a). Transmission spectra were measured using a