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A. Pors et al.
losses are negligibly small with respect to the absorption losses. On the other hand,
environmental sensing relies on the detection of scattered light so that, for practical
purposes, nanoparticles have to be chosen large enough to obtain measurable signals.
In order to boost the FOM, alternative ways have been investigated to create sharp
spectral features that are sensitive to the surrounding medium. For example, one may
take advantage of diffractive coupling present in periodic arrays of nanoparticles
[40] or in complementary hole structures [41] when the period is on the order of the
wavelength. Especially at the onset of diffraction it is possible to excite the so-called
Rayleigh anomaly. The Rayleigh anomaly corresponds to light that is diffracted
parallel to the grating, and it appears in reflection and transmission measurements
as a sharp spectral feature that is sensitive to the surroundings. As a prominent
example, the coupling of SPPs and the Rayleigh anomaly in multiscale patterned
hole arrays in gold films demonstrates FOM as large as 23.3 [42]. The diffractive
coupling approach, however, does not allow for measuring local changes in nanoscale
volumes or for a high integration density of sensing devices.
A second approach that alleviates the above problems, yet with a high-Q resonance, involves interference between coupled nanostructures and the creation of
Fano resonances. The Fano resonance occurs due to the interference between radiant and subradiant plasmonic modes resulting (typically) in asymmetric resonances
with narrow linewidths [43]. For this reason, a multitude of complex plasmonic
nanostructures exhibiting Fano resonances have been investigated in relation to plasmonic sensing, though the FOM, generally, never exceeds 10 [5, 44, 45]. Note that
Fano resonances have also been advantageously exploited within biosensing [46].
Our approach still rely on DED configurations exhibiting an EIT-like response.
However, this time we take advantage of the scattering asymmetry present near the
central frequency [47]. The idea can be elaborated by considering scattering in ±ydirection for two non-interacting point scatterers placed similarly to the nanorods
in (Fig. 11.1a) with their electric dipole moment along the x-axis. If each scatterer
is described by the polarizability in Eq. (11.1), it is straightforward to show that in
the limit of weak detuning (ε 0 ≈ π) the mutual phase difference at the central
frequency is
πΦ(ε 0 ) = η − 2 tan
−1 [ω /(2π)] .
(11.10)
The scattering asymmetry along the line connecting the scatterers (y-direction) can
then be maximized by requiring πΦ ± k 0 n d d = η(0) (k 0 is the wavenumber in
vacuum), which implies complete scattering cancellation in one direction and constructive interference in the other. By satisfying the two equations one finds that the
separation d and frequency detuning π must be chosen as follows
d =
ϕ
4n d
, π =
ω
2
.
(11.11)
Although these parameter choices can only be seen as a guide to a realistic optimal
configuration, they still underline the possibility of pronounced scattering asymmetry along the y-direction for which the ratio can be used as a sensitive probe for
A. Pors et al.
losses are negligibly small with respect to the absorption losses. On the other hand,
environmental sensing relies on the detection of scattered light so that, for practical
purposes, nanoparticles have to be chosen large enough to obtain measurable signals.
In order to boost the FOM, alternative ways have been investigated to create sharp
spectral features that are sensitive to the surrounding medium. For example, one may
take advantage of diffractive coupling present in periodic arrays of nanoparticles
[40] or in complementary hole structures [41] when the period is on the order of the
wavelength. Especially at the onset of diffraction it is possible to excite the so-called
Rayleigh anomaly. The Rayleigh anomaly corresponds to light that is diffracted
parallel to the grating, and it appears in reflection and transmission measurements
as a sharp spectral feature that is sensitive to the surroundings. As a prominent
example, the coupling of SPPs and the Rayleigh anomaly in multiscale patterned
hole arrays in gold films demonstrates FOM as large as 23.3 [42]. The diffractive
coupling approach, however, does not allow for measuring local changes in nanoscale
volumes or for a high integration density of sensing devices.
A second approach that alleviates the above problems, yet with a high-Q resonance, involves interference between coupled nanostructures and the creation of
Fano resonances. The Fano resonance occurs due to the interference between radiant and subradiant plasmonic modes resulting (typically) in asymmetric resonances
with narrow linewidths [43]. For this reason, a multitude of complex plasmonic
nanostructures exhibiting Fano resonances have been investigated in relation to plasmonic sensing, though the FOM, generally, never exceeds 10 [5, 44, 45]. Note that
Fano resonances have also been advantageously exploited within biosensing [46].
Our approach still rely on DED configurations exhibiting an EIT-like response.
However, this time we take advantage of the scattering asymmetry present near the
central frequency [47]. The idea can be elaborated by considering scattering in ±ydirection for two non-interacting point scatterers placed similarly to the nanorods
in (Fig. 11.1a) with their electric dipole moment along the x-axis. If each scatterer
is described by the polarizability in Eq. (11.1), it is straightforward to show that in
the limit of weak detuning (ε 0 ≈ π) the mutual phase difference at the central
frequency is
πΦ(ε 0 ) = η − 2 tan
−1 [ω /(2π)] .
(11.10)
The scattering asymmetry along the line connecting the scatterers (y-direction) can
then be maximized by requiring πΦ ± k 0 n d d = η(0) (k 0 is the wavenumber in
vacuum), which implies complete scattering cancellation in one direction and constructive interference in the other. By satisfying the two equations one finds that the
separation d and frequency detuning π must be chosen as follows
d =
ϕ
4n d
, π =
ω
2
.
(11.11)
Although these parameter choices can only be seen as a guide to a realistic optimal
configuration, they still underline the possibility of pronounced scattering asymmetry along the y-direction for which the ratio can be used as a sensitive probe for