486
E. Hasman and V. Kleiner
The transmission spectrum of the coupled plasmonic chain, immersed in an indexmatching oil to obtain symmetric configuration, bears a signature of two modes
centered at the wavelengths of 700 and 780 nm corresponding to transversal and
longitudinal polarization excitations [70], respectively (Fig. 13.16a).
Figure 13.16c shows the measured OSHE-LI observed from the chain
corresponding to Eq. (13.5). In experiment the structure was sandwiched between
circular polarizers and illuminated with a laser beam at a wavelength of 780 nm in
order to excite the longitudinal mode. The intensity distribution is measured in the
far-field, which corresponds to the momentum space.
Polarization analysis reveals that the scattering from the curved chain comprising
two components: ballistic and spin-flip. The ballistic component doesn’t experience
any diffraction and maintains the polarization state of the incident beam, while the
spin-flip component, with an opposite spin state, undergoes diffraction.
Spin-dependent beam deflection is observed in the experiment via orthogonal
circular polarizers, corresponds to a momentum shift of Δk x = −2λ α/a, where λ
is the incident spin state. The peculiarity of the observed effect lies in its geometric
nature. Light scattering by a system with spatially non-uniform anisotropy has a close
analogy with a scattering from a revolving medium [39], as was shown recently [38].
Hence, the scattering by the bent chain is most conveniently studied using a rotating
reference frame [52, 38] (u, v), which is attached to the axis of the local anisotropy
of the chain and follows the chain’s route ϕ (x, y) (Fig. 13.15a). This is accompanied
by spatial rotation of the frame with a rate ∂ ϕ = dτ (ϕ )/dϕ , where τ (ϕ ) is the
orientation angle. As a result, a spin-dependent momentum deviation Δk ϕ = −2λ ∂ ϕ
which corresponds to an additional phase of γ =
Δk ϕ dϕ = −2λ τ, appears in the
spin-flip scattered component. The experimentally observed spin-Hall momentum
deviation concurs with the expected correction of Δk x = ∇ x γ = −2λ α/a. This
effect is regarded as the OSHE-LI.
When the chain unit cell is anisotropic itself, the local anisotropy is also allowed
to be arbitrarily oriented along the path. The reference frame attached to the unit
cell anisotropy is presented as the system
u , v
in Fig. 13.15b. It was previously
shown that plasmonic structures consisting of nanorods exhibit a high polarization
anisotropy that follows the orientation of the rods [71, 72]. An element consisting
of randomly arranged but similarly oriented rectangular apertures with dimensions
of 80×220 nm (Fig. 13.17a, top inset) demonstrates the localized mode resonance at
a wavelength of 730 nm by measuring the transmission spectrum with linear polarization excitation parallel to its minor axis. High anisotropy is clearly observed
between the two orthogonal linear polarization excitations, which results from the
local anisotropy of the nanorod (Fig. 13.17a). A straight chain of subwavelength
nanorods with a period of 430 nm (Fig. 13.17a, bottom inset) gives a narrow resonant
line shape of the transmitted light in correspondence with the momentum matching
condition, when the structure is illuminated by a linear polarization parallel to the
nanorod’s minor axis (Fig. 13.17a). When the orientation of the nanorods is varied
linearly along the x-axis to obtain a spatial rotation rate of ∂ = dτ /dx = α/a
(Fig. 13.17b), the beam deflection of the spin-flip component corresponding to the
spin-Hall momentum deviation of Δk x = −2λ ∂ arises (Fig. 13.17c). This beam
E. Hasman and V. Kleiner
The transmission spectrum of the coupled plasmonic chain, immersed in an indexmatching oil to obtain symmetric configuration, bears a signature of two modes
centered at the wavelengths of 700 and 780 nm corresponding to transversal and
longitudinal polarization excitations [70], respectively (Fig. 13.16a).
Figure 13.16c shows the measured OSHE-LI observed from the chain
corresponding to Eq. (13.5). In experiment the structure was sandwiched between
circular polarizers and illuminated with a laser beam at a wavelength of 780 nm in
order to excite the longitudinal mode. The intensity distribution is measured in the
far-field, which corresponds to the momentum space.
Polarization analysis reveals that the scattering from the curved chain comprising
two components: ballistic and spin-flip. The ballistic component doesn’t experience
any diffraction and maintains the polarization state of the incident beam, while the
spin-flip component, with an opposite spin state, undergoes diffraction.
Spin-dependent beam deflection is observed in the experiment via orthogonal
circular polarizers, corresponds to a momentum shift of Δk x = −2λ α/a, where λ
is the incident spin state. The peculiarity of the observed effect lies in its geometric
nature. Light scattering by a system with spatially non-uniform anisotropy has a close
analogy with a scattering from a revolving medium [39], as was shown recently [38].
Hence, the scattering by the bent chain is most conveniently studied using a rotating
reference frame [52, 38] (u, v), which is attached to the axis of the local anisotropy
of the chain and follows the chain’s route ϕ (x, y) (Fig. 13.15a). This is accompanied
by spatial rotation of the frame with a rate ∂ ϕ = dτ (ϕ )/dϕ , where τ (ϕ ) is the
orientation angle. As a result, a spin-dependent momentum deviation Δk ϕ = −2λ ∂ ϕ
which corresponds to an additional phase of γ =
Δk ϕ dϕ = −2λ τ, appears in the
spin-flip scattered component. The experimentally observed spin-Hall momentum
deviation concurs with the expected correction of Δk x = ∇ x γ = −2λ α/a. This
effect is regarded as the OSHE-LI.
When the chain unit cell is anisotropic itself, the local anisotropy is also allowed
to be arbitrarily oriented along the path. The reference frame attached to the unit
cell anisotropy is presented as the system
u , v
in Fig. 13.15b. It was previously
shown that plasmonic structures consisting of nanorods exhibit a high polarization
anisotropy that follows the orientation of the rods [71, 72]. An element consisting
of randomly arranged but similarly oriented rectangular apertures with dimensions
of 80×220 nm (Fig. 13.17a, top inset) demonstrates the localized mode resonance at
a wavelength of 730 nm by measuring the transmission spectrum with linear polarization excitation parallel to its minor axis. High anisotropy is clearly observed
between the two orthogonal linear polarization excitations, which results from the
local anisotropy of the nanorod (Fig. 13.17a). A straight chain of subwavelength
nanorods with a period of 430 nm (Fig. 13.17a, bottom inset) gives a narrow resonant
line shape of the transmitted light in correspondence with the momentum matching
condition, when the structure is illuminated by a linear polarization parallel to the
nanorod’s minor axis (Fig. 13.17a). When the orientation of the nanorods is varied
linearly along the x-axis to obtain a spatial rotation rate of ∂ = dτ /dx = α/a
(Fig. 13.17b), the beam deflection of the spin-flip component corresponding to the
spin-Hall momentum deviation of Δk x = −2λ ∂ arises (Fig. 13.17c). This beam