480
E. Hasman and V. Kleiner
13.5 Spin-Dependent Plasmonics: Interfering
Topological Defects
The results of the previous section show that the electromagnetic field scattered from
subwavelength nanoaperture has an essential property of a topological defect (TD).
The TD is a singular spatial configuration of a vector field which cannot unwind
under continuous deformations [55]. Topological defects (TDs) are among the most
intriguing signatures of symmetry breaking in the laws of physics [54]. TDs have
attracted extensive attention in various realms such as condensed matter physics
[56–58], superfluidics [59], hydrodynamics [60], cosmology [61], liquid crystals
[62], and optics [63]. The optical TDs are termed vortices and they carry an OAM
of l per photon manifested by the spiral phase lπ of the beam, where the integer
number l is the topological charge and π is the azimuthal angle. Observation of TDs
in plasmonic systems is possible via the spin-orbit interaction (SOI), which provides
a suitable mechanism to couple the optical spin to an OAM carried by the surface
plasmons (SPs). Moreover, a measurement of a wavefront phase dislocation due to
the scattering of SPs from a macro-wavelength TD was recently presented [64].
When a linearly polarized light illuminates a local scatterer, a typical dipolar
SP polariton emission pattern is observed, aligned with the incident polarization
direction [65, 66], and comprises a perpendicular dislocation line. The scattering of
the SP waves propagating away from the point scatterer is described as a source of
spherical (Huygens) wave [66], with α -phase retardation between the two sections
intersected by the dislocation line (Fig. 13.12c). In this section we consider a spindependent plasmonics as result of scattering the circularly polarized wave from local
defect on surface maintaining SP [67]. We choose an annular nanoslit as a source for
a propagating plasmonic wavefront.
A FDTD simulation gives the near-field electromagnetic fields distribution for
annular nanoantenna (Fig. 13.12a, inset), illuminated with a circular polarization.
Figure 13.12a shows the horizontal cross sections of the electric field components.
In the vicinity of the slit, all the field components have comparable amplitudes, while
those components in the out-launching plasmonic wave decay in a different manner.
After propagation to a distance of half a plasmonic wavelength, the contribution of
the normal E z component to the intensity distribution is an order of magnitude larger
than those of the E x and E y components. Hence, for multi-wavelength propagation
distances, the complex plasmonic wavefront launched from the nanoantenna mainly
contains the E z signature. Figure 13.12b shows the spin-degenerated magnitude of
the electric field component E z with zero-field amplitude in the origin. Moreover,
the phase of the E z field is spiral and its helicity is spin-dependent (Fig. 13.12d, e),
resulting from the optical SOI. Due to the SOI, the excited SPs acquire an OAM
which is equal to the incident spin, resulting in a nanoscale TD: a plasmonic vortex
source.
We give below the analytical evaluation result for the E z field launched from an
annular nanoantenna—infinitely thin circular slit with a radius r 0 , in a medium supporting SPs. The selected shape of the nanoantenna as a circular nanoslit originates
E. Hasman and V. Kleiner
13.5 Spin-Dependent Plasmonics: Interfering
Topological Defects
The results of the previous section show that the electromagnetic field scattered from
subwavelength nanoaperture has an essential property of a topological defect (TD).
The TD is a singular spatial configuration of a vector field which cannot unwind
under continuous deformations [55]. Topological defects (TDs) are among the most
intriguing signatures of symmetry breaking in the laws of physics [54]. TDs have
attracted extensive attention in various realms such as condensed matter physics
[56–58], superfluidics [59], hydrodynamics [60], cosmology [61], liquid crystals
[62], and optics [63]. The optical TDs are termed vortices and they carry an OAM
of l per photon manifested by the spiral phase lπ of the beam, where the integer
number l is the topological charge and π is the azimuthal angle. Observation of TDs
in plasmonic systems is possible via the spin-orbit interaction (SOI), which provides
a suitable mechanism to couple the optical spin to an OAM carried by the surface
plasmons (SPs). Moreover, a measurement of a wavefront phase dislocation due to
the scattering of SPs from a macro-wavelength TD was recently presented [64].
When a linearly polarized light illuminates a local scatterer, a typical dipolar
SP polariton emission pattern is observed, aligned with the incident polarization
direction [65, 66], and comprises a perpendicular dislocation line. The scattering of
the SP waves propagating away from the point scatterer is described as a source of
spherical (Huygens) wave [66], with α -phase retardation between the two sections
intersected by the dislocation line (Fig. 13.12c). In this section we consider a spindependent plasmonics as result of scattering the circularly polarized wave from local
defect on surface maintaining SP [67]. We choose an annular nanoslit as a source for
a propagating plasmonic wavefront.
A FDTD simulation gives the near-field electromagnetic fields distribution for
annular nanoantenna (Fig. 13.12a, inset), illuminated with a circular polarization.
Figure 13.12a shows the horizontal cross sections of the electric field components.
In the vicinity of the slit, all the field components have comparable amplitudes, while
those components in the out-launching plasmonic wave decay in a different manner.
After propagation to a distance of half a plasmonic wavelength, the contribution of
the normal E z component to the intensity distribution is an order of magnitude larger
than those of the E x and E y components. Hence, for multi-wavelength propagation
distances, the complex plasmonic wavefront launched from the nanoantenna mainly
contains the E z signature. Figure 13.12b shows the spin-degenerated magnitude of
the electric field component E z with zero-field amplitude in the origin. Moreover,
the phase of the E z field is spiral and its helicity is spin-dependent (Fig. 13.12d, e),
resulting from the optical SOI. Due to the SOI, the excited SPs acquire an OAM
which is equal to the incident spin, resulting in a nanoscale TD: a plasmonic vortex
source.
We give below the analytical evaluation result for the E z field launched from an
annular nanoantenna—infinitely thin circular slit with a radius r 0 , in a medium supporting SPs. The selected shape of the nanoantenna as a circular nanoslit originates