12 Plasmonics with a Twist: Taming Optical Tornadoes on the Nanoscale
439
The most striking feature of the on-resonance powerflow pattern shown in
Fig. 12.4a is the reversal of the energy flow in the particle shadow area, with a portion
of energy entering the particle from behind. This powerflow reversal is driven by the
formation of a topological feature in the Poynting vector field—a saddle node. The
direction of the powerflow around the saddle node is highlighted with red arrows in
Fig. 12.4a. A presence of another saddle node inside the particle volume drives the
exchange of the electromagnetic energy between the E- and H-planes. As the energy
re-circulation occurs through the volume of the metal–where energy dissipation takes
place (12.5)–the LSP resonance is accompanied by high absorption losses. The saddle
nodes observed in Fig. 12.4a are the local topological features in the Poynting vector
field at which the intensity of the time-averaged Poynting vector is zero, and thus its
phase cannot be defined [63–67]. The powerflow lines around the saddle points are
hyperbolas (see Fig. 12.4a). It has previously been observed that the decrease of the
material dissipation losses results in even more complex picture of the powerflow
through the particle [61, 68]. This effect may explain the inverse dependence of the
absorption efficiency on the imaginary part of the dielectric function due to more
efficient light re-circulation through the metal volume.
The scattering efficiency as well as the intensity of the local electric field concentrated on the particle surface can be further enhanced by combining the individual
particles into ordered arrays and making use of the constructive interference of the
scattered partial fields. The scattering, absorption and emission spectra of such arrays
exhibit sharp resonant peaks [20, 41, 42, 46, 69–71] corresponding to the well-known
Rayleigh anomalies associated with the opening of new array diffraction orders. For
discrete values of array periods proportional to the wavelength of the incident field,
the dipoles induced in individual particles oscillate in phase, inducing coherent correlations across the array. This collective effect – known as superradiance–was initially
predicted by Dicke for a system of two-level atoms [72] and results in the generation
of a signal proportional to the square of the number of dipoles in the directions of
their constructive interference.
A complex picture of energy flow through a periodic chain of gold nanoparticles at the frequency of the chain superradiant collective mode resulting from the
spectral overlap of a particle dipole LSP resonance and a chain Rayleigh anomaly
is illustrated in Fig. 12.5b. It can be seen that–similarly to the case of individual
nanoparticles–the field lines strongly deflect towards particles, and the energy is recirculated through their metal volumes. Furthermore, formation of a collective mode
is associated with appearance of additional topological features around the particle
chain (the direction of powerflow around additional saddle nodes is indicated with
red arrows in Fig. 12.5b). The net result of this effect is a more efficient light trapping
and re-circulation through the particle chain, which increases its collective scattering, absorption, and field enhancement efficiency over that of a sum of efficiencies
of individual nanoparticles.
439
The most striking feature of the on-resonance powerflow pattern shown in
Fig. 12.4a is the reversal of the energy flow in the particle shadow area, with a portion
of energy entering the particle from behind. This powerflow reversal is driven by the
formation of a topological feature in the Poynting vector field—a saddle node. The
direction of the powerflow around the saddle node is highlighted with red arrows in
Fig. 12.4a. A presence of another saddle node inside the particle volume drives the
exchange of the electromagnetic energy between the E- and H-planes. As the energy
re-circulation occurs through the volume of the metal–where energy dissipation takes
place (12.5)–the LSP resonance is accompanied by high absorption losses. The saddle
nodes observed in Fig. 12.4a are the local topological features in the Poynting vector
field at which the intensity of the time-averaged Poynting vector is zero, and thus its
phase cannot be defined [63–67]. The powerflow lines around the saddle points are
hyperbolas (see Fig. 12.4a). It has previously been observed that the decrease of the
material dissipation losses results in even more complex picture of the powerflow
through the particle [61, 68]. This effect may explain the inverse dependence of the
absorption efficiency on the imaginary part of the dielectric function due to more
efficient light re-circulation through the metal volume.
The scattering efficiency as well as the intensity of the local electric field concentrated on the particle surface can be further enhanced by combining the individual
particles into ordered arrays and making use of the constructive interference of the
scattered partial fields. The scattering, absorption and emission spectra of such arrays
exhibit sharp resonant peaks [20, 41, 42, 46, 69–71] corresponding to the well-known
Rayleigh anomalies associated with the opening of new array diffraction orders. For
discrete values of array periods proportional to the wavelength of the incident field,
the dipoles induced in individual particles oscillate in phase, inducing coherent correlations across the array. This collective effect – known as superradiance–was initially
predicted by Dicke for a system of two-level atoms [72] and results in the generation
of a signal proportional to the square of the number of dipoles in the directions of
their constructive interference.
A complex picture of energy flow through a periodic chain of gold nanoparticles at the frequency of the chain superradiant collective mode resulting from the
spectral overlap of a particle dipole LSP resonance and a chain Rayleigh anomaly
is illustrated in Fig. 12.5b. It can be seen that–similarly to the case of individual
nanoparticles–the field lines strongly deflect towards particles, and the energy is recirculated through their metal volumes. Furthermore, formation of a collective mode
is associated with appearance of additional topological features around the particle
chain (the direction of powerflow around additional saddle nodes is indicated with
red arrows in Fig. 12.5b). The net result of this effect is a more efficient light trapping
and re-circulation through the particle chain, which increases its collective scattering, absorption, and field enhancement efficiency over that of a sum of efficiencies
of individual nanoparticles.