38
M. I. Stockman
be in vacuum). The nanosystem is excited by an external ultrafast (femtosecond)
nanosource of radiation at its surface. As such we choose an oscillating dipole indicated by a double red arrow. This dipole generates a local optical electric field shown
by a bold red waveform. This field excites SP oscillations of the system in its vicinity. In turn these oscillations excite other, more distant regions, and so forth until the
excitation spreads out over the entire system. The relatively long relaxation time of
these SP modes leads to the long “reverberations” of the plasmonic fields and the
corresponding far-zone optical electric field. The latter is shown in Fig. 1.15b where
one can see that a complicated vector waveform is predicted. This waveform is time
reversed, as shown in panel (c), and send back to the system as an excitation plane
wave from the far-field zone. If the entire field, in the whole space including the
near-field (evanescent) zone, were time reversed and the system would have been
completely time-reversible, which would imply the absence of any dielectric losses,
then the system would have been compelled by this field exactly to back-trace its
own evolution in time. This would have lead to the concentration of the local optical
energy exactly at the position of the initial dipole at a time corresponding to the end
of the excitation pulse.
Indeed, the system is somewhat lossy, which means that it is not exactly time
reversible. Nevertheless, these losses are small, and one may expect that they will
not fundamentally change the behavior of the system. Another problem appear to
be more significant: the evanescent fields contain the main information of the nanodistribution of the local fields in the system, and they cannot be time reversed from
the far zone because they are exponentially small, practically lost there. However, our
idea is that the nanostructured metal system itself plays the role of the metal brush of
Ref. [221] continuously coupling the evanescent fields to the far zone. Therefore the
fields in the far zone actually contain, in their reverberations, most information about
the evanescent fields that will be regenerated in the process of the time reversal.
We will illustrate this idea by considering a random planar composite (RPC) whose
geometry is shown in gray in the center of Fig. 1.16. In specific computations, as the
plasmonic metal, we consider silver whose dielectric permittivity ε m we adopt from
bulk data [32]. This system has been generated by randomly positioning 2 ×2 ×2 nm 3
metal cubes on a plane, which for certainty we will consider as the xz coordinate
plane. The random system shown in the center of Fig. 1.16 has filling factor of
f = 0.5.
The interaction of a nanosystem with electromagnetic pulses is described in
Green’s function approach using quasistatic approximation [148, 195, 222]—see
Sect. 1.3.3. It is known that the optical excitation energy in random plasmonic nanostructures localizes in “hot spots” whose size is on the nanoscale and is determined
by the minimum scale of the system inhomogeneities [78, 158, 159, 223]—see
Sect. 1.3.5.
Initially, to find positions of these hot spots in our system, we apply an ultrashort near-infrared (near-ir) pulse whose spectral width was very large, covering a
frequency band from 1.1 to 1.7 eV. The pulse polarization is along the z axis (the
incidence direction is normal to the plane of the nanostructure, i.e. along the y axis).
The resulting optical electric field E is expressed in terms of the external electric
M. I. Stockman
be in vacuum). The nanosystem is excited by an external ultrafast (femtosecond)
nanosource of radiation at its surface. As such we choose an oscillating dipole indicated by a double red arrow. This dipole generates a local optical electric field shown
by a bold red waveform. This field excites SP oscillations of the system in its vicinity. In turn these oscillations excite other, more distant regions, and so forth until the
excitation spreads out over the entire system. The relatively long relaxation time of
these SP modes leads to the long “reverberations” of the plasmonic fields and the
corresponding far-zone optical electric field. The latter is shown in Fig. 1.15b where
one can see that a complicated vector waveform is predicted. This waveform is time
reversed, as shown in panel (c), and send back to the system as an excitation plane
wave from the far-field zone. If the entire field, in the whole space including the
near-field (evanescent) zone, were time reversed and the system would have been
completely time-reversible, which would imply the absence of any dielectric losses,
then the system would have been compelled by this field exactly to back-trace its
own evolution in time. This would have lead to the concentration of the local optical
energy exactly at the position of the initial dipole at a time corresponding to the end
of the excitation pulse.
Indeed, the system is somewhat lossy, which means that it is not exactly time
reversible. Nevertheless, these losses are small, and one may expect that they will
not fundamentally change the behavior of the system. Another problem appear to
be more significant: the evanescent fields contain the main information of the nanodistribution of the local fields in the system, and they cannot be time reversed from
the far zone because they are exponentially small, practically lost there. However, our
idea is that the nanostructured metal system itself plays the role of the metal brush of
Ref. [221] continuously coupling the evanescent fields to the far zone. Therefore the
fields in the far zone actually contain, in their reverberations, most information about
the evanescent fields that will be regenerated in the process of the time reversal.
We will illustrate this idea by considering a random planar composite (RPC) whose
geometry is shown in gray in the center of Fig. 1.16. In specific computations, as the
plasmonic metal, we consider silver whose dielectric permittivity ε m we adopt from
bulk data [32]. This system has been generated by randomly positioning 2 ×2 ×2 nm 3
metal cubes on a plane, which for certainty we will consider as the xz coordinate
plane. The random system shown in the center of Fig. 1.16 has filling factor of
f = 0.5.
The interaction of a nanosystem with electromagnetic pulses is described in
Green’s function approach using quasistatic approximation [148, 195, 222]—see
Sect. 1.3.3. It is known that the optical excitation energy in random plasmonic nanostructures localizes in “hot spots” whose size is on the nanoscale and is determined
by the minimum scale of the system inhomogeneities [78, 158, 159, 223]—see
Sect. 1.3.5.
Initially, to find positions of these hot spots in our system, we apply an ultrashort near-infrared (near-ir) pulse whose spectral width was very large, covering a
frequency band from 1.1 to 1.7 eV. The pulse polarization is along the z axis (the
incidence direction is normal to the plane of the nanostructure, i.e. along the y axis).
The resulting optical electric field E is expressed in terms of the external electric