1 Nanoplasmonics: From Present into Future
41
the excitation-dipole 12 fs pulses. This confirms our understanding that the initial
dipole field excites local SP fields that, in a cascade manner, excite a sequence of the
system SPs, which ring down relatively long time (over 200 fs, as shown in the figure).
This long ring-down process is exactly what is required for the nanostructure to
transfer to the far-field zone the information on the near-zone local (evanescent) fields
as is suggested by our idea presented above in the introduction. The obtained fields
are by shape resembling the controlling pulses for the microwave radiation [221].
However, a fundamental difference is that in the microwave case the long ringingdown is due to the external reverberation chamber, while for the nanoplasmonic
systems it is due to the intrinsic evolution of the highly resonant SP eigenmodes that
possess high Q-factors (setting a reverberation chamber around a nanosystem would
have been, indeed, unrealistic).
Second, one can see that the pulses in Fig. 1.16 have a very nontrivial polarization
properties ranging from the pure linear polarization (indicated by red as explained
in the caption to Fig. 1.16) to the circular polarization indicated by blue, including
all intermediate degrees of circularity. The temporal-polarization structure of pulses
A–H in Fig. 1.16 is very complicated, somewhat reminding that of Ref. [215], which
was obtained by a genetic adaptive algorithm. However, in our case these pulses
are obtained in a straightforward manner, by applying the well-known, deterministic
Green’s function of the system, which is a highly efficient and fast method.
Third, and most important, feature of the waveforms in Fig. 1.16 is that they are
highly site-specific: pulses generated by the initial dipole in different positions are
completely different. This is a very strong indication that they do transfer to the far
far-field zone the information about the complicated spatio-temporal structure of the
local, near-zone fields. This creates a pre-requisite for studying a possibility to use
these pulses for the coherently-controlled nano-targeting.
Now we turn to the crucial test of the nanofocusing induced by the excitation
pulses discussed above in conjunction with Fig. 1.16. Because of the finite time
window (T = 228 fs) used for the time reversal, all these excitation pulses end and
should cause the concentration of the optical energy (at the corresponding sites) at
the same time, t = T = 228 fs (counted from the moment the excitation pulse starts
impinging on the system). After this concentration instant, the nanofocused fields
can, in principle, disappear (dephase) during a very short period on the order of the
initial dipole pulse length, i.e. ∼12 fs. Thus this nanofocusing is a dynamic, transient
phenomenon.
Note that averaging (or, integration) of the local-field intensity I (r, t) = |E(r, t)| 2
over time t would lead to the loss of the effects of the phase modulation. This is due
to a mathematical equality
∞
−∞ I (r, t)dt =
∞
−∞ |E(r, ω)| 2 dω/(2π), where the
spectral-phase modulation of the field certainly eliminates from the expression in
the right-hand side. Thus the averaged intensity of the local fields is determined only
by the local power spectrum of the excitation |E(r, ω)| 2 and, consequently, is not
coherently controllable. Very importantly, such a cancellation does not take place for
nonlinear phenomena. In particular, two-photon processes such as two-photon fluorescence or two-photon electron emission that can be considered as proportional to
the squared intensity I 2 (r, t) = |E(r, t)| 4 are coherently controllable even after time
41
the excitation-dipole 12 fs pulses. This confirms our understanding that the initial
dipole field excites local SP fields that, in a cascade manner, excite a sequence of the
system SPs, which ring down relatively long time (over 200 fs, as shown in the figure).
This long ring-down process is exactly what is required for the nanostructure to
transfer to the far-field zone the information on the near-zone local (evanescent) fields
as is suggested by our idea presented above in the introduction. The obtained fields
are by shape resembling the controlling pulses for the microwave radiation [221].
However, a fundamental difference is that in the microwave case the long ringingdown is due to the external reverberation chamber, while for the nanoplasmonic
systems it is due to the intrinsic evolution of the highly resonant SP eigenmodes that
possess high Q-factors (setting a reverberation chamber around a nanosystem would
have been, indeed, unrealistic).
Second, one can see that the pulses in Fig. 1.16 have a very nontrivial polarization
properties ranging from the pure linear polarization (indicated by red as explained
in the caption to Fig. 1.16) to the circular polarization indicated by blue, including
all intermediate degrees of circularity. The temporal-polarization structure of pulses
A–H in Fig. 1.16 is very complicated, somewhat reminding that of Ref. [215], which
was obtained by a genetic adaptive algorithm. However, in our case these pulses
are obtained in a straightforward manner, by applying the well-known, deterministic
Green’s function of the system, which is a highly efficient and fast method.
Third, and most important, feature of the waveforms in Fig. 1.16 is that they are
highly site-specific: pulses generated by the initial dipole in different positions are
completely different. This is a very strong indication that they do transfer to the far
far-field zone the information about the complicated spatio-temporal structure of the
local, near-zone fields. This creates a pre-requisite for studying a possibility to use
these pulses for the coherently-controlled nano-targeting.
Now we turn to the crucial test of the nanofocusing induced by the excitation
pulses discussed above in conjunction with Fig. 1.16. Because of the finite time
window (T = 228 fs) used for the time reversal, all these excitation pulses end and
should cause the concentration of the optical energy (at the corresponding sites) at
the same time, t = T = 228 fs (counted from the moment the excitation pulse starts
impinging on the system). After this concentration instant, the nanofocused fields
can, in principle, disappear (dephase) during a very short period on the order of the
initial dipole pulse length, i.e. ∼12 fs. Thus this nanofocusing is a dynamic, transient
phenomenon.
Note that averaging (or, integration) of the local-field intensity I (r, t) = |E(r, t)| 2
over time t would lead to the loss of the effects of the phase modulation. This is due
to a mathematical equality
∞
−∞ I (r, t)dt =
∞
−∞ |E(r, ω)| 2 dω/(2π), where the
spectral-phase modulation of the field certainly eliminates from the expression in
the right-hand side. Thus the averaged intensity of the local fields is determined only
by the local power spectrum of the excitation |E(r, ω)| 2 and, consequently, is not
coherently controllable. Very importantly, such a cancellation does not take place for
nonlinear phenomena. In particular, two-photon processes such as two-photon fluorescence or two-photon electron emission that can be considered as proportional to
the squared intensity I 2 (r, t) = |E(r, t)| 4 are coherently controllable even after time