40
M. I. Stockman
eight of these hot spots for our computations as denoted by letters A to H in the
figure.
To generate the field in the far zone, we take a point dipole and position it at a
surface of the metal at point r 0 at such a hot spot, as described in the discussion of
Fig. 1.15. The near-zone field E L (r, t) generated in response to this point dipole is
found from Green’s function relation
E
L
(r, t) =
4π
ε d
dt
G
r
(r, r 0 ; t − t
) d(r 0 , t
).
(1.59)
Knowing this local electric field, we calculate the total radiating optical dipole
moment of the nanosystem in the frequency domain as
D(ω) =
1
4π
d
3 r [ε m (ω) − ε d ] Θ(r)E
L
(r, ω).
(1.60)
Here and below, the frequency- and time-domain quantities, as indicated by their
arguments ω and t, are Fourier transforms of each other. The field in the far zone
produced by this radiating dipole is given by standard electrodynamic formula—see,
e.g. Sect. 67 in Ref. [224]. The time-reversed field is generated by time-reversed
dipole D T (t) that is complex-conjugated in the frequency domain, D T (ω) = D(ω) ∗ .
The dependence on time of the initial excitation dipole, d(r 0 , t) is set as an ultrashort Gaussian-shaped pulse of 12 fs duration with the carrier frequency ω 0 =
1.2 eV. Following the procedure described above, the fields shown in Figs. 1.15 and
1.16 have been calculated for the radiation propagating in the y direction (normal to
the plane of the nanostructure). These fields simply copy the retarded time evolution
of the emitting dipole.
At the completing stage of our calculations, the time-reversed excitation pulse is
sent back to the system as a plane wave propagating along the y direction (normal to
the nanosystem plane). To calculate the resulting local fields, we again use Green’s
function Eq. (1.43) where the shaped excitation pulse substitutes for field E 0 .
1.4.4 Numerical Results for Time-Reversal Coherent Control
The electric field of the excitation wave is chosen as a modulated waveform (including amplitude, phase, and polarization modulation) that has been computed as
described above in the previous subsection. The optical excitation energy can only be
concentrated at sites where SP eigenmodes localize. For the present system, these are
the hot spots shown by color in the central insert of Fig. 1.16, labeled A–H. The corresponding calculated excitation waveforms are displayed in panels as vector plots
shown as functions of time {E x (t), E z (t)}.
There are several important features of these waveforms deserving our attention
and discussion. First, these waveforms are rather long in duration: much longer than
M. I. Stockman
eight of these hot spots for our computations as denoted by letters A to H in the
figure.
To generate the field in the far zone, we take a point dipole and position it at a
surface of the metal at point r 0 at such a hot spot, as described in the discussion of
Fig. 1.15. The near-zone field E L (r, t) generated in response to this point dipole is
found from Green’s function relation
E
L
(r, t) =
4π
ε d
dt
G
r
(r, r 0 ; t − t
) d(r 0 , t
).
(1.59)
Knowing this local electric field, we calculate the total radiating optical dipole
moment of the nanosystem in the frequency domain as
D(ω) =
1
4π
d
3 r [ε m (ω) − ε d ] Θ(r)E
L
(r, ω).
(1.60)
Here and below, the frequency- and time-domain quantities, as indicated by their
arguments ω and t, are Fourier transforms of each other. The field in the far zone
produced by this radiating dipole is given by standard electrodynamic formula—see,
e.g. Sect. 67 in Ref. [224]. The time-reversed field is generated by time-reversed
dipole D T (t) that is complex-conjugated in the frequency domain, D T (ω) = D(ω) ∗ .
The dependence on time of the initial excitation dipole, d(r 0 , t) is set as an ultrashort Gaussian-shaped pulse of 12 fs duration with the carrier frequency ω 0 =
1.2 eV. Following the procedure described above, the fields shown in Figs. 1.15 and
1.16 have been calculated for the radiation propagating in the y direction (normal to
the plane of the nanostructure). These fields simply copy the retarded time evolution
of the emitting dipole.
At the completing stage of our calculations, the time-reversed excitation pulse is
sent back to the system as a plane wave propagating along the y direction (normal to
the nanosystem plane). To calculate the resulting local fields, we again use Green’s
function Eq. (1.43) where the shaped excitation pulse substitutes for field E 0 .
1.4.4 Numerical Results for Time-Reversal Coherent Control
The electric field of the excitation wave is chosen as a modulated waveform (including amplitude, phase, and polarization modulation) that has been computed as
described above in the previous subsection. The optical excitation energy can only be
concentrated at sites where SP eigenmodes localize. For the present system, these are
the hot spots shown by color in the central insert of Fig. 1.16, labeled A–H. The corresponding calculated excitation waveforms are displayed in panels as vector plots
shown as functions of time {E x (t), E z (t)}.
There are several important features of these waveforms deserving our attention
and discussion. First, these waveforms are rather long in duration: much longer than