36
M. I. Stockman
Theoretically, the number of the effective degrees of freedom that a shaped femtosecond pulse may apply to a nanoplasmonic system can be estimated in the following way. The number of the independent frequency bands is ∼Δω/γ, where Δω is
the bandwidth of the plasmonic system. For each such a band, there are two degrees
of freedom: amplitude and phase. Thus, the total number N DF of the degrees of
freedom for coherent control can be estimated as
N DF ∼ 2
Δω
γ
.
(1.57)
For a plasmonic system with the maximum bandwidth Δω ∼ ω, and Eq. (1.57)
becomes
N DF ∼ 4Q,
(1.58)
where we took into account Eq. (1.5). In the optical region for noble metals Q ∼ 100
(see Fig. 1.2), providing a rich, ∼100-dimensional space of controlling parameters.
The coherent control approach is non-invasive: in principle, it does not perturb or
change the nanosystem’s material structure in any way.
However, how to actually determine a shaped femtosecond pulse that compels
the optical fields in the nanosystem to localize at a targeted nanosite at the required
femtosecond time interval is a formidable problem to which until now there has been
no general and efficient approach. To compare, our original chirped pulses possessed
only two effective degrees of freedom (carrier frequency ω 0 and chirp), which allowed
one to concentrate optical energy at the tip of a V-shape structure versus its opening
[148, 195]. Similarly, the two unmodulated pulses with the regulated delay τ between
them used in the interferometric coherent control [123, 213, 216] also possess only
two degrees of freedom (τ and ω 0 ) and can only select one of any two local-field hot
spots against the other; it is impossible, in particular, to select one desired hot spot
against several others.
There exists another method based on the adaptive genetic algorithms [202]. However, its application to the spatial-temporal localization in nanosystem is difficult due
to the complexity of the problem. To date, the only example is the spatial concentration of the excitation on one arm of the three-pronged metal nanostar [215] where
the obtained controlling pulses are very complicated and difficult to interpret though
the nanosystem itself is rather simple. A general problem with this method is that the
adaptive genetic algorithms are actually refined trial-and-error methods; they do not
allow one to obtain the required controlling pulses as a result of the solution of a set
of deterministic equations or an application of any regular deterministic procedure
such as Green’s function integration.
1.4.2 Time-Reversal Solution for Coherent Control
Our solution of this major problem of the coherent control, which is proposed and
theoretically developed in Ref. [218], is based on an idea of time-reversal that has
M. I. Stockman
Theoretically, the number of the effective degrees of freedom that a shaped femtosecond pulse may apply to a nanoplasmonic system can be estimated in the following way. The number of the independent frequency bands is ∼Δω/γ, where Δω is
the bandwidth of the plasmonic system. For each such a band, there are two degrees
of freedom: amplitude and phase. Thus, the total number N DF of the degrees of
freedom for coherent control can be estimated as
N DF ∼ 2
Δω
γ
.
(1.57)
For a plasmonic system with the maximum bandwidth Δω ∼ ω, and Eq. (1.57)
becomes
N DF ∼ 4Q,
(1.58)
where we took into account Eq. (1.5). In the optical region for noble metals Q ∼ 100
(see Fig. 1.2), providing a rich, ∼100-dimensional space of controlling parameters.
The coherent control approach is non-invasive: in principle, it does not perturb or
change the nanosystem’s material structure in any way.
However, how to actually determine a shaped femtosecond pulse that compels
the optical fields in the nanosystem to localize at a targeted nanosite at the required
femtosecond time interval is a formidable problem to which until now there has been
no general and efficient approach. To compare, our original chirped pulses possessed
only two effective degrees of freedom (carrier frequency ω 0 and chirp), which allowed
one to concentrate optical energy at the tip of a V-shape structure versus its opening
[148, 195]. Similarly, the two unmodulated pulses with the regulated delay τ between
them used in the interferometric coherent control [123, 213, 216] also possess only
two degrees of freedom (τ and ω 0 ) and can only select one of any two local-field hot
spots against the other; it is impossible, in particular, to select one desired hot spot
against several others.
There exists another method based on the adaptive genetic algorithms [202]. However, its application to the spatial-temporal localization in nanosystem is difficult due
to the complexity of the problem. To date, the only example is the spatial concentration of the excitation on one arm of the three-pronged metal nanostar [215] where
the obtained controlling pulses are very complicated and difficult to interpret though
the nanosystem itself is rather simple. A general problem with this method is that the
adaptive genetic algorithms are actually refined trial-and-error methods; they do not
allow one to obtain the required controlling pulses as a result of the solution of a set
of deterministic equations or an application of any regular deterministic procedure
such as Green’s function integration.
1.4.2 Time-Reversal Solution for Coherent Control
Our solution of this major problem of the coherent control, which is proposed and
theoretically developed in Ref. [218], is based on an idea of time-reversal that has