34
M. I. Stockman
nanolocalization and such ultrafast kinetics make plasmonic nanostructures promising for various applications, especially for the ultrafast computations, data control
and storage on the nanoscale.
These and potentially many other applications require precise control over the
optical excitations of the nanostructures in time and space on the femtosecondnanometer scale. Such a control cannot be imposed by far-field focusing of the
optical radiation because the diffraction limits its dimension to greater than half
wavelength. In other words, the optical radiation does not have spatial degrees of
freedom on the nanoscale. There is a different class of approaches to control a system
on nanoscale based on plasmonic nanoparticles or waveguides brought to the nearfield region of the system. Among these we mention: the tips of scanning nearfield optical microscopes [190], adiabatic plasmonic waveguides [12], nanowires
[191, 192], plasmonic superlenses [193] or hyperlenses [194]. In all these cases,
massive amount of metal is brought to the vicinity of the plasmonic nanosystem,
which will produce strong perturbations of its spectrum and SP eigenmodes, cause
additional optical losses, and adversely affect the ultrafast dynamics and energy
nanolocalization in the system. This nanowaveguide approach also may not work
because of the excitation delocalization due to the strong interaction (capacitive
coupling) at the nanoscale distances for optical frequencies.
We have proposed [195] a principally different approach to ultrafast optical control on the nanoscale based on the general idea of coherent control. The coherent
control of the quantum state of atom and molecules is based on the directed interference of the different quantum pathways of the optical excitation [196–205], which
is carried out by properly defining the phases of the corresponding excitation waves.
This coherent control can also be imposed by an appropriate phase modulation of
the excitation ultrashort (femtosecond) pulse [202, 206–208]. Shaping the polarization of a femtosecond pulse has proven to be a useful tool in controlling quantum
systems [209].
Our idea of the coherent control on the nanoscale by the phase modulation of
the excitation pulse can be explained with a schematic shown in Fig. 1.14. Phase
modulation of the excitation pulse can be thought of as changing the frequency (color)
of light as the pulse progresses in time. For the sake of argument, let us assume, as
shown in Fig. 1.14, that initially the pulse contains blue colors that gradually change
to red with the time progression. At earlier times, the dominating blue component of
the pulse will excite the SP eigenmodes with corresponding high optical frequencies.
As the pulse progresses, the lower-frequency eigenmodes are excited. It is assumed
that the total duration τ p of the pulse is less than the decay (decoherence) time
τ = γ −1 of the SPs , i.e., τ p τ [for the decay rates and life times of the SPs
see Eq. (1.3) or (1.49) and Fig. 1.3]. In such a case, the SPs of different frequencies
will coexist simultaneously, and their fields will interfere. This interference depends
on the relative phases and amplitudes of the SPs of different frequencies which,
in turn, are determined by the relative phases of different spectral components of
the excitation pulse. The ultimate goal of the spatio-temporal coherent control on
the nanoscale is to have a hot spot of the local fields at a given nanosite at a given
M. I. Stockman
nanolocalization and such ultrafast kinetics make plasmonic nanostructures promising for various applications, especially for the ultrafast computations, data control
and storage on the nanoscale.
These and potentially many other applications require precise control over the
optical excitations of the nanostructures in time and space on the femtosecondnanometer scale. Such a control cannot be imposed by far-field focusing of the
optical radiation because the diffraction limits its dimension to greater than half
wavelength. In other words, the optical radiation does not have spatial degrees of
freedom on the nanoscale. There is a different class of approaches to control a system
on nanoscale based on plasmonic nanoparticles or waveguides brought to the nearfield region of the system. Among these we mention: the tips of scanning nearfield optical microscopes [190], adiabatic plasmonic waveguides [12], nanowires
[191, 192], plasmonic superlenses [193] or hyperlenses [194]. In all these cases,
massive amount of metal is brought to the vicinity of the plasmonic nanosystem,
which will produce strong perturbations of its spectrum and SP eigenmodes, cause
additional optical losses, and adversely affect the ultrafast dynamics and energy
nanolocalization in the system. This nanowaveguide approach also may not work
because of the excitation delocalization due to the strong interaction (capacitive
coupling) at the nanoscale distances for optical frequencies.
We have proposed [195] a principally different approach to ultrafast optical control on the nanoscale based on the general idea of coherent control. The coherent
control of the quantum state of atom and molecules is based on the directed interference of the different quantum pathways of the optical excitation [196–205], which
is carried out by properly defining the phases of the corresponding excitation waves.
This coherent control can also be imposed by an appropriate phase modulation of
the excitation ultrashort (femtosecond) pulse [202, 206–208]. Shaping the polarization of a femtosecond pulse has proven to be a useful tool in controlling quantum
systems [209].
Our idea of the coherent control on the nanoscale by the phase modulation of
the excitation pulse can be explained with a schematic shown in Fig. 1.14. Phase
modulation of the excitation pulse can be thought of as changing the frequency (color)
of light as the pulse progresses in time. For the sake of argument, let us assume, as
shown in Fig. 1.14, that initially the pulse contains blue colors that gradually change
to red with the time progression. At earlier times, the dominating blue component of
the pulse will excite the SP eigenmodes with corresponding high optical frequencies.
As the pulse progresses, the lower-frequency eigenmodes are excited. It is assumed
that the total duration τ p of the pulse is less than the decay (decoherence) time
τ = γ −1 of the SPs , i.e., τ p τ [for the decay rates and life times of the SPs
see Eq. (1.3) or (1.49) and Fig. 1.3]. In such a case, the SPs of different frequencies
will coexist simultaneously, and their fields will interfere. This interference depends
on the relative phases and amplitudes of the SPs of different frequencies which,
in turn, are determined by the relative phases of different spectral components of
the excitation pulse. The ultimate goal of the spatio-temporal coherent control on
the nanoscale is to have a hot spot of the local fields at a given nanosite at a given