1 Nanoplasmonics: From Present into Future
9
vice versa. The mechanism of the efficiency enhancement in the radio frequency
range is a combination of spatial focusing (e.g., for parabolic antennas) and resonant
enhancement (e.g., for a dipole antenna). In all cases, the size of the radio antenna is
comparable to or greater than the wavelength. Thus one may think that a receiving
antenna collects energy from a large geometric cross and concentrates it in a small,
subwalength area.
The receiving antennas in radio and microwave technology are loaded by matched
impedance loads that effectively withdraw the energy from them. This suppresses the
radiation by such antennas but simultaneously dampens their resonances and makes
them poor resonators.
In majority of cases, the optical antennas are not matched-loaded because they are
designed not to transduce energy efficiently but to create high local fields interacting
with molecules or atoms, which do not load these antennas significantly. (There
are exceptions though: for instance, the nanoantenna in Ref. [66] is loaded with an
adiabatic nanofocusing waveguide.) The unloaded antennas efficiently loose energy
to radiation (scattering), which also dampens their resonances.
A question is whether this concept of collecting energy form a large geometric
cross section is a necessary paradigm also in nanoplasmonics. The answer is no,
which is clear already from the fact that the enhancement of the rates of both the
excitation and emission of a small chromophore (molecule, rear earth ion, etc.) in
the near field of a small (R l s ) plasmonic nanoparticle is ∼Q 2 and does not
depend on the nanoparticle size R. This enhancement is due to the coherent resonant
accumulation of the energy of the SPs during ∼Q plasmonic oscillations and has
nothing to do with the size of the nanoparticle. Thus such an enhancement does
not quite fit into the concept of antennas as established in the radio or microwave
technology.
Another test of the nanoantenna concept is whether the efficiency of a nanoantenna
is necessarily increased with its size. The answer to this question is generally no.
This is because for plasmonic nanoparticles, with the increase of size there is also
an increased radiative loss—see below Sect. 1.2.3. In contrast, for many types of
radio-frequency antennas (dish antennas or microwave-horn antennas, for instance),
the efficiency does increase with the size.
1.2.3 Radiative Loss
As we described above in conjunction with Fig. 1.1c, the interaction of optical radiation with a nanoplasmonic system occurs predominantly via the dipole oscillations.
The radiative decay of SPs occur via spontaneous emission of photons, which is a
process that does not exist in classical physics and requires a quantum-mechanical
treatment. To find the radiative life time of a SP state quantum-mechanically, we need
to determine the transitional dipole matrix element d 0 p between the ground state |0
and a single-plasmon excited state | p. To carry out such a computation consistently,
9
vice versa. The mechanism of the efficiency enhancement in the radio frequency
range is a combination of spatial focusing (e.g., for parabolic antennas) and resonant
enhancement (e.g., for a dipole antenna). In all cases, the size of the radio antenna is
comparable to or greater than the wavelength. Thus one may think that a receiving
antenna collects energy from a large geometric cross and concentrates it in a small,
subwalength area.
The receiving antennas in radio and microwave technology are loaded by matched
impedance loads that effectively withdraw the energy from them. This suppresses the
radiation by such antennas but simultaneously dampens their resonances and makes
them poor resonators.
In majority of cases, the optical antennas are not matched-loaded because they are
designed not to transduce energy efficiently but to create high local fields interacting
with molecules or atoms, which do not load these antennas significantly. (There
are exceptions though: for instance, the nanoantenna in Ref. [66] is loaded with an
adiabatic nanofocusing waveguide.) The unloaded antennas efficiently loose energy
to radiation (scattering), which also dampens their resonances.
A question is whether this concept of collecting energy form a large geometric
cross section is a necessary paradigm also in nanoplasmonics. The answer is no,
which is clear already from the fact that the enhancement of the rates of both the
excitation and emission of a small chromophore (molecule, rear earth ion, etc.) in
the near field of a small (R l s ) plasmonic nanoparticle is ∼Q 2 and does not
depend on the nanoparticle size R. This enhancement is due to the coherent resonant
accumulation of the energy of the SPs during ∼Q plasmonic oscillations and has
nothing to do with the size of the nanoparticle. Thus such an enhancement does
not quite fit into the concept of antennas as established in the radio or microwave
technology.
Another test of the nanoantenna concept is whether the efficiency of a nanoantenna
is necessarily increased with its size. The answer to this question is generally no.
This is because for plasmonic nanoparticles, with the increase of size there is also
an increased radiative loss—see below Sect. 1.2.3. In contrast, for many types of
radio-frequency antennas (dish antennas or microwave-horn antennas, for instance),
the efficiency does increase with the size.
1.2.3 Radiative Loss
As we described above in conjunction with Fig. 1.1c, the interaction of optical radiation with a nanoplasmonic system occurs predominantly via the dipole oscillations.
The radiative decay of SPs occur via spontaneous emission of photons, which is a
process that does not exist in classical physics and requires a quantum-mechanical
treatment. To find the radiative life time of a SP state quantum-mechanically, we need
to determine the transitional dipole matrix element d 0 p between the ground state |0
and a single-plasmon excited state | p. To carry out such a computation consistently,