ISSN 1064-2269, Journal of Communications Technology and Electronics, 2011, Vol. 56, No. 12, pp. 1471–1479. © Pleiades Publishing, Inc., 2011.
Original Russian Text © E.S. Andrianov, A.A. Pukhov, A.V. Dorofeenko, A.P. Vinogradov, A.A. Lisyansky, 2011, published in Radiotekhnika i Elektronika, 2011, Vol. 56, No. 12,
pp. 1501–1510.
1471
INTRODUCTION
The fundamental limitation on the operation rate of
future computers is imposed by ratio of the size of the
system to the velocity of light. The rapid progress in
plasmonics can be used to solve the problem owing to
the application of metamaterials and the creation of the
devices with subwavelength sizes. Recent interest in the
optics of metamaterials (substances with negative per-
mittivity or permeability) [1] has been driven mainly by
the Pendry’s work [2], in which a superlens with the res-
olution exceeding the diffraction limit was proposed.
The new electrodynamics of metamaterials stimulated
the development of theoretical proposals on the possi-
ble applications: clocking [3, 4], hyperlenses [5–7],
energy concentrators [8], etc. In spite of the absence of
the natural metamaterials, the progress in plasmonics
and nanotechnology allowed the creation of artificial
optical metamaterials [9]. The working principle is
based on the plasmon resonance of metal nanoparticles.
A significant disadvantage of such materials is related to
inadmissibly high loss. Active (amplifying) impurities
can be used in the artificial metamaterials for the loss
compensation [7, 10–12].
An example of such impurities in metamaterials is
the simplest object of quantum plasmonics—metal
nanoparticle that is surrounded by inversely excited
quantum systems (molecules or quantum dots). The
interaction of the surface plasmons (SPs) that are
excited in the nanoparticles with the electromagnetic
field of the inversely excited quantum dots (QDs)
allows the transformation of the system into a quan-
tum generator of plasmons (nanolaser). Note that the
dipole nanolaser [13], spaser [12–14], and the nanola-
ser on the magnetic mode [11] can be classified as
nanolasers. The spaser, which was experimentally
implemented in [15], is the most promising device.
The spaser schematically represents a system of
inversely excited two-level QDs that surround the
plasmon nanoparticles. The working principle of the
spaser is similar to the working principle of laser. SPs
that are localized on the nanoparticle play the role of
photons [14, 16–18], and the nanoparticle plays the
role of cavity. In other words, the generation and
amplification of the near fields of nanoparticles take
place in the spaser. The amplification of the SPs is due
to the nonradiative energy transfer from the QD. The
process is based on the dipole–dipole or any alterna-
tive near-field interaction [19] of the QD and plasmon
nanoparticle. The process is effective owing to the fact
that the probability of the nonradiative excitation of
plasmon is greater than the probability of the radiative
emission of photon by a factor of , where r is the
distance between the centers of QD and nanoparticle
and [20]. The generation of a relatively large
number of plasmons leads to the stimulated emission
of the QD to the plasmon mode and the development
of the plasmon generation. Thus, the excitation of the
plasmon mode by pump is performed via the QD exci-
tation.
The spaser operation can be controlled using rela-
tively weak external fields. In the presence of the exter-
nal field, the spaser can start working at the field fre-
quency but the oscillation amplitude of the dipole
moment will be determined by the pump level rather
than the external field. The characteristic time and
dynamics of the spaser transition from the intrinsic fre-
quency to the field frequency are practically important.
We may assume that the spaser can be used as an ampli-
fier or switch.
It may seem that the independence of the oscillation
amplitude on the external fields impedes the applica-
tion with amplification [21]. However, the results from
[18] show that the spaser can work as an amplifier in the
transient regime. In particular, in the transient regime,
the spaser exhibits complicated nonlinear dynamics
and the amplitude of the spaser oscillations can be sig-
nificantly higher than the amplitudes of the initial and
steady-state spaser oscillations.
( )
3
kr
-
2 k = πλ
RADIO PHENOMENA
IN SOLIDS AND PLASMA
Dynamics of the Transient Regime of Spaser
E. S. Andrianov, A. A. Pukhov, A. V. Dorofeenko, A. P. Vinogradov, and A. A. Lisyansky
Received July 19, 2011
Abstract—The dynamics of the nonradiative excitation of plasmons in the surface plasmon amplifier by
stimulated emission of radiation (spaser) that represents a two-level quantum dot in the vicinity of the metal
(plasmon) nanoparticle is considered. It is demonstrated that the steady-state generation of spaser is pre-
ceded by the regime with the oscillations at the Rabi frequency in which the phase difference between the
dipole moments and the direction of the energy flux from the quantum dot to the nanoparticle exhibit the
sign alternation.
DOI: 10.1134/S1064226911120151