1 Nanoplasmonics: From Present into Future
73
regime at a very low level—cf. Fig. 1.29b. This CW regime corresponds to the net
amplification equal zero, which means that the gain exactly compensates the loss,
which condition is expressed by Eq. (1.76). This is a consequence of the nonlinear
gain saturation. This holds for any stable CW generator (including any spaser or
laser) and precludes using them as amplifiers.
There are several ways to set a spaser as a quantum amplifier. One of them is
to reduce the feedback, i.e., to allow some or most of the SP energy in the spaser
to escape from the active region, so the spaser will not generate in the region of
amplification. Such a root has successfully been employed to build a SPP plasmonic
amplifier on the long-range plasmon polaritons [277]. A similar root for the SP spasers
would be to allow some optical energy to escape either by a near-field coupling or
by a radiative coupling to far-field radiation. The near-field coupling approach is
promising for building integrated active circuits out of the spasers. Another root has
been used in Ref. [288], which employed symmetric SPP modes in a thin gold strip.
Such modes have much lower loss that the antisymmetric modes at the expense of
much weaker confinement (transverse modal area ∼λ 2 ). The lower loss allows one
to use the correspondingly lower gain and, therefore, avoid both spasing at localized
SP modes and random lasing due to back-scattering from gold imperfections.
Following Ref. [139], we consider here two distinct approaches for setting the
spasers as quantum nanoamplifiers. The first is a transient regime based on the fact
that the establishment of the CW regime and the consequent inversion clamping and
the total gain vanishing require some time that is determined mainly by the rate of
the quantum feedback and depends also on the relaxation rates of the SPs and the
gain medium. After the population inversion is created by the onset of pumping and
before the spasing spontaneously develops, as we show below in this section, there
is a time interval of approximately 250 fs, during which the spaser provides usable
(and as predicted, quite high) amplification—see Sect. 1.5.6.2 below.
The second approach to set the spaser as a logical quantum nanoamplifier is a
bistable regime that is achieved by introducing a saturable absorber into the active
region, which prevents the spontaneous spasing. Then injection of a certain abovethreshold amount of SP quanta will saturate the absorber and initiate the spasing.
Such a bistable quantum amplifier will be considered in Sect. 1.5.6.3.
The temporal behavior of the spaser has been found by direct numerical solution of Eqs. (1.67)–(1.70). This solution is facilitated by the fact that in the model
under consideration all the chromophores experience the same local field inside the
nanoshell, and there are only two types of such chromophores: belonging to the gain
medium and the saturable absorber, if it is present.
1.5.6.2 Monostable Spaser as a Nanoamplifier in Transient Regime
Here we consider a monostable spaser in a transient regime. This implies that no
saturable absorber is present. We will consider two pumping regimes: stationary and
pulse.
73
regime at a very low level—cf. Fig. 1.29b. This CW regime corresponds to the net
amplification equal zero, which means that the gain exactly compensates the loss,
which condition is expressed by Eq. (1.76). This is a consequence of the nonlinear
gain saturation. This holds for any stable CW generator (including any spaser or
laser) and precludes using them as amplifiers.
There are several ways to set a spaser as a quantum amplifier. One of them is
to reduce the feedback, i.e., to allow some or most of the SP energy in the spaser
to escape from the active region, so the spaser will not generate in the region of
amplification. Such a root has successfully been employed to build a SPP plasmonic
amplifier on the long-range plasmon polaritons [277]. A similar root for the SP spasers
would be to allow some optical energy to escape either by a near-field coupling or
by a radiative coupling to far-field radiation. The near-field coupling approach is
promising for building integrated active circuits out of the spasers. Another root has
been used in Ref. [288], which employed symmetric SPP modes in a thin gold strip.
Such modes have much lower loss that the antisymmetric modes at the expense of
much weaker confinement (transverse modal area ∼λ 2 ). The lower loss allows one
to use the correspondingly lower gain and, therefore, avoid both spasing at localized
SP modes and random lasing due to back-scattering from gold imperfections.
Following Ref. [139], we consider here two distinct approaches for setting the
spasers as quantum nanoamplifiers. The first is a transient regime based on the fact
that the establishment of the CW regime and the consequent inversion clamping and
the total gain vanishing require some time that is determined mainly by the rate of
the quantum feedback and depends also on the relaxation rates of the SPs and the
gain medium. After the population inversion is created by the onset of pumping and
before the spasing spontaneously develops, as we show below in this section, there
is a time interval of approximately 250 fs, during which the spaser provides usable
(and as predicted, quite high) amplification—see Sect. 1.5.6.2 below.
The second approach to set the spaser as a logical quantum nanoamplifier is a
bistable regime that is achieved by introducing a saturable absorber into the active
region, which prevents the spontaneous spasing. Then injection of a certain abovethreshold amount of SP quanta will saturate the absorber and initiate the spasing.
Such a bistable quantum amplifier will be considered in Sect. 1.5.6.3.
The temporal behavior of the spaser has been found by direct numerical solution of Eqs. (1.67)–(1.70). This solution is facilitated by the fact that in the model
under consideration all the chromophores experience the same local field inside the
nanoshell, and there are only two types of such chromophores: belonging to the gain
medium and the saturable absorber, if it is present.
1.5.6.2 Monostable Spaser as a Nanoamplifier in Transient Regime
Here we consider a monostable spaser in a transient regime. This implies that no
saturable absorber is present. We will consider two pumping regimes: stationary and
pulse.