72
M. I. Stockman
The developed spasing in a dipole SP mode will show itself in the far field as an
anomalously narrow and intense radiation line. The shape and intensity of this line
in relation to the lines of the spontaneous fluorescence of the isolated gain medium
and its SP-enhanced fluorescence line in the spaser is illustrated in Figs. 1.29d–f.
Note that for the system under consideration, there is a 20 meV red shift of the
gain medium fluorescence with respect to the SP line center. It is chosen so to
illustrate the spectral walk-off of the spaser line. For one percent in the excitation rate
above the threshold of the spasing (panel d), a broad spasing line (red color) appears
comparable in intensity to the SP-enhanced spontaneous fluorescence line (blue
color). The width of this spasing line is approximately the same as of the fluorescence,
but its position is shifted appreciably (spectral walk-off) toward the isolated gain
medium line (green color). For the pumping twice more intense (panel e), the spaserline radiation dominates, but its width is still close to that of the SP line due to
significant quantum fluctuations of the spasing state phase. Only when the pumping
rate is an order of magnitude above the threshold, the spaser line strongly narrows
(panel f), and it also completely dominates the spectrum of the radiation. This is a
regime of small quantum fluctuations, which is desired in applications.
These results in the spasing region are different in the most dramatic way from previous phenomenological models, which are based on linear electrodynamics where
the gain medium that has negative imaginary part of its permittivity plus lossy metal
nanosystem, described purely electrodynamically [258, 265]. For instance, in a “toy
model” [265], the width of the resonance line tends to zero at the threshold of spasing
and then broadens up again. This distinction of the present theory is due the nature
of the spasing as a spontaneous symmetry breaking (nonequilibrium phase transition
with a randomly established but sustained phase) leading to the establishment of a
coherent SP state. This non-equilibrium phase transition to spasing and the spasing
itself are contained in the present theory due to the fact that the fundamental equations
of the spasing (1.67), (1.69), and (1.70) are nonlinear, as we have already discussed
above in conjunction with these equations—see the text after Eq. (1.70). The previous publications on gain compensation by loss [258, 265, 267] based on linear
electrodynamic equations do not contain spasing. Therefore, they are not applicable
in the region of the complete loss compensation and spasing, though their results are
presented for that region.
1.5.6 Spaser as Ultrafast Quantum Nanoamplifier
1.5.6.1 Problem of Setting Spaser as an Amplifier
As we have already mentioned in Sect. 1.5.1, a fundamental and formidable problem
is that, in contrast to the conventional lasers and amplifiers in quantum electronics,
the spaser has an inherent feedback that typically cannot be removed. Such a spaser
will develop generation and accumulation of the macroscopic number of coherent
SPs in the spasing mode. This leads to the population inversion clamping in the CW
M. I. Stockman
The developed spasing in a dipole SP mode will show itself in the far field as an
anomalously narrow and intense radiation line. The shape and intensity of this line
in relation to the lines of the spontaneous fluorescence of the isolated gain medium
and its SP-enhanced fluorescence line in the spaser is illustrated in Figs. 1.29d–f.
Note that for the system under consideration, there is a 20 meV red shift of the
gain medium fluorescence with respect to the SP line center. It is chosen so to
illustrate the spectral walk-off of the spaser line. For one percent in the excitation rate
above the threshold of the spasing (panel d), a broad spasing line (red color) appears
comparable in intensity to the SP-enhanced spontaneous fluorescence line (blue
color). The width of this spasing line is approximately the same as of the fluorescence,
but its position is shifted appreciably (spectral walk-off) toward the isolated gain
medium line (green color). For the pumping twice more intense (panel e), the spaserline radiation dominates, but its width is still close to that of the SP line due to
significant quantum fluctuations of the spasing state phase. Only when the pumping
rate is an order of magnitude above the threshold, the spaser line strongly narrows
(panel f), and it also completely dominates the spectrum of the radiation. This is a
regime of small quantum fluctuations, which is desired in applications.
These results in the spasing region are different in the most dramatic way from previous phenomenological models, which are based on linear electrodynamics where
the gain medium that has negative imaginary part of its permittivity plus lossy metal
nanosystem, described purely electrodynamically [258, 265]. For instance, in a “toy
model” [265], the width of the resonance line tends to zero at the threshold of spasing
and then broadens up again. This distinction of the present theory is due the nature
of the spasing as a spontaneous symmetry breaking (nonequilibrium phase transition
with a randomly established but sustained phase) leading to the establishment of a
coherent SP state. This non-equilibrium phase transition to spasing and the spasing
itself are contained in the present theory due to the fact that the fundamental equations
of the spasing (1.67), (1.69), and (1.70) are nonlinear, as we have already discussed
above in conjunction with these equations—see the text after Eq. (1.70). The previous publications on gain compensation by loss [258, 265, 267] based on linear
electrodynamic equations do not contain spasing. Therefore, they are not applicable
in the region of the complete loss compensation and spasing, though their results are
presented for that region.
1.5.6 Spaser as Ultrafast Quantum Nanoamplifier
1.5.6.1 Problem of Setting Spaser as an Amplifier
As we have already mentioned in Sect. 1.5.1, a fundamental and formidable problem
is that, in contrast to the conventional lasers and amplifiers in quantum electronics,
the spaser has an inherent feedback that typically cannot be removed. Such a spaser
will develop generation and accumulation of the macroscopic number of coherent
SPs in the spasing mode. This leads to the population inversion clamping in the CW