76
M. I. Stockman
1.5.6.3 Bistable Spaser with Saturable Absorber as an Ultrafast
Nanoamplifier
Now let us consider a bistable spaser as a quantum threshold (or, logical) nanoamplifier. Such a spaser contains a saturable absorber mixed with the gain medium with
parameters indicated at the end of Sect. 1.5.4.1 and the concentration of the saturable
absorber n a = 0.66n c . This case of a bistable spaser amplifier is of a particular interest because in this regime the spaser comes as close as possible in its functioning
to the semiconductor-based (mostly, MOSFET-based) digital nanoamplifiers. As in
the previous subsection, we will consider two cases: the stationary and short-pulse
pumping.
We again start with the case of the stationary pumping at a rate of g = 5×10 12 s −1 .
We show in Figs. 1.30e, f the dynamics of such a spaser. For a small initial population
N n = 5 × 10 −3 simulating the spontaneous noise, the spaser is rapidly (faster than
in 50 fs) relaxing to the zero population (panel e), while its gain-medium population
is equally rapidly approaching a high level (panel f) n 21 = 0.65 that is defined by the
competition of the pumping and the enhanced decay into the SP mode (the purple
curves). This level is so high because the spasing SP mode population vanishes
and the stimulated emission is absent. After reaching this stable state (which one can
call, say, “logical zero”), the spaser stays in it indefinitely long despite the continuing
pumping.
In contrast, for initial values N n of the SP population large enough (for instance,
for N n = 5, as shown by the blue curves in Figs. 1.30e, f), the spaser tends to the
“logical one” state where the stationary SP population reaches the value of N n ≈ 60.
Due to the relaxation oscillations, it actually exceeds this level within a short time
of 100 fs after the seeding with the initial SPs. As the SP population N n reaches
its stationary (CW) level, the gain medium inversion n 21 is clamped down at a low
level of a few percent, as typical for the CW regime of the spaser. This “logical one”
state salso persists indefinitely, as long as the inversion is supported by the pumping.
There is a critical curve (separatrix) that divide the two stable dynamics types
(leading to the logical levels of zero and one). For the present set of parameters this
separatrix starts with the initial population of N n ≈ 1. For a value of the initial N n
slightly below 1, the SP population N n experiences a slow (hundreds fs in time)
relaxation oscillation but eventually relaxes to zero (Fig. 1.30e, black curve), while
the corresponding chromophore population inversion n 21 relaxes to the high value
n 21 = 0.65 (panel f, black curve). In contrast, for a value of N n slightly higher than 1
(light blue curves in panels e and f), the dynamics is initially close to the separaratrix
but eventually the initial slow dynamics tends to the high SP population and low
chromophore inversion through a series of the relaxation oscillations. The dynamics
close to the separatrix is characterized by a wide range of oscillation times due to its
highly nonlinear character. The initial dynamics is slowest (the “decision stage” of
the bistable spaser that lasts 1 ps). The “decision time” is diverging infinitesimally
close to the separatrix, as is characteristic of any threshold (logical) amplifier.
The gain (amplification coefficient) of the spaser as a logical amplifier is the
ratio of the high CW level to the threshold level of the SP population N n . For this
M. I. Stockman
1.5.6.3 Bistable Spaser with Saturable Absorber as an Ultrafast
Nanoamplifier
Now let us consider a bistable spaser as a quantum threshold (or, logical) nanoamplifier. Such a spaser contains a saturable absorber mixed with the gain medium with
parameters indicated at the end of Sect. 1.5.4.1 and the concentration of the saturable
absorber n a = 0.66n c . This case of a bistable spaser amplifier is of a particular interest because in this regime the spaser comes as close as possible in its functioning
to the semiconductor-based (mostly, MOSFET-based) digital nanoamplifiers. As in
the previous subsection, we will consider two cases: the stationary and short-pulse
pumping.
We again start with the case of the stationary pumping at a rate of g = 5×10 12 s −1 .
We show in Figs. 1.30e, f the dynamics of such a spaser. For a small initial population
N n = 5 × 10 −3 simulating the spontaneous noise, the spaser is rapidly (faster than
in 50 fs) relaxing to the zero population (panel e), while its gain-medium population
is equally rapidly approaching a high level (panel f) n 21 = 0.65 that is defined by the
competition of the pumping and the enhanced decay into the SP mode (the purple
curves). This level is so high because the spasing SP mode population vanishes
and the stimulated emission is absent. After reaching this stable state (which one can
call, say, “logical zero”), the spaser stays in it indefinitely long despite the continuing
pumping.
In contrast, for initial values N n of the SP population large enough (for instance,
for N n = 5, as shown by the blue curves in Figs. 1.30e, f), the spaser tends to the
“logical one” state where the stationary SP population reaches the value of N n ≈ 60.
Due to the relaxation oscillations, it actually exceeds this level within a short time
of 100 fs after the seeding with the initial SPs. As the SP population N n reaches
its stationary (CW) level, the gain medium inversion n 21 is clamped down at a low
level of a few percent, as typical for the CW regime of the spaser. This “logical one”
state salso persists indefinitely, as long as the inversion is supported by the pumping.
There is a critical curve (separatrix) that divide the two stable dynamics types
(leading to the logical levels of zero and one). For the present set of parameters this
separatrix starts with the initial population of N n ≈ 1. For a value of the initial N n
slightly below 1, the SP population N n experiences a slow (hundreds fs in time)
relaxation oscillation but eventually relaxes to zero (Fig. 1.30e, black curve), while
the corresponding chromophore population inversion n 21 relaxes to the high value
n 21 = 0.65 (panel f, black curve). In contrast, for a value of N n slightly higher than 1
(light blue curves in panels e and f), the dynamics is initially close to the separaratrix
but eventually the initial slow dynamics tends to the high SP population and low
chromophore inversion through a series of the relaxation oscillations. The dynamics
close to the separatrix is characterized by a wide range of oscillation times due to its
highly nonlinear character. The initial dynamics is slowest (the “decision stage” of
the bistable spaser that lasts 1 ps). The “decision time” is diverging infinitesimally
close to the separatrix, as is characteristic of any threshold (logical) amplifier.
The gain (amplification coefficient) of the spaser as a logical amplifier is the
ratio of the high CW level to the threshold level of the SP population N n . For this