56
M. I. Stockman
S u b s t r a t e
Q u a n t u m
d o t s
M e t a l n a n o p a r t ic le
Fig. 1.25 Schematic of the spaser as originally proposed in Ref. [31]. The resonator of the spaser
is a metal nanoparticle shown as a gold V-shape. It is covered by the gain medium depicted as
nanocrystal quantum dots. This active medium is supported by a substrate
1.5.2 Spaser Fundamentals
As we have already mentioned, the spaser is a nanoplasmonic counterpart of the laser
[31, 251]. The laser has two principal elements: resonator (or cavity) that supports
photonic mode(s) and the gain (or active) medium that is population-inverted and
supplies energy to the lasing mode(s). An inherent limitation of the laser is that the
size of the laser cavity in the propagation direction is at least half wavelength and
practically more than that even for the smallest lasers developed [253, 254, 257]. In
the spaser [31] this limitation is overcome. The spasing modes are surface plasmons
(SPs) whose localization length is on the nanoscale [78] and is only limited by the
minimum inhomogeneity scale of the plasmonic metal and the nonlocality radius
[35] l nl ∼ 1 nm. So, the spaser is truly nanoscopic—its minimum total size can be
just a few nanometers.
The resonator of a spaser can be any plasmonic metal nanoparticle whose total
size R is much less than the wavelength λ and whose metal thickness is between l nl
and l s , which supports a SP mode with required frequency ω n . This metal nanoparticle should be surrounded by the gain medium that overlaps with the spasing SP
eigenmode spatially and whose emission line overlaps with this eigenmode spectrally [31]. As an example, we consider a model of a nanoshell spaser [139, 251,
258], which is illustrated in Fig. 1.26. Panel (a) shows a silver nanoshell carrying
a single SP (plasmon population number N n = 1) in the dipole eigenmode. It is
characterized by a uniform field inside the core and hot spots at the poles outside
the shell with the maximum field reaching ∼10 6 V/cm. Similarly, Fig. 1.26b shows
the quadrupole mode in the same nanoshell. In this case, the mode electric field is
non-uniform, exhibiting hot spots of ∼1.5 × 10 6 V/cm of the modal electric field
at the poles. These high values of the modal fields is the underlying physical reason
for a very strong feedback in the spaser. Under our conditions, the electromagnetic
retardation within the spaser volume can be safely neglected. Also, the radiation of
such a spaser is a weak effect: the decay rate of plasmonic eigenmodes is dominated
M. I. Stockman
S u b s t r a t e
Q u a n t u m
d o t s
M e t a l n a n o p a r t ic le
Fig. 1.25 Schematic of the spaser as originally proposed in Ref. [31]. The resonator of the spaser
is a metal nanoparticle shown as a gold V-shape. It is covered by the gain medium depicted as
nanocrystal quantum dots. This active medium is supported by a substrate
1.5.2 Spaser Fundamentals
As we have already mentioned, the spaser is a nanoplasmonic counterpart of the laser
[31, 251]. The laser has two principal elements: resonator (or cavity) that supports
photonic mode(s) and the gain (or active) medium that is population-inverted and
supplies energy to the lasing mode(s). An inherent limitation of the laser is that the
size of the laser cavity in the propagation direction is at least half wavelength and
practically more than that even for the smallest lasers developed [253, 254, 257]. In
the spaser [31] this limitation is overcome. The spasing modes are surface plasmons
(SPs) whose localization length is on the nanoscale [78] and is only limited by the
minimum inhomogeneity scale of the plasmonic metal and the nonlocality radius
[35] l nl ∼ 1 nm. So, the spaser is truly nanoscopic—its minimum total size can be
just a few nanometers.
The resonator of a spaser can be any plasmonic metal nanoparticle whose total
size R is much less than the wavelength λ and whose metal thickness is between l nl
and l s , which supports a SP mode with required frequency ω n . This metal nanoparticle should be surrounded by the gain medium that overlaps with the spasing SP
eigenmode spatially and whose emission line overlaps with this eigenmode spectrally [31]. As an example, we consider a model of a nanoshell spaser [139, 251,
258], which is illustrated in Fig. 1.26. Panel (a) shows a silver nanoshell carrying
a single SP (plasmon population number N n = 1) in the dipole eigenmode. It is
characterized by a uniform field inside the core and hot spots at the poles outside
the shell with the maximum field reaching ∼10 6 V/cm. Similarly, Fig. 1.26b shows
the quadrupole mode in the same nanoshell. In this case, the mode electric field is
non-uniform, exhibiting hot spots of ∼1.5 × 10 6 V/cm of the modal electric field
at the poles. These high values of the modal fields is the underlying physical reason
for a very strong feedback in the spaser. Under our conditions, the electromagnetic
retardation within the spaser volume can be safely neglected. Also, the radiation of
such a spaser is a weak effect: the decay rate of plasmonic eigenmodes is dominated