58
M. I. Stockman
was originally proposed in Ref. [258]. As we have verified, these two designs lead to
comparable characteristics of the spaser. However, the placement of the gain medium
inside the core illustrated in Fig. 1.26d has a significant advantage because the hot
spots of the local field are not covered by the gain medium and are sterically available
for applications.
Note that any l-multipole mode of a spherical particle is, indeed, 2l + 1-times
degenerate. This may make the spasing mode to be polarization unstable, like in
lasers without polarizing elements. In reality, the polarization may be clamped and
become stable due to deviations from the perfect spherical symmetry, which exist
naturally or can be introduced deliberately. More practical shape for a spaser may
be a nanorod, which has a mode with the stable polarization along the major axis.
However, a nanorod is a more complicated geometry for theoretical treatment, and
we will consider it elsewhere.
The level diagram of the spaser gain medium and the plasmonic metal nanoparticle
is displayed in Fig. 1.26e along with a schematic of the relevant energy transitions
in the system. The gain medium chromophores may be semiconductor nanocrystal
quantum dots [31, 260], dye molecules [261, 262], rare-earth ions [258], or electronhole excitations of an unstructured semiconductor [253, 257]. For certainty, we will
use a semiconductor-science language of electrons and holes in quantum dots.
The pump excites electron-hole pairs in the chromophores (Fig. 1.26e), as indicated by the vertical black arrow, which relax to form excitons. The excitons constitute the two-level systems that are the donors of energy for the SP emission into the
spasing mode. In vacuum, the excitons would recombine emitting photons. However,
in the spaser geometry, the photoemission is strongly quenched due to the resonance
energy transfer to the SP modes, as indicated by the red arrows in the panel. The probability of the radiativeless energy transfer to the SPs relative to that of the radiative
decay (photon emission) is given by the so-called Purcell factor
∼
λ 3 Q
R 3 1,
(1.61)
where R is a characteristic size of the spaser metal core. Thus this radiativeless energy
transfer to the spaser mode is the dominant process whose probability is by orders
of magnitude greater than that of the free-space (far-field) emission.
The plasmons already in the spaser mode create the high local fields that excite
the gain medium and stimulate more emission to this mode, which is the feedback
mechanism. If this feedback is strong enough, and the life time of the spaser SP
mode is long enough, then an instability develops leading to the avalanche of the
SP emission in the spasing mode and spontaneous symmetry breaking, establishing
the phase coherence of the spasing state. Thus the establishment of spasing is a
non-equilibrium phase transition, as in the physics of lasers.
M. I. Stockman
was originally proposed in Ref. [258]. As we have verified, these two designs lead to
comparable characteristics of the spaser. However, the placement of the gain medium
inside the core illustrated in Fig. 1.26d has a significant advantage because the hot
spots of the local field are not covered by the gain medium and are sterically available
for applications.
Note that any l-multipole mode of a spherical particle is, indeed, 2l + 1-times
degenerate. This may make the spasing mode to be polarization unstable, like in
lasers without polarizing elements. In reality, the polarization may be clamped and
become stable due to deviations from the perfect spherical symmetry, which exist
naturally or can be introduced deliberately. More practical shape for a spaser may
be a nanorod, which has a mode with the stable polarization along the major axis.
However, a nanorod is a more complicated geometry for theoretical treatment, and
we will consider it elsewhere.
The level diagram of the spaser gain medium and the plasmonic metal nanoparticle
is displayed in Fig. 1.26e along with a schematic of the relevant energy transitions
in the system. The gain medium chromophores may be semiconductor nanocrystal
quantum dots [31, 260], dye molecules [261, 262], rare-earth ions [258], or electronhole excitations of an unstructured semiconductor [253, 257]. For certainty, we will
use a semiconductor-science language of electrons and holes in quantum dots.
The pump excites electron-hole pairs in the chromophores (Fig. 1.26e), as indicated by the vertical black arrow, which relax to form excitons. The excitons constitute the two-level systems that are the donors of energy for the SP emission into the
spasing mode. In vacuum, the excitons would recombine emitting photons. However,
in the spaser geometry, the photoemission is strongly quenched due to the resonance
energy transfer to the SP modes, as indicated by the red arrows in the panel. The probability of the radiativeless energy transfer to the SPs relative to that of the radiative
decay (photon emission) is given by the so-called Purcell factor
∼
λ 3 Q
R 3 1,
(1.61)
where R is a characteristic size of the spaser metal core. Thus this radiativeless energy
transfer to the spaser mode is the dominant process whose probability is by orders
of magnitude greater than that of the free-space (far-field) emission.
The plasmons already in the spaser mode create the high local fields that excite
the gain medium and stimulate more emission to this mode, which is the feedback
mechanism. If this feedback is strong enough, and the life time of the spaser SP
mode is long enough, then an instability develops leading to the avalanche of the
SP emission in the spasing mode and spontaneous symmetry breaking, establishing
the phase coherence of the spasing state. Thus the establishment of spasing is a
non-equilibrium phase transition, as in the physics of lasers.