1 Nanoplasmonics: From Present into Future
59
1.5.3 Brief Overview of Latest Progress in Spasers
After the original theoretical proposal and prediction of the spaser [31], there has
been an active development in this field, both theoretical and experimental. There
has also been a US patent issued on spaser [250].
Among theoretical developments, a nanolens spaser has been proposed [263],
which possesses a nanofocus (“the hottest spot”) of the local fields. In Refs. [31,
263], the necessary condition of spasing has been established on the basis of the
perturbation theory.
There have been theories published describing the SPP spasers (or, “nanolasers” as
sometimes they are called) phenomenologically, on the basis of classic linear electrodynamics by considering the gain medium as a dielectric with a negative imaginary
part of the permittivity, e.g., [258]. Very close fundamentally and technically are
works on the loss compensation in metamaterials [264–267]. Such linear-response
approaches do not take into account the nature of the spasing as a non-equilibrium
phase transition, at the foundation of which is spontaneous symmetry breaking:
establishing coherence with an arbitrary but sustained phase of the SP quanta in the
system [139]. Spaser is necessarily a deeply-nonlinear (nonperturbative) phenomenon where the coherent SP field always saturates the gain medium, which eventually
brings about establishment of the stationary (or, continuous wave, CW) regime of
the spasing [139]. This leads to principal differences of the linear-response results
from the microscopic quantum-mechanical theory in the region of spasing, as we
discuss below in conjunction with Fig. 1.29.
There has also been a theoretical publication on a bowtie spaser (nanolaser) with
electrical pumping [268]. It is based on balance equations and only the CW spasing
generation intensity is described. Yet another theoretical development has been a
proposal of the lasing spaser [269], which is made of a plane array of spasers.
There have also been a theoretical proposal of a spaser (“nanolaser”) consisting
of a metal nanoparticle coupled to a single chromophore [270]. In this paper, a
dipole–dipole interaction is illegitimately used at very small distances r where it has
a singularity (diverging for r → 0), leading to a dramatically overestimated coupling
with the SP mode. As a result, a completely unphysical prediction of CW spasing due
to single chromophore has been obtained [270]. In contrast, our theory [139] is based
on the full (exact) field of the spasing SP mode without the dipole (or, any multipole)
approximation. As our results of Sect. 1.5.5 below show, hundreds of chromophores
per metal nanoparticle are realistically requited for the spasing even under the most
favorable conditions.
There has been a vigorous experimental investigation of the spaser and the concepts of spaser. Stimulated emission of SPPs has been observed in a proof-ofprinciple experiment using pumped dye molecules as an active (gain) medium [261].
There have also been later experiments that demonstrated strong stimulated emission
compensating a significant part of the SPP loss [262, 271–274]. As a step toward
the lasing spaser, the first experimental demonstration has been reported of a partial
compensation of the Joule losses in a metallic photonic metamaterial using optically
59
1.5.3 Brief Overview of Latest Progress in Spasers
After the original theoretical proposal and prediction of the spaser [31], there has
been an active development in this field, both theoretical and experimental. There
has also been a US patent issued on spaser [250].
Among theoretical developments, a nanolens spaser has been proposed [263],
which possesses a nanofocus (“the hottest spot”) of the local fields. In Refs. [31,
263], the necessary condition of spasing has been established on the basis of the
perturbation theory.
There have been theories published describing the SPP spasers (or, “nanolasers” as
sometimes they are called) phenomenologically, on the basis of classic linear electrodynamics by considering the gain medium as a dielectric with a negative imaginary
part of the permittivity, e.g., [258]. Very close fundamentally and technically are
works on the loss compensation in metamaterials [264–267]. Such linear-response
approaches do not take into account the nature of the spasing as a non-equilibrium
phase transition, at the foundation of which is spontaneous symmetry breaking:
establishing coherence with an arbitrary but sustained phase of the SP quanta in the
system [139]. Spaser is necessarily a deeply-nonlinear (nonperturbative) phenomenon where the coherent SP field always saturates the gain medium, which eventually
brings about establishment of the stationary (or, continuous wave, CW) regime of
the spasing [139]. This leads to principal differences of the linear-response results
from the microscopic quantum-mechanical theory in the region of spasing, as we
discuss below in conjunction with Fig. 1.29.
There has also been a theoretical publication on a bowtie spaser (nanolaser) with
electrical pumping [268]. It is based on balance equations and only the CW spasing
generation intensity is described. Yet another theoretical development has been a
proposal of the lasing spaser [269], which is made of a plane array of spasers.
There have also been a theoretical proposal of a spaser (“nanolaser”) consisting
of a metal nanoparticle coupled to a single chromophore [270]. In this paper, a
dipole–dipole interaction is illegitimately used at very small distances r where it has
a singularity (diverging for r → 0), leading to a dramatically overestimated coupling
with the SP mode. As a result, a completely unphysical prediction of CW spasing due
to single chromophore has been obtained [270]. In contrast, our theory [139] is based
on the full (exact) field of the spasing SP mode without the dipole (or, any multipole)
approximation. As our results of Sect. 1.5.5 below show, hundreds of chromophores
per metal nanoparticle are realistically requited for the spasing even under the most
favorable conditions.
There has been a vigorous experimental investigation of the spaser and the concepts of spaser. Stimulated emission of SPPs has been observed in a proof-ofprinciple experiment using pumped dye molecules as an active (gain) medium [261].
There have also been later experiments that demonstrated strong stimulated emission
compensating a significant part of the SPP loss [262, 271–274]. As a step toward
the lasing spaser, the first experimental demonstration has been reported of a partial
compensation of the Joule losses in a metallic photonic metamaterial using optically