1 Nanoplasmonics: From Present into Future
3
amplifiers of optical energy. In Sect. 1.5, we present theory and a significant number
of experimental results available to date regarding the spaser and related polaritonic
spasers (nanolasers or plasmonic lasers). We also consider a related problem of loss
compensation in metamaterials.
1.2 Basics of Nanoplasmonics
1.2.1 Fundamentals
Nanoplasmonics is a branch of optical condensed matter science devoted to optical
phenomena on the nanoscale in nanostructured metal systems. A remarkable property of such systems is their ability to keep the optical energy concentrated on the
nanoscale due to modes called surface plasmons (SPs). It is well known [29] and
reviewed below in this chapter that the existence of SPs depends entirely on the fact
that dielectric function ε m has a negative real part, Re ε m < 0. The SPs are well
pronounced as resonances when the losses are small enough, i.e., Im ε m ∪ −Re ε m .
This is a known property of a good plasmonic metal, valid, e.g., for silver in the most
of the visible region. We will call a substance a good plasmonic metal if these two
properties
Re ε m < 0, Im ε m ∪ −Re ε m
(1.1)
are satisfied simultaneously.
There is a limit to which an electromagnetic wave can be concentrated. We
immediately note that, as we explain below, nanoplasmonics is about concentration
of electromechanical energy at optical frequencies (in contrast to electromagnetic
energy) on the nanoscale.
The scale of the concentration of electromagnetic energy is determined by the
wavelength and can be understood from Fig. 1.1a. Naively, let us try to achieve the
strongest light localization using two parallel perfect mirrors forming an ideal FabryPerot resonator. A confined wave (resonator mode) should propagate normally to the
surface of the mirrors. In this case, its electric field E is parallel to the surface of the
mirror. The ideal mirror can be thought of as a metal with a zero skin depth that does
not allow the electric field of the wave E to penetrate inside. Therefore the field is
zero inside the mirror and, due to the Maxwell boundary conditions, must be zero on
the surface of the mirror. The same condition should be satisfied at the surface of the
second mirror. Thus, length L of this Fabry-Perot cavity should be equal an integer
number n of the half-wavelengths of light in the inner dielectric, L = nλ/2. The
minimum length of this resonator is, obviously λ/2. This implies that light cannot be
confined tighter than to a length of λ/2 in each direction, with the minimum modal
volume of λ 3 /8.
3
amplifiers of optical energy. In Sect. 1.5, we present theory and a significant number
of experimental results available to date regarding the spaser and related polaritonic
spasers (nanolasers or plasmonic lasers). We also consider a related problem of loss
compensation in metamaterials.
1.2 Basics of Nanoplasmonics
1.2.1 Fundamentals
Nanoplasmonics is a branch of optical condensed matter science devoted to optical
phenomena on the nanoscale in nanostructured metal systems. A remarkable property of such systems is their ability to keep the optical energy concentrated on the
nanoscale due to modes called surface plasmons (SPs). It is well known [29] and
reviewed below in this chapter that the existence of SPs depends entirely on the fact
that dielectric function ε m has a negative real part, Re ε m < 0. The SPs are well
pronounced as resonances when the losses are small enough, i.e., Im ε m ∪ −Re ε m .
This is a known property of a good plasmonic metal, valid, e.g., for silver in the most
of the visible region. We will call a substance a good plasmonic metal if these two
properties
Re ε m < 0, Im ε m ∪ −Re ε m
(1.1)
are satisfied simultaneously.
There is a limit to which an electromagnetic wave can be concentrated. We
immediately note that, as we explain below, nanoplasmonics is about concentration
of electromechanical energy at optical frequencies (in contrast to electromagnetic
energy) on the nanoscale.
The scale of the concentration of electromagnetic energy is determined by the
wavelength and can be understood from Fig. 1.1a. Naively, let us try to achieve the
strongest light localization using two parallel perfect mirrors forming an ideal FabryPerot resonator. A confined wave (resonator mode) should propagate normally to the
surface of the mirrors. In this case, its electric field E is parallel to the surface of the
mirror. The ideal mirror can be thought of as a metal with a zero skin depth that does
not allow the electric field of the wave E to penetrate inside. Therefore the field is
zero inside the mirror and, due to the Maxwell boundary conditions, must be zero on
the surface of the mirror. The same condition should be satisfied at the surface of the
second mirror. Thus, length L of this Fabry-Perot cavity should be equal an integer
number n of the half-wavelengths of light in the inner dielectric, L = nλ/2. The
minimum length of this resonator is, obviously λ/2. This implies that light cannot be
confined tighter than to a length of λ/2 in each direction, with the minimum modal
volume of λ 3 /8.