MARCO LEGAL

In this section I will briefly discuss the plasmon resonance of particles beyond the

quasi-static regime. Here, the proprieties of polarizability will be discussed qualita-

tively. The plasmon resonance of particles beyond the quasi-static regime is described

by two competing processes [28] [see Fig. 2.8]: a radiativedecay process into photons shown in Fig. 2.8(a) (this process dominates for large particles), where the quasi-static

approximation-breaks down due to retardation effects. Radiative decay is caused by

a direct radiative route of the coherent electron oscillation into photons [31], which is

the main reason for the weakening in the strength of the dipole plasmon resonance as

the particle volume increases [32]. The second process: non-radiativeprocess is shown in Fig. 2.8(c). The non-radiative decay is a result of the creation of electron-hole pairs

via either intraband excitations within the conduction band or interband transitions

from lower-lying d-bands to the sp-conduction band (for noble metal nanoparticles),

which is due to the Pauli exclusion principle: the electrons can only be excited into

empty states in the conduction band. In other words, non-radiative decay is due to

a dephasing of the oscillation of individual electrons.

Figure 2.8: Schematic of radiative (a) and non-radiative (c) decay of localized surface plasmons in noble metal nanoparticles. The non-radiative decay occurs via excitation of electron-hole pairs either within the conduction band (intraband excitation) or between the d band and the sp conduction band (interbandexcitation).

V, can be expressed as [29], αm(ω) = 1− (εm(ω₁₀)+εa)x2 +O(x4) εm(ω) 3(εm(ω)−εa) − (εm(ω)+εa)x2 10 −i 4π2ε3_a/2 3 V λ3 +O(x4) V, (2.20)

where x = πa/λ is the so called size parameter, which combines the radius a with free-space wavelength λ. In contrast to the simple quasi-static solution Eq. (2.13),

this expression has couple of additional terms, where each term has a distinct physical

meaning to it. The x2 _{term in the numerator describes the effect of retardation of}

the exciting field over the volume of the sphere, leading to a shift in the plasmon res-

onance. A similar term in the denominator includes an energy shift of the resonance,

Chapter 3

Surface plasmon polaritons in

nanostructured systems

3.1

Introduction

The aim in this Chapter is to present a discussion of the propagating part of the

surface plasmon, which are called surface plasmon polaritons. Surface plasmon polari-

tons are electromagnetic waves propagating at and bound to surfaces and interfaces

between two different media [12]. The electromagnetic fields of surface plasmon po-

laritons are typically localized to within a few wavelengths of a surface, in the sense

that their amplitude is a maximum at the surface and decays exponentially away

from it. Therefore, these waves are evanescent waves. These electromagnetic surface

tor’s electron plasma. The specific properties of the surface polaritons depend on the

characteristics of the material, normally as described by their dielectric function.

Robert Wood back in 1902 reported the observation of sudden drop of the light

intensity, scattered from a metallic diffraction grating, from maximum to minimum

which occurred within a very narrow range of wavelength [3]. Wood was unable to

explain his own results and therefore named them singular anomalies. However, now one of these anomalies is known to correspond to the excitation of surface plasmon

polaritons.

The coupling of light to these oscillations results in guided polariton modes that

are confined and propagate along the interface [12]. The generation of surface plas-

mon polaritons by incident light is forbidden for translationally invariant interfaces

due to a mismatch between the momentum of the incident light and that of the sur-

face plasmon polaritons at the same frequency, since the surface plasmon polaritons

have greater momentum than a free-space photon. The general approach to provide

additional momentum and satisfy the momentum conservation law for the coupling

of the incident light and the surface plasmon polaritons is to introduce some inho-

mogeneous structure at the interface. Such structures can be subwavelength defects

(holes), or periodic corrugation, i.e., grating, on the metallic surface. Placing a grat-

ing on top of the plasmon waveguide can facilitate an additional wave vector which

is equal to a multiple of the grating vector [12]. The generation of surface plasmon

An important application of surface plasmon polaritons is related to the enhance-

ment of an electro-magnetic field near a metal-dielectric interface due to the gener-

ation of surface plasmon polaritons. Such enhancement opens up the possibility of

manipulating the interaction strength between light and matter. One of the applica-

tions of surface plasmon polaritons is strong signal enhancement in surface-enhanced

Raman spectroscopy [36, 37], where a molecule is placed near the metallic nanostruc-

ture. The enhancement of optical effects by generation of plasmon polaritons at the

surface of small metallic objects was the topic of broad research not only in physics,

but also in biology, chemistry, and material science. Recently, there has been a great

deal of interest in studying the optical properties of semiconductor layered systems

using grating couplers [38, 39, 40] with surface plasmon effects [55, 56]. Grating

couplers are a widely used and promising tool in the semiconductor nano-systems to

design optoelectronic devices [55, 56].

Taking the wave equation as a starting point, this chapter describes the fun-

damentals of surface plasmon polaritons both at a single, flat interface and in a

metal/dielectric interface.