ABSTRACT
The optical properties of metallic colloids smaller than the wavelength of the visible light have been empirically known since the antiquity and medieval ages. They were used to create colorful glasses by reduction of gold and silver oxides during the fabrication process. This phenomenon results from the absorption by the metal particles of a narrow portion of the visible spectrum of sun light. Indeed, at a specific wavelength depending on the shape, nature and environment of the nanoparticle takes place a resonant oscillation between the surface charge of the metal free electrons and the electromagnetic field scattered by the particle, the so-called localized surface plasmon resonance. The earliest publications about localized surface plasmons date back to 1857 with the experimental work of Michael Faraday (Faraday, 1857). On the theoretical side, Gustav Mie (Mie, 1908) and Richard Gans (Gans,
1912) were the first to propose, at the end of the nineteenth cen-tury, a theoretical description of the phenomenon respectively
for spheres or for spheroids in the quasi-static limit. Appealing properties of localized surface plasmons are first the strong localization of light around the metal particle, which results from the large contribution of the evanescent waves to the
mode structure. The optical field can be squeezed into very small volumes (few nanometers), associated to a large intensity enhancement called hotspots. They are usually located at sharp tips of metal particles (Martin, 2003), or inside gaps of a particle dimer (Novotny et van Hulst, 2011) or between particles and surfaces (Mubeen et al., 2012). Hotspots formation on rough metallic surfaces is widely used in material sciences, biology, and chemistry with surface-enhanced Raman spectroscopy, an improved version of Raman spectroscopy (Fleischmann et al., 1974) efficient enough for single molecule detection. Second, the dependency of the localized surface plasmon wavelength to the particle environment makes it interesting for sensing purpose in medical and biological applications, as a change of refractive index within the volume close the nanoparticle can be detected by a change in the transmission spectrum (Underwood and Mulvaney, 1994). In the following, first we present the basics of localized surface plasmons for a single particle and then give two examples of
systems of coupled metal nanoparticles, and finally present some properties of periodic plasmonic systems. 7.1 Localized Surface Plasmon Resonance of a
Single Particle In a typical experimental setup, plasmonic samples (obtained by either lithography or chemical synthesis) are characterized by measuring the transmission through the samples on a wide range of wavelengths. The profile of the different peaks gives access to the plasmon wavelength and lifetime, but much more information can be obtained on the mode nature through the shape of the peak and its shift under certain modification of the system (for example, the refractive index of the substrate, the size or aspect ratio of the particle, the distance between the particle and a
substrate...). Experimentally, the extinction under a monochromatic excitation of pulsation corresponds to the decrease of the intensity of the incident light when it goes through the sample, through either absorption inside the sample or scattering of light out of the direction of the direction of propagation of the incident light. In the following, we will frequently refer to the extinction cross section, often calculated in theoretical investigations: Cext() = Cabs() + Cdiff () = Pabs_____Iinc + Pdiff_____Iincwhere Pabs and Pdiff are respectively the power of the light absorbed inside the particle and scattered by the particle, where as Iinc is the intensity of the incident light.Let us consider a metal nanoparticle of volume V, dielectric constant () = () + i(), placed in a transparent substrate of dielectric constant B and refractive index n = √___ B. The particle is illuminated by a monochromatic planewave E0(r, ), of amplitude |E0|. The absorption cross section is a function of the distribution of the electric field inside the particle through
*ext 020 0 .( )= ( , ) ( , )| | VC d Enc rP r rEwith0 B( , )= [ ( ) – ] ( , ) P r E rwhere 0 denotes the vacuum permittivity, the imaginary part, the star the complex conjugate, P the polarization density and E the total electric field inside the particle. Similarly, the absorption cross section is *abs 20 0 .( ) = ( , ) ( , ) | | VC d Enc rP r rE The difference between the extinction and the absorption cross sections is the diffusion cross section:
Cdiff f ()= Cext() − Cabs().