chapter  7
The Unique Characteristics of Localized Surface Plasmon Resonance
Pages 30

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().