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Surface Plasmon Resonances of Metal Polyhedral Nanoparticles

A.L. González and C. Noguez
UNAM, MX

Keywords:
surface plasmons, metal nanoparticles, optical response

Abstract:
In this work, we show that it is possible to elucidate among different polyhedral shapes of silver nanoparticles of less than 10 nm, by studying their surface plasmon resonances. When a particle is excited by an electromagnetic field (EM), the electrons start to oscillate with the same frequency as the one of the incident EM. The excited charges can transform energy from the incident EM wave into, for example, thermal energy in a so-called absorption process. However, the charges can be also accelerated and they can radiate energy in any direction in a so-called scattering process. The sum of both effects is called the light extinction. For nanoparticles of less than 10 nm, radiation process is negligible, so the particle only absorbs energy. There are mainly three different absorption mechanisms related with the size of the particles: i) surface plasma resonances, ii) surface dispersion, and iii) radiation damping. The latter becomes important when the size of the particle is larger than 20 nm, and for nanoparticles of less than 10 nm, the surface resonances are independent of the size. Therefore, for small particles (< 10 nm) the surface dispersion effect is the only one that depends on the size; as smaller is the particle, the surface dispersion is more important. Notice that these absorption mechanisms also depend on the shape of the nanoparticles.
 
The surface plasma resonances of small particles can be study in terms of the strength of the coupling to the applied field of the optically active surface modes of the system. The location of the resonant frequencies of the proper modes of the system and the calculation of their coupling strength to the applied field are not immediate, because it usually requires taking the non-dissipation limit, a procedure that might call for a vast amount of numerical effort. However, using a spectral representation of the polarizability of the particle, we could construct, in principle, a theory that yields both the frequencies of the proper modes and the size of their coupling strength to the applied field. In the spectral representation of the particle, the polarizability is expressed as a sum of terms with single poles. The location of the poles is associated with the frequencies of the normal modes of the particle and their strength with the coupling of these modes to the applied field. The main advantage of this type of representation is that the location of the poles and their strength are independent of the size and dielectric properties of the particle and depend only on its shape.
 
Here, we study the optical response of different polyhedral shapes of silver nanoparticles of less than 10 nm. Then, we show that colloidal suspensions made under well-controlled synthesis conditions not only exhibit narrow-size distributions but also very few structural

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