Delocalized Surface Plasmon Resonances

The imaginary part of the dielectric constant for intra-band transition is obtained directly from Eq. (1.144)  

Inter-band transitions can be considered as well, directly from Eq. (1.139) [5]. 

In the previous sections we have considered electromagnetic waves which propagate in an homogeneous material or which are reflected at an interface. A different type of electromagnetic waves which are important in metal optics are the delocalized surface plasmon resonances or surface plasmon polaritons (SPPs), which consist in propagating, dispersive electromagnetic waves coupled to the electron plasma of a metal at a dielectric interface, but evanescently confined in the perpendicular direction [7,12,13]. 

In order to investigate the origin and the physical properties of SPPs, we consider a metal-dielectric interface described by the plane z = 0 (see Fig. 1.6). The local frequency-dependent dielectric function is supposed to change in a stepwise manner from the dielectric with e z) = (for z 0) to the metal with c(z) = 

153) define the form of a SPP solution, which must propagate along the x direction and must be confined along the z direction such requirements imply the following conditions fcf( y) Re[/ ( u)] 0, (1.156) 

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Whereas the resonance frequency of delocalized surface plasmons is given by the adjacent medium, which for Ag at the electrolyte interface is located in the near-UV range (350 nm), localized excitations from noble metal nanoparticles occur in the visible spectral range [121] and their resonance frequency can be tuned by their size and shape [122]. 

The third-order optical nonlinearity of the conjugated polymers is based on the electron delocalization, which makes the electron cloud easily polarizable. Because of this nonresonant origin, the nonlinearity is very fast with subpicosecond response times [120]. Fukaya etal [121] have measured the intensity-dependent index of refraction of P30T using a surface plasmon resonance method. TTie result was nj = 5-10 i m /W at the wavelength 1.06 Xm, which is of the same order of magnitude as the values obtained for polydiacetylenes. 

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