By Leibniz Gottfried Wilhelm

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25) enters only through α0 (ω). For convenience, we introduce the variable Z(ω) ≡ 1/α0 (ω) = −[X(ω) + iδ(ω)]. 27), we obtain −3 [1 + 3 h ( − X ≡ −Re[α0−1 ] = −Rm −3 δ ≡ −Im[α0−1 ] = 3Rm h /| − 2 h| . 31) The variable X indicates the proximity of ω to the resonance of an individual particle, occurring for a spherical particle at = −2 h , and it plays the role of a frequency parameter; δ characterizes dielectric losses. The resonance quality factor is proportional to δ −1 . At the resonance of a spherical particle 3 = −2 h , we have (Rm δ)−1 = (3/2)| / |.

6 Surface-Enhanced Optical Nonlinearities in Fractals 49 As was pointed out above, when monomers are the constituents of a cluster, the field acting upon the ith monomer is the local field Ei rather than the external field E(0) . Also, dipole interactions of the monomers at the Stokesshifted frequency ωs should be included. These interactions occur through the linear polarizability α(ωs ) = αs at the Stokes frequency ωs . 51) jβ where α0s is the linear polarizability of an isolated monomer at the Stokesshifted frequency ωs .

It is interesting to note that a fractal itself can be considered (when it is mathematically defined) as a fluctuation, and this is because the fractal’s average density is asymptotically zero. The fluctuative nature of fractals is fully manifested in the resonance optical properties of fractal clusters, as described below in this chapter. Note that, as shown by Stockman and his colleagues [48, 49], a pattern of localization of optical modes in fractals is complicated and can be called inhomogeneous.

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A Unitary Principle of Optics, Catoptrics, and Dioptrics by Leibniz Gottfried Wilhelm
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