Extinction, Scattering and Absorption Cross-Sections

Scattering and absorption of light changes the characteristics of the incident beam after it passes the particle. Let us assume that the particle is placed in a beam of electromagnetic radiation and a detector located in the far-held region measures the radiation in the forward scattering direction (e = e ). Let W 

We now consider extinction from a computational point of view. In order to simplify the notations we will use the conventional expressions of the Poynting vectors and the electromagnetic powers in terms of the transformed fields introduced in Sect. 1.1 (we will omit the multiplicative factor 1/ eoMo)- The time-averaged Poynting vector S) can be written as [17] 

Taking into account the boundary conditions nxE =nxE and nxH = nx H on S, we express the time-averaged power absorbed by the particle as 

With Sc being an auxiliary surface enclosing S (Fig. 1.11), we apply the Green second vector theorem to the vector fields E and E in the domain D bounded by S and Sc- We obtain 

The time-averaged power absorbed by the particle then becomes 

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It is interesting to compare these results with calculations of the triangle anteima in ftee space. Plots of the extinction, scattering, and absorption cross sections for the 100-nm triangle antenna in free space along with the peak field intensity at the apex are shown in Fig. 32. The resonance occurs at 675 nm, significantly shifted from the resonance wavelength in the presence of the medium. The peak field intensity occurs at the apex of the antenna, and is clearly... 

Figure 32. Extinction, scattering, and absorption cross sections normalized by the area of the antenna for the 100-nm triangle antenna on a glass substrate as a function of wavelength. The peak E field intensity versus wavelength is also plotted.

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