Aluminum particles, extinction

There are some notable differences apparent in Fig. 11.14 between the extinction curves for aluminum spheres and those for water droplets. For example, av is still constant for sufficiently small aluminum particles but the range of sizes is more restricted. The large peak is not an interference maximum aluminum is too absorbing for that. Rather it is the dominance of the magnetic dipole term bx in the series (4.62). Physically, this absorption arises from eddy current losses, which are strong when the particle size is near, but less than, the skin depth. At X = 0.1 jam the skin depth is less than the radius, so the interior of the particle is shielded from the field eddy current losses are confined to the vicinity of the surface and therefore the volume of absorbing material is reduced. 

The extinction curves for magnesium oxide particles (Fig. 11.2) and aluminum particles (Fig. 11.4) show the dominance of surface modes. The strong extinction by MgO particles near 0.07 eV( - 17 ju.m) is a surface mode associated with lattice vibrations. Even more striking is the extinction feature in aluminum that dominates the ultraviolet region near 8 eV no corresponding feature exists in the bulk solid. Magnesium oxide and aluminum particles will be treated in more detail, both theoretically and experimentally, in this chapter. 

Extinction calculations for aluminum spheres and a continuous distribution of ellipsoids (CDE) are compared in Fig. 12.6 the dielectric function was approximated by the Drude formula. The sum rule (12.32) implies that integrated absorption by an aluminum particle in air is nearly independent of its shape a change of shape merely shifts the resonance to another frequency between 0 and 15 eV, the region over which e for aluminum is negative. Thus, a distribution of shapes causes the surface plasmon band to be broadened, the... 

Rathmann, J., 1981. The extinction by small aluminum particles from the far infrared to the vacuum ultraviolet, Ph.D. thesis, University of Arizona. 

The calculated extinction spectrum of a polydispersion of small aluminum spheres (mean radius 0.01 jam, fractional standard deviation 0.15) is shown in Fig. 11.4 both scales are logarithmic. In some ways spectral extinction by metallic particles is less interesting than that by insulating particles, such as those discussed in the preceding two sections. The free-electron contribution to absorption in metals, which dominates other absorption bands, extends from radio to far-ultraviolet frequencies. Hence, extinction features in the transparent region of insulating particles, such as ripple and interference structure, are suppressed in metallic particles because of their inherent opacity. But extinction by metallic particles is not without its interesting aspects. 

Note that there is no bulk absorption band in aluminum corresponding to the prominent extinction feature at about 8 eV. Indeed, the extinction maximum occurs where bulk absorption is monotonically decreasing. This feature arises from a resonance in the collective motion of free electrons constrained to oscillate within a small sphere. It is similar to the dominant infrared extinction feature in small MgO spheres (Fig. 11.2), which arises from a collective oscillation of the lattice ions. As will be shown in Chapter 12, these resonances can be quite strongly dependent on particle shape and are excited at energies where the real part of the dielectric function is negative. For a metal such as aluminum, this region extends from radio to far-ultraviolet frequencies. So the... 

As an example of extinction by spherical particles in the surface plasmon region, Fig. 12.3 shows calculated results for aluminum spheres using optical constants from the Drude model taking into account the variation of the mean free path with radius by means of (12.23). Figure 9.11 and the attendant discussion have shown that the free-electron model accurately represents the bulk dielectric function of aluminum in the ultraviolet. In contrast with the Qext plot for SiC (Fig. 12.1), we now plot volume-normalized extinction. Because this measure of extinction is independent of radius in the small size... 

Figure 8.1 Far-field extinction spectrum of single aluminum nanosphere (dashed] and sphere dimer (soiid]. Dipolar resonance peaks were tuned toward 244 nm (a] and 325 nm (b]. The radius of a single sphere is R1 = 39 nm, whiie those of the dimer are R2 = 20 nm, with gap G = 1.5 nm in (a], in contrast to R1 = 55 nm, R2 = 30 nm, G = 1.2 nm in panel b. The incident piane-wave for particle dimer is shown in the inset. Reprinted with permission from Ref. [33]. Copyright (2009] American Chemical Society.

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