Ellipsoids surface modes

For any real material, the frequency at which (12.27) is satisfied is complex—the surface modes are virtual. However, its real part is approximately the frequency where the cross sections have maxima, provided that the imaginary part is small compared with the real part. We shall denote this frequency by us. For a sphere, o>s is the Frohlich frequency wF. If used intelligently, always keeping in mind its limitations, (12.27) is a guide to the whereabouts of peaks in extinction spectra of small ellipsoidal particles but it will not necessarily lead to the exact frequency. 

In the preceding paragraphs we discussed only the conditions for surface mode resonances in the cross sections of small ellipsoidal particles. We now turn to specific examples to further our understanding of these resonances. 

By means of this combination of the cross section for an ellipsoid with the Drude dielectric function we arrive at resonance absorption where there is no comparable structure in the bulk metal absorption. The absorption cross section is a maximum at co = ojs and falls to approximately one-half its maximum value at the frequencies = us y/2 (provided that v2 ). That is, the surface mode frequency is us or, in quantum-mechanical language, the surface plasmon energy is hcos. We have assumed that the dielectric function of the surrounding medium is constant or weakly dependent on frequency. 

When L = 1, the surface mode frequency is the plasma frequency, which for most metals lies in the ultraviolet when L = 0, us vanishes. So there is an enormous range of possible collective excitations in small, ellipsoidal, metallic particles their frequencies can be anywhere from the ultraviolet to the radio. For a given shape, the surface mode frequency is a monotonically decreasing function of em so in going from free space to a denser medium, the surface mode frequencies shift to lower values. 

Gilra (1972ab) has very thoroughly discussed absorption by small ellipsoidal particles, including those with coatings, in the surface mode region. 

The observed darkening of the indium slides results from a shift of the absorption peak because of the coating on the particles. Because of the cumbersomeness of the expressions for coated ellipsoids (Section 5.4) this shift can be understood most easily by appealing to (12.15), the condition for surface mode excitation in a coated sphere. For a small metallic sphere with dielectric function given by the Drude formula (9.26) and coated with a nonabsorbing material with dielectric function c2, the wavelength of maximum absorption is approximately... 

The shift of the amide I mode (FTIR spectra) from 1657 to 1646 cm-1 was attributed to a change in the a-helix native structure to fl-sheets, secondary structure conformations. Atomic Force Microscopy (AFM) images display the coating of the manganese oxide surface as well as the unfolding in a ellipsoidal chain of the protein molecules after adsorption and immobilization on the surface. 

When the applied electric field is directed along the long axis of the ellipsoid, a further enhancement of the electric field in the space between the ellipsoids and a red shift of the resonance frequency take place due to the strong electric field coupling that cannot occur when the electric field is directed along the short axis. This coupling, which is called surface plasmon resonance (SPR), broadens the surface plasmon modes at IR wavelengths [294, 349, 350,404] and promotes the SEIRA effect. 

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