Ellipsoids and spheroids

A particularly convenient case of particle whose shape deviates from that of a sphere, is that of an ellipsoid with semiaxes a aj 

From the solution of the scattering problem in this case, the polarizability turns out to be a diagonal tensor whose components along the three axes are  

A particular class of ellipsoids are spheroids which are axially symmetric ellipsoidal particles in which two axes are equal the two major ones for oblate spheroids (oi = 02) and the two minor ones for prolate spheroids (02 = 03). 

In Fig. 3.3 the extinction efficiency is reported for a prolate spheroid excited with an electric field E polarized at tt/4 respect to the y-axis. As we can observe, the dipolar resonance mode splits into one mode at small wavelengths (the transverse mode) and one mode at longer wavelengths (the longitudinal mode) this in agreement with Eq. (3.7) which for axially symmetric ellipsoidal particles provides two resonances. 

It is interesting to observe that the splitting between the resonances along the two axes is much more evident for larger aspect ratio (panel (a) in Fig. 3.4). 

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