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Published online by Cambridge University Press: 02 December 2009
The phenomenon of resonance is, however, most striking in cases where a very accurate equality of periods is necessary in order to ellicit the full effect.
(Lord Rayleigh 1877)We now deal with the last of the critical effects listed in Chapter 1: orbiting, which, as was mentioned in Sec. 1.3, is often associated with the presence of resonances. This is also true here.
The main feature of Mie scattering that we have not treated so far, the existence of sharp ripple fluctuations for ReN > 1, is due to resonances. These resonances, in the idealized model of a perfectly transparent sphere, grow arbitrarily sharp with increasing size parameter; in real life, they can still be extremely narrow, leading to a variety of interesting applications that will be described in Chapter 15.
The origin and physical interpretation of the resonances are greatly clarified by employing the effective potential picture. The resonances appear as ‘quasibound states of light’, associated with orbiting-like paths of light rays around the scatterer. Tunneling through the centrifugal barrier plays an essential role in determining the resonance widths and in explaining the ‘sensitivity to initial conditions’ that characterizes the ripple fluctuations.
CAM theory describes the resonances in terms of families of Regge trajectories, a concept that has found important applications in high-energy physics (Collins 1977). It allows one to determine the resonance positions and widths with high accuracy.
The resonance contributions correspond to residues at the Regge poles, following their trajectories. By adding them to the background that results from the other effects already treated by CAM methods, one can finally obtain complete fits of the Mie cross sections, including the ripple.
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