Abstract
The scattering from spherical inhomogeneities has been a major historical topic in acoustics, optics, and electromagnetics and the phenomenon shapes our perception of the world including the blue sky. The long wavelength limit of “Rayleigh scattering” is characterized by intensity proportional to k4 (or λ−4) where k is the wavenumber and λ is the wavelength. With the advance of nanotechnology, it is possible to produce scatterers that are inhomogeneous with material properties that are functions of radius r, such as concentric shells. We demonstrate that with proper choice of material properties linked to the Hermite polynomials in r, scatterers can have long wavelength scattering behavior of higher powers: k8, k16, and higher. These “Hermite scatterers” could be useful in providing unique signatures (or colors) to regions where they are present. If suspended in air under white light, the back-scattered spectrum would be shifted from blue towards violet and then ultraviolet as the higher order Hermite scatterers were illuminated.
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