Asymptotic Methods in the Theory of Light Scattering by Nonspherical Particles

  • Aleksey MalinkaEmail author
Part of the Springer Series in Light Scattering book series (SSLS)


The method of stationary phase is applied to calculate the amplitudes of scattering by nonspherical particles that are much larger than the wavelength. The method is valid for scattering angles outside the narrow cone around the forward direction (\({\theta>\it{1}/x}\), \(x\) is the dimensionless particle size). The scattering amplitudes, and therefore the scattering phase functions, can be calculated using Stokes’ theorem for the cases when the field inside the particle is known. These cases match different approximations of physical optics: Fraunhofer diffraction, the Rayleigh-Gans and Wentzel-Kramers-Brillouin approximations. The integral of the field over the particle is converted to the integral over its boundary and then, considering the particles much larger than the wavelength, is calculated with the method of stationary phase that assumes that the essential contribution to the integral comes from the points of the constructive interference, i.e. where the phase of the wave is stationary. The differential cross-section of scattering by an ensemble of chaotically oriented particles is calculated by the non-coherent averaging over particles orientation. Simple approximating formulas are given that relates the scattering properties in the abovementioned cases directly to the microphysical characteristics of the particle ensemble.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Physics, National Academy of Sciences of BelarusMinskBelarus

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