Retrieving the refractive index of a sphere from the phase spectrum of its light-scattering profile

We studied the Fourier spectrum of the light-scattering profiles of single particles in the Rayleigh-Gans-Debye (RGD) and Wentzel–Kramers–Brillouin (WKB) approximations. In the case of a homogeneous sphere, we found the relationship between the key parameters of the spectrum (including its phase) and the sphere characteristics – both analytically and numerically in the framework of the approximations and the rigorous Lorentz–Mie theory, respectively. Based on these results, we have improved the existing spectral characterization method for spheres extending the applicability range to particles with a higher refractive index.

О сфероидальной модели рассеяния света несферическими частицами

We have constructed a spheroidal model to solve the problem of light scattering by nonspherical particles. The semiaxes of the model spheroid are determined based on the requirement that the volumes of initial and model particles are equal, as well as the ratios of their longitudinal and transverse dimensions. This ensures the closeness of the optical properties of initial and model particles. This approach has been applied to prolate and oblate parallelepipeds, cylinders, and cones with the ratios between their larger and smaller dimensions equal to 2 or 10. The direction of propagation of the incident TE or TM plane wave was either parallel or perpendicular to the symmetry axis of particles and model spheroid. The particle size has been determined by dimensionless parameter $${{x}_{{v}}}$$ = $$2\pi {{r}_{{v}}}$$ /λ, which depends on the particle volume, since $${{r}_{{v}}}$$ is the radius of the equivolume sphere. In calculations, this parameter has been varied from small values to fairly large ones, $${{x}_{{v}}}$$ = 10. The applicability range of the model has been determined by comparing the results of numerical calculations performed by the rigorous separation of variables method for spheroids and the method of discrete dipoles for other nonspherical particles. It has been shown that the applicability range of the model for parallelepipeds, cylinders, and cones is wide enough for different parameters of the problem, in particular, if the parameter $${{x}_{{v}}}$$ ≤ 6, then the relative error of the model does not exceed 10–15%. To a large extent, this is related to the fact that the first maximum of the dependence of scattering factor Q _sca on $${{x}_{{v}}}$$ is similar for particles of different shapes approximated by one and the same model spheroid.