Unveiling the Bright Spot with Mie Scattering

TL;DR

This work applies full vector Mie scattering to elucidate the Bright Spot in diffraction around circular and spherical obstacles, unifying the 2D disk and 3D sphere perspectives within a single framework. By deriving and employing TE/TM Mie coefficients for a plane-wave incidence, the study reveals a polarization-dependent deformation of the central spot and shows that the on-axis intensity $I(z)$ provides a robust signature to distinguish circles from spheres, especially at short propagation distances and larger radii. The results offer a vector-based, boundary-condition-driven description of diffraction phenomena, with practical implications for optical metrology and nanofabrication where precise object characterization is required. Overall, the approach reinforces the importance of vector scattering in diffraction theory and provides actionable criteria for differentiating geometries via central diffraction hot spots.

Abstract

This work applies Mie scattering theory to provide a new perspective on the propagation of light through a spherical obstacle, offering a novel explanation for the formation of the Poisson spot (also known as the Arago or Fresnel spot). We demonstrate that the diffraction patterns generated by a sphere and by a circular disk can be understood as complementary outcomes of the same underlying scattering process. Our analysis highlights the constructive interference responsible for the bright central spot, and extends the classical wave optics framework by connecting it directly with the scattering coefficients of spherical harmonics. This approach not only deepens the theoretical understanding of diffraction phenomena, but also provides a practical framework that may be applied in modern optical experiments and photonic device design.

Figures (11)

• Figure 1: Schematic of light propagation around a circular disk, with $R =$15 µm (A) and the resulting diffraction pattern featuring the Bright Spot at a distance $z =$1800$\cdot$ R µm, with zoom in the center region to show bright spot (B). Images generated using Fourier Optics.
• Figure 2: Calculated diffraction pattern from a perfectly conducting sphere using Mie theory, showing a central Bright Spot. Parameters, as indicated in the Methods section, and observation plane at $z =$ 1000 µm from the sphere's edge.
• Figure 3: Comparison of intensity profiles for a circular disk (analytical solution) and a sphere (Mie theory). Both objects have same radius $R=$100 µm, as indicated in the Methods section. Profiles are shown at multiple distances ($z$) from the object's edge.
• Figure 4: Calculations of on--axis intensity of the Bright Spot as a function of distance ($z$) from the object's edge for a disk and a sphere. The differing profiles offer a clear method for distinguishing the two geometries.
• Figure 5: The simulation of the pattern generated by a disk with a $R = 100$ µ m, the same patter and in Figure 1 (B) in the text, but in log scale.