Global Mie Scattering: Polarization Morphologies and the Underlying Topological Invariant

Area of Science:

• Optics and Photonics
• Topological Photonics

Background:

• Mie theory is fundamental in optics and photonics, but conventional studies focus on local scattering properties.
• Existing methods for total cross-sections are morphology-dependent and lack global invariance.

Purpose of the Study:

• To propose a global Mie scattering theory for characterizing scattering by arbitrary obstacles and coherent light.
• To explore topological invariants in light scattering phenomena.

Main Methods:

• Developing a global Mie scattering theory.
• Analyzing far-field scattering patterns for various obstacles and incident light polarizations.

Main Results:

• Identified universal directions of zero or circularly polarized scattering, independent of scatterer geometry and light properties.
• Assigned half-integer topological indices to singular scattering directions, summing to a global invariant of 2.

Conclusions:

• The proposed global Mie theory offers a new, mathematically simple yet conceptually profound framework for understanding light scattering.
• This approach has potential applications in topological photonics, acoustics, and matter wave scattering in both linear and nonlinear regimes.