[Paper Review] Mie scattering theory: A review of physical features and limitations

Yuriy Akimov|ArXiv.org|Jan 8, 2024

Atmospheric Ozone and Climate6 citations

TL;DR

The paper performs a detailed spherical harmonic analysis of Mie theory to reveal the dual nature of scattered fields (source-free and current-sourced) and discusses limitations and refinements for excitation, interfaces, and localization.

ABSTRACT

Mie theory is the classical problem for modeling of light scattering by spherical particles. In this paper, we perform a spherical harmonic analysis of its solution for the induced fields to reveal the physics underlying the resonant behavior predicted for scattering and absorption. We disclose the two distinct groups of current-sourced and current-free scattered fields, whose interference makes light-matter interaction resonant in Mie theory for every orbital index. Being a model, the current-free scattered fields naturally limit applicability of the classical solution. We discuss those limitations and demonstrate the ways for further refinement of the theory for description of the excitation source, sphere interface and scatterer localization.

Motivation & Objective

• Explain the physical origins of resonances in Mie scattering and absorption.
• Demonstrate the split between source-free and current-sourced scattered fields and their interference.
• Identify limitations of classical Mie theory related to excitation, sphere interfaces, and scatterer localization.
• Propose avenues to refine Mie theory for more accurate descriptions of real excitations and structures.

Proposed method

• Perform a spherical harmonic analysis of Mie solutions to separate radial and angular dependencies.
• Decompose incident fields into spherical harmonics and analyze contributions from source-free and current-sourced scattered fields.
• Express scattering and absorption cross-sections in terms of Mie coefficients a_l and b_l and their decomposed parts.
• Introduce modified scattering coefficients to account for external excitation currents and transition layers between sphere and environment.
• Discuss extensions to radially inhomogeneous media and impedance/admittance formulations across transition layers.

Experimental results

Research questions

• RQ1 What is the physical origin of resonances in the Mie scattering coefficients a_l and b_l?
• RQ2 How do source-free and current-sourced scattered fields interfere to produce super-radiating or non-radiating states?
• RQ3 What are the fundamental limitations of classical Mie theory in describing excitation sources and interfaces?
• RQ4 How can Mie theory be refined to include external excitation currents, transition layers, and radially inhomogeneous media?
• RQ5 What impact do these refinements have on computed scattering and absorption cross-sections?

Key findings

• Mie theory inherently mixes current-sourced and source-free scattered fields, whose interference governs resonances for every orbital index l.
• Super-radiating and non-radiating (anapole) states can be defined for each l, though real materials with dispersion prevent exact realization of these states.
• Absorption and scattering limits can be approached via super-absorbing and super-radiating states, with specific relations between TM/TE and l.
• Modifications to account for external excitation currents and transition layers alter the standard Mie coefficients and cross-sections, especially at low l.
• A transition layer or boundless extension of the scatterer can remove unphysical source-free scattering by preventing annihilation with the incident field.