mieroots

Resonances and anapoles of spherical particles are roots of a polynomial. Here they are.

The zeros and poles of the standard Mie multipolar coefficients of a sphere are roots of explicit polynomials in the relative permittivity ε = εp/ε1, with coefficients that depend only on the size parameter. mieroots builds those polynomials and solves them — no auxiliary eigenvalue problems, no biorthogonal modal bases, no scanning a transcendental expression for a sign change.

Two families of intrinsic, excitation-independent material quantities follow:

• Anapole permittivities — the numerator roots: the contrasts at which a multipolar channel is exactly extinguished. Because the scattering cross-section is a sum of strictly non-negative multipolar terms, suppression can only happen channel by channel, so these roots are the complete algebraic inventory of radiationless conditions.
• Resonant permittivities — the denominator roots, whose imaginary part encodes the radiative decay of each channel.

Status: pre-alpha. The repository scaffolding is in place; the physics is being ported from the research code. The API sketched below is the target, not yet the shipped surface.

Installation

pip install mieroots

Quick look

import mieroots  # noqa: F401

print(mieroots.__version__)

Citation

If you use mieroots in academic work, please cite both the software and the paper:

C. Silvestre Castro, A. Bruyant and R. Vincent, Anapole and resonant permittivities of spherical particles as polynomial roots, Optics Letters (submitted).

Machine-readable metadata is in CITATION.cff.

Documentation

https://claudio-sc.github.io/mieroots

Contributing

See CONTRIBUTING.md. Commits follow Conventional Commits; releases are automated with python-semantic-release and gated on a green test run of the same commit — lint, mypy --strict, the full Python/OS test matrix and the docs build all run as a job the release needs:, so a red run blocks the version bump, the GitHub release and the PyPI upload.

Funding

Graduate School NANO-PHOT (ANR-18-EURE-0013) and Agence Nationale de la Recherche (ANR-19-CE42-0008).

License

MIT — see LICENSE.