# Revisit Kerker's conditions by means of the phase diagram

## TL;DR

This paper revisits Kerker's conditions for directional electromagnetic scattering by analyzing phase diagrams, providing new interpretations, physical limits, and practical parameters for experimental realization at optical frequencies.

## Contribution

It offers an alternative interpretation of Kerker's conditions using phase diagrams and explores their physical boundaries and experimental feasibility.

## Key findings

- Phase diagrams reveal limits of directional scattering patterns.
- Generalized Kerker conditions with implicit parameters are proposed.
- Gold-silicon core-shell nanoparticles can achieve ZBS and NZFS at optical frequencies.

## Abstract

For passive electromagnetic scatterers, we explore a variety of extreme limits on directional scattering patterns in phase diagram, regardless of details on the geometric configurations and material properties. By demonstrating the extinction cross-sections with the power conservation intrinsically embedded in phase diagram, we give an alternative interpretation for Kerker first and second conditions, associated with zero backward scattering (ZBS) and nearly zero forward scattering (NZFS). The physical boundary and limitation for these directional radiations are illustrated, along with a generalized Kerker condition with implicit parameters. By taking the dispersion relations of gold-silicon core-shell nanoparticles into account, based on the of phase diagram, we reveal the realistic parameters to experimentally implement ZBS and NZFS at optical frequencies.