Rayleigh scattering and absorption by spherical particles: The Lorentz–Lorenz factor and the Fröhlich resonance

The optical properties of small particles in the Rayleigh regime provide fundamental insights into light–matter interactions relevant to aerosols, colloids, and engineered nanoparticles. Here, we present a systematic analysis of scattering and absorption by homogeneous spherical particles in the complex refractive index (CRI) plane. The dependence of Rayleigh optics on the CRI can be clearly separated from that on particle size with the Lorentz–Lorenz factor containing the CRI dependence. This allows to investigate and visualize optical behavior in the Rayleigh regime as a function of CRI. Contour representations of scattering and absorption in the CRI plane reveal distinct regions governing them as function of real (n) and imaginary (κ) components of the CRI. Within the positive CRI range studied, we identify three regimes for scattering and four for absorption, each characterized by different monotonic dependencies on n and κ. Attention is given to the role of the Fröhlich resonance, where both scattering and absorption exhibit singular behavior due to enhanced polarizability. While most atmospheric particles lie away from this resonance, it can be approached by metallic nanoparticles, such as silver particles, and its influence extends throughout the CRI plane, significantly affecting optical properties. Extensions to non-spherical particles are briefly explored using prolate spheroids, demonstrating the emergence of multiple resonance conditions driven by particle shape that may be used to further engineer optical properties. Our findings provide a unified framework for interpreting and predicting particle optical properties and for future investigations and applications ranging from atmospheric sensing to advanced optical materials.