[Paper Review] First principles derivation of a Rayleigh Gans Debye model for scattering from anisotropic inhomogeneities

M. H. Shachar, J. E. Garay|arXiv (Cornell University)|May 2, 2023

Atmospheric aerosols and clouds4 citations

TL;DR

This paper presents a first-principles derivation of a generalized Rayleigh Gans Debye (RGD) model for light scattering from anisotropic inhomogeneities in linear media. By deriving the formulation from perturbative solutions to Maxwell's equations, it reveals that scattering arises from excess accelerating charges emitting uncompensated radiation—rather than interfaces—enabling modeling of stochastic processes, lossy media, and multi-scale anisotropic inhomogeneities with explicit physical assumptions and deeper insight into soft scattering mechanisms.

ABSTRACT

Scattering problems are important in describing light propagation in wide ranging media such as the atmosphere, colloidal solutions, metamaterials, glass ceramic composites, transparent polycrystalline ceramics, and surfaces. The Rayleigh Gans Debye (RGD) approximation has enjoyed great success in describing a wide range of scattering phenomena. We derive a generalized RGD formulation from the perturbation of Maxwell equations. In contrast to most treatments of RGD scattering, our formulation can model any soft scattering phenomena in linear media, including scattering by stochastic process, lossy media, and by anisotropic inhomogeneities occurring at multiple length scales. Our first-principles derivation makes explicit underlying assumptions and provides jumping off points for more general treatments. The derivation also facilitates a deeper understanding of soft scattering. It is demonstrated that sources of scattering are not interfaces as is often presumed, but excess accelerating charges emitting uncompensated radiation. Approximations to the equations are also presented and discussed. For example, the scattering coefficient in the large size RGD limit is shown to be proportional to the correlation length and the variance of a projected phase shift.

Motivation & Objective

• To develop a generalized Rayleigh Gans Debye (RGD) model applicable to anisotropic inhomogeneities in linear media.
• To clarify the physical origin of scattering in soft matter and complex materials by deriving the model from first principles.
• To extend the RGD approximation beyond isotropic and non-lossy media to include stochastic processes and multi-scale inhomogeneities.
• To identify and formalize the underlying assumptions of the RGD model for future generalization and deeper physical understanding.
• To demonstrate that scattering arises from excess accelerating charges emitting uncompensated radiation, not from interfaces as commonly assumed.

Proposed method

• Derives the generalized RGD model from perturbative solutions to the time-harmonic Maxwell equations in linear, non-magnetic media.
• Uses a first-order perturbation approach to the electric field, assuming weak inhomogeneities in permittivity.
• Models anisotropic inhomogeneities through spatially varying, stochastic dielectric functions with defined correlation lengths and phase shift variances.
• Identifies scattering sources as excess accelerating charges that emit radiation without full charge compensation.
• Derives the scattering coefficient in the large-size limit, showing proportionality to the correlation length and variance of the projected phase shift.
• Applies the formalism to lossy media and stochastic processes by incorporating complex permittivity and statistical phase distributions.

Experimental results

Research questions

• RQ1 What are the fundamental physical mechanisms underlying soft scattering in anisotropic, inhomogeneous media?
• RQ2 How can the Rayleigh Gans Debye approximation be generalized to include anisotropic, multi-scale, and lossy inhomogeneities?
• RQ3 What is the true source of scattering in linear media—interfaces or accelerating charges?
• RQ4 How do correlation length and phase shift variance influence the scattering coefficient in the large-size limit?
• RQ5 What assumptions underlie the standard RGD model, and how can they be made explicit for broader applicability?

Key findings

• Scattering in linear media originates from excess accelerating charges emitting uncompensated radiation, not from interfaces.
• The scattering coefficient in the large-size RGD limit is proportional to the correlation length and the variance of the projected phase shift.
• The first-principles derivation explicitly identifies the assumptions of the RGD model, enabling its extension to stochastic, lossy, and anisotropic systems.
• The generalized RGD model successfully describes scattering in multi-scale, anisotropic inhomogeneities beyond the scope of traditional formulations.
• The formalism provides a deeper physical understanding of soft scattering by grounding it in charge dynamics and radiation emission.
• The model is applicable to a broad range of materials, including transparent polycrystalline ceramics, glass-ceramic composites, and metamaterials.