Power-law patterns in electromagnetic scattering: A selected review and recent progress

The angular scattered-light intensity, or scattering curve, for a spherical particle is known to display approximate power-law structures when formulated in terms of the scattering wave vector and plotted in log-log scale. Empirically based studies reveal that the structures have common behavior across a wide variety of particle size and refractive index. These patterns, as they are called, are useful as they can relate the scattering curve to particle properties in some cases. The cause of the patterns, however, has not been satisfactorily derived from first principles until recently and the formal analysis has yet to be applied to nonspherical particles. This paper reviews the patterns for spherical particles and shows how they can be derived from the Maxwell equations for weakly refracting particles. The derivation is then extended to spheroidal particles where similar patterns are seen. A graphically based technique is used to show how interference between particular regions within a particle can account for so-called crossovers, which are transitions from one power-law to another in a given curve. Application of the phasor analysis to strongly refractive spheres and spheroids demonstrates that the interference interpretation remains valid despite the absence of a direct analytical derivation from the Maxwell equations. Finally, several laboratory experiments are discussed that demonstrate how the patterns are seen in measurements and how they may be used in practice to size particles.

► Power-law patterns in scattering from spherical particles is reviewed. ► New patterns for nonspherical particles are discussed. ► The patterns are derived from first principles. ► Explanations for the patterns are given and interpreted. ► Laboratory measurements displaying the patterns are discussed.