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• Impact of fractal dimension on aggregate scattering cross-section predicted by EMA was assessed. • Condition when EMA is more accurate than RDG-FA was proposed with reference to MSTM. • A critical aggregate size parameter value for which EMA is applicable was suggested. Particles within aggregates are commonly in a status of dependent scattering due to the near-field multiple scattering and far-field interferences from neighboring particles. The integral radiative characteristics of fractal aggregates are consequently not only influenced by the monomer size parameter x s , the refractive index n m , and the monomer number N s , but also tied to the fractal dimension D f. The effective-medium approximation (EMA) simplifies the calculation of aggregate radiative characteristics by treating an aggregate and its surrounding medium as a homogeneous sphere with an effective refractive index, and by applying the Lorenz-Mie theory to this equivalent sphere. The study aims to assess the applicability of EMA to predict the scattering cross-section of fractal aggregates consisting of non-absorbing monomers with x s , varying from 0.001 to 1.25, N s ranging from 10 to 500, under different fractal dimensions D f. The accurate results obtained using the multiple spheres T-matrix were used as a reference. In addition, the RDG-FA (Rayleigh-Deybe-Gans Fractal Aggregates) theory, which is widely used for aggregates with monomer size x s ≪ 1, was also evaluated for comparison. The finding reveals that both EMA and RDG-FA provide accurate predictions for aggregates satisfying the equivalent aggregate size parameter χ m less than D f , where the dependent scattering is limited. As the dependent scattering effect increases, the fractal dimension D f emerges as a critical factor influencing EMA's accuracy, with EMA excelling for aggregates with larger fractal dimensions close to 3. Furthermore, 2.1 is a critical value of D f above which EMA outperforms RDG-FA. [ABSTRACT FROM AUTHOR]

Relying on the time averaged Poynting vector expressed in terms of beam shape coefficients, dark and superdark theorems are discussed generalizing a previously published dark theorem. The superdark theorem allows one to characterize helical beams (that is to say beams possessing a topological charge) in terms of beam shape coefficients, and to demonstrate that beams with a topological charge equal to ± 2 are not necessarily vortex beams, although it is erroneously traditional to state that helical beams are all vortex beams. • Dark and superdark theorems are established in terms of beam shape coefficients of GLMT. • They allow one to decide on the properties of light intensities (null or not) on the axis of a beam. • And then to decide whether a beam with topological charge is a vortex beam or not. • We may then exhibit examples of beams with topological charges which are not vortex beams. [ABSTRACT FROM AUTHOR]

Previous works have been devoted to the symmetry properties of the Poynting vector for longitudinal axisymmetric beams expressed in terms of beam shape coefficients (BSCs). In the present paper, we examine the case of circularly axisymmetric beams. The former is defined as beams whose longitudinal component of the Poynting vector does not depend on the azimuthal angle. The latter is defined as beams whose all components of the Poynting vector do not depend on the azimuthal angle. We establish that two previously studied families of longitudinal axisymmetric beams are actually circularly axisymmetric beams as well. Examples are provided. • Symmetries of Poynting vector may be expressed in terms of beam shape coefficients of the GLMT. • Such symmetries are studied in the case of circularly symmetric beams. • Two families of such circularly symmetric beams are examined. • Examples and counter-examples are provided. [ABSTRACT FROM AUTHOR]

The T-matrix is a powerful tool that provides the complete description of the linear interaction between the electromagnetic field and a given object. In here, we generalize the usual monochromatic formalism to the case of polychromatic field-matter interaction. The group of transformations of special relativity provides the guidance for building the new formalism, which is inherently polychromatic. The polychromatic T-matrix affords the direct treatment of the interaction of electromagnetic pulses with objects, even when the objects move at constant relativistic speeds. • We expand the T-matrix method to the domain of polychromatic fields. • We put the T-matrix method in the framework of representations of the Poincare group. • We derive the matrix element of the Lorentz boost for the T-matrix in closed form. [ABSTRACT FROM AUTHOR]