Electromagnetic scattering by rough polyhedral particles on a substrate

The data sets contain Mueller scattering matrices and integral scattering quantities ensemble-averaged for individual irregular polyhedral particles, with 12 or 20 faces and modest surface roughness, lying on a semi-infinite substrate. The scattering properties were computed using the surface mode of a discrete-dipole approximation code (ADDA, v1.4.0; Yurkin and Hoekstra, JQSRT 112, pp. 2234-2247, 2011; Yurkin and Hoekstra, User manual for the discrete-dipole approximation code ADDA 1.4.0, 2020, URL: https://github.com/adda-team/adda/raw/v1.4.0/doc/manual.pdf).

The data file names consist of the particle shape designation (12 or 20 for the number of faces), the refractive index designation ("m217i0004” refers to a refractive index m=2.17 + 0.004i (relative permittivity 4.71 + 0.02i); and “m279i00155” refers to a refractive index m=2.79 + 0.0155i (relative permittivity 7.78 + 0.09i), and the volume-equivalent size parameter designation (x; 2pi times radius per wavelength) ranging from 0.5 to 8, so that x=0.5 is designated as x05 and x=8 as x80, for instance. Size parameters from 0.5 to 3 are available at intervals of 0.5 and from 3 to 8 at intervals of 1. The number after “Ensemble” in the directory names describes how many particle realizations are included in the ensemble averages. The number (10–16) was determined partially based on the relative contribution when the sizes are weighted using a power-law size distribution with an index from -3.5 to -2.5, partially on the variance of the scattering properties for particles of a specific size (e.g., at x=0.5 the particles scatter as Rayleigh scatterers regardless of the shape), and partially on how accurate data was needed for the research goals (see Related works for further details).

The directory names beginning “Prop49” are ensemble averages for individual incidence propagation directions given in the file “Prop49_incidence.txt” as the Cartesian coordinates of the direction unit vector. The file names beginning “inc” include the azimuthally averaged Mueller scattering matrices (see below for more details) for all individual cases with a specific incidence angle given in the file name: e.g., inc20_mueller_scatgrid” is an azimuthal average of all eight individual ensemble-averaged scattering matrices for which the incidence angle is 20°. The azimuthal directions of the scattering matrices are shifted in the azimuthal averaging so that the resulting scattering matrix is effectively equal to that of a particle that has been rotated through eight orientations at 45° intervals, while the incident vector’s azimuth angle is fixed to 0°, although it is, in fact, the scattering plane that is rotated. Note that the case of azimuthally-averaged normal incidence was computed using an incidence zenith angle 0.8° for computational reasons. In this specific release, the azimuthally averaged normal incidence case is included for all cases of m=2.17 + 0.004i and some of m=2.79 + 0.0155i. For the latter, the missing cases will be amended in a future release.

All Mueller scattering matrices in the mueller_scatgrid files include 16 elements for 181 zenith angles from the surface normal (zenith) to the nadir, and 25 azimuthal directions (15° intervals), regardless of the propagation direction of the incident radiation. The scattering matrix files include a descriptive header line detailing the order of the zenith angle (theta), azimuth angle (phi), and the 4 x 4 elements of the scattering matrix line by line (e.g., s12 is the element on the first line, second column of the matrix), following the format of the original output computed using ADDA before the averaging. The integral scattering quantities in the CrossSec files include the extinction cross section, the extinction efficiency, the absorption cross section, and the absorption efficiency in two orthogonal polarizations: Y (parallel to the scattering plane defined by the incident vector and the surface normal) and X (perpendicular to the scattering plane), with the unique exception of Prop49-or1, where Y and X are respectively perpendicular and parallel to the scattering plane (this case is not included in the azimuthal averages). The efficiencies are equal to the cross sections divided by pi*x^2. The scattering properties consider the interaction between the substrate and the particle but not the unique contribution of the surface reflection, i.e., radiation that scatters from the substrate but not the particle is excluded. Due to the surface interaction, the traditional definition of the integral scattering quantities is potentially ambiguous.

The ADDA code uses scatterer shape models that have been discretised into equally-sized cubic voxels. The shape models of the particles are included in “Shapemodels1-16.zip” in the wavefront file format (obj), which can be discretized into voxels using the Point-inside-polyhedron (PIP) code included in the ADDA package. The number of dipoles per wavelength was in all cases greater than 9|m|, while the number of dipoles per dimension was in all cases at least 37. The distance of the particle from the surface was given as the smallest computable value at a precision of two decimals, where no voxel overlaps the substrate. Thus, the distance is unique to each particle shape and size. The refractive index of the substrate is in all cases 1.55 + 0.004i (relative permittivity 2.40 + 0.012i).

The wavelength used in the computations was 6.283185307, the polarizability prescription and the interaction term were "Filtered coupled dipoles” (FCD) and the iterative solver was “Modified quasi-minimal residual” (QMR2). The threshold for the relative norm of the residual in the iterative solver was set to 10^(-4).

The software information provides a link to example Python codes for plotting the scattering matrix elements in the mueller_scatgrid files provided here. In the example codes, the s11 element can be plotted as a function of both the zenith and azimuth angles, and the diagonal, s12, and s34 elements (as relative to s11) are plotted only as a function of the zenith angle in the upper (zenith's) hemisphere restricted to the scattering plane. All plot examples display the results in incidence angles 20°, 40°, and 60°. The case of normal incidence is included in the zenith+azimuth maps. For visualised examples, see the publication provided in Related works.