Design considerations and structure of the CDA package

Description of a cluster at the R level

A cluster describes the geometry of N particles in a list,

• r is a data.frame of 3 columns (x, y, z) and N rows

• angles is a data.frame of 3 columns (x, y, z) and N rows

• sizes is a data.frame of 3 columns (x, y, z) and N rows

Polarisability

The principal values of the inverse polarisability tensor of every particle are passed in a matrix Beta, with 3N rows (1/\(\alpha_x\),1/\(\alpha_y\),1/\(\alpha_z\)) for N particles, and Nlambda columns.

This matrix is formed from the sizes of the cluster, and the material and medium properties.

Functions at the R level

Modelling spectra

• circular_dichroism_spectrum

• dispersion_spectrum

Clusters

• cluster_chain

• cluster_dimer

• cluster_dimer_end

• cluster_helix

Utilities

• array_factor

• alpha_kuwata

• equal_angles

• equal_sizes

• helix

• inverse_polarizability

• La

• polarizability_ellipsoid

Visualisation

• curve_povray

• particles_povray

• rgl.ellipsoid

• rgl.ellipsoids

Structure of the core C++ components

• A is a 3Nx3N complex matrix

• Adiag is a 3Nx3N complex matrix

• Beta is a 3NxNlambda complex matrix

Functions at the C++ level

Array

array_factor Dipole sum (truncated) for 2D square array

CDA

• incident_field Calculate the incident field at each dipole location

• block_diagonal Construct the diagonal blocks of the interaction matrix

• interaction_matrix Construct the full interaction matrix

• extinction Calculate the extinction cross-section for multiple incident angles

• absorption Calculate the absorption cross-section for multiple incident angles

CD

• averaging Performs full angular averaging for both circular polarisations

• average_spectrum Angular-average spectra for LCP and RCP polarisations

Dispersion

• multiple_incident_field Incident field along multiple axes

• dispersion Angle-resolved cross-sections for multiple directions of incidence

• dispersion_spectrum Angle-resolved spectra for linear or circular polarisations

Utils

• euler Euler rotation matrix

• axis_rotation Rotation matrix about a cartesian axis