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The transition matrix method, or T-Matrix method, is one of the most powerful and widely used tools for rigorously computing electromagnetic scattering by single and compounded particles.
Homogeneous axisymmetric shapes (via EBCM and IITM): Spheroids, Cylinders, Chebyshev particles. Arbitrary shapes (via IITM): Prisms

Python module to calculate scattering amplitude and phase matrices of rotationally symmetric particles based on the T-matrix method. Based on the original Fortran T-matrix code by M.I. Mishchenko.
VGF-Scattering-Code is Fortran code for scattering by 3D particles based on the Variational Greens Function.
Python wrapper for Multiple Sphere T-Matrix (MSTM) code for the calculation of extinction spectra of nanoparticle aggregates.
TransitionMatrices.jl
The Julia package `TransitionMatrices.jl` by Zihua Wu implements the classic EBCM method, supporting arbitrary precision and automatic differentiation. To calculate the T-Matrix of various types of scatterers the EBCM and the Invariant Imbedding T-Matrix Method (IITM) is implemented.
Scattering Dynamics
scadyn is a code for scattering dynamics calculations, which utilizes a volume integral equation solution to compute the T-matrices of non-spherical scatterers (T-VIE) .

CosTuuM
An open-source C++-based Python library CosTuuM that can be used to generate infrared absorption and emission coefficients for arbitrary mixtures of spheroidal dust grains that are (partially) aligned with a magnetic field.
TERMS
T-matrix for Electromagnetic Radiation with Multiple Scatterers — a set of Fortran modules/routines and Python scripts for T-matrix-based calculations and analysis of light scattering by clusters of individual scatterers.

Wave Scattering Toolbox
TMATROM is a simple and easy to use reduced order model toolbox for simulating 2D wave propagation, acoustic and electromagnetic waves, wave propagation exterior to one or more scatterers; sound soft/sound hard/ transverse electric (TE)/ transverse magnetic (TM)/ absorbing/ dielectric scatterers; low, medium and high frequencies

SMUTHI
SMUTHI by Amos Egel solves 3D light scattering problems involving one or multiple particles (spheres, spheroids and finite cylinders) inside a planarly layered medium. It is based on the T-matrix method for the individual particles and on the scattering-matrix method for the propagation through the layered medium. For spheroids and finite cylinders, the particles' T-matrices are computed using the NFM-DS package by Adrian Doicu, Thomas Wriedt and Yuri Eremin.

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