TERMS stands for T-matrix for Electromagnetic Radiation with Multiple Scatterers — it is a Fortran program to simulate the near-field and far-field optical properties of collections of particles. TERMS solves rigorously the Maxwell equations via the superposition T-matrix method, where incident and scattered fields are decomposed into a basis of multipolar electric and magnetic spherical waves.

In a multiple-scattering problem the net field exciting a given particle is composed of the incident field plus the scattering contribution from neighbouring particles, restulting in a coupled system of equations to be solved for the total fields. TERMS implements several algorithms to describe the self-consistent electromagnetic interaction between multiple scatterers, and from there compute optical properties such as absorption, scattering, extinction, circular dichroism, as well as near-field intensities and the local degree of optical chirality.

By describing the incident and scattered fields in a basis of spherical waves the T-matrix framework lends itself to analytical formulas for orientation-averaged quantities such as far-field cross-sections and near-field intensities, greatly reducing the computational time needed to simulate particles and systems of particles in random orientation.


The possible computations are divided into three main modes:

  • Far-field quantities (absorption, scattering, extinction, circular dichroism) for multiple wavelengths and angles of incidence, as well as orientation-averages
  • Near-field calculations for multiple wavelengths and incident angles, also computing the local degree of chirality, as well as orientation-averages
  • Stokes parameters and differential scattering cross-sections for multiple incidence or scattering angles

The computational cost scales with the size of the linear system, proportional to the number of particles Np, and to the square of the maximum multipolar order Nmax. On a typical PC we may treat up to  ∼ 500 particles with Nmax = 1, and a dimer with Nmax up to  ∼ 60.

Notable features of TERMS include:

  • Incident plane waves along arbitrary directions, with linear or circular polarisation
  • Built-in calculation of individual T-matrices for coated spheres; import of general T-matrices from other programs (e.g. SMARTIES)
  • Built-in dielectric functions for common materials such as Au, Ag, Al, Cr, Pt, Pd, Si, and Water, or from tabulated values
  • Per-layer absorption in layered spheres
  • Orientation-averaging of far-field cross-sections, as well as linear and circular dichroism
  • Near-field maps of electric and magnetic field components, |E|2, |E|4, 𝒞 ∝ ℑ(E* ⋅ B)
  • Calculation of the global cluster T-matrix
  • “Masking” of specific multipolar orders
  • Calculation of Stokes parameters, phase matrix, differential scattering
  • Plain text or HDF5 I/O format
  • Possible compilation in quad-precision

System requirements

  • Fortran 90 compiler
  • Cmake
  • (optional) HDF5 library
  • (optional) LAPACK

The electromagnetic field is expanded in the basis of vector spherical waves, with the Bessel/Hankel functions computed using TOMS644 library (source included in TERMS). Determining the collective scattering amounts to either solving or inverting a large linear system, which is done using LAPACK. All the relevant LAPACK routines are included in TERMS, but it is recommended to link with your system installed BLAS/LAPACK at compilation stage, because it can enable multi-threading during runtime.
Results are output in plain text files, or, alternatively, in HDF5 data format, which requires suitable hdf5 libraries to be available on your system.


We recommend using the cross platform compilation tool cmake, to resolve all dependencies for your system. From within the build/ directory, type

> cmake ..
> make

to produce the executable terms. Note: if Cmake doesn’t find hdf5 (or another library path) by default, you may need to export it explicitly beforehand. For example on MacOS, the following has proved useful:

# brew install hdf5
export HDF5_ROOT=/usr/local/Cellar/hdf5/1.12.0_3/

Alternatively, a minimal build script is available in the build/ directory; the program can be compiled by executing bash buildTERMS.sh from a Linux terminal with bash. Edit ‘buildTERMS.sh’ to specify a compiler other than GFortran.

Downloading the code

We recommend downloading the latest release here [terms_code_1.0.0(.zip|.tar)]. You can also browse/clone/fork the entire repository, but note that it contains many files used to generate the website, which are not relevant for using TERMS.

The input file

When running the stand-alone executable, main input parameters are read from a plain text input file (line by line and from left to right). Each line is interpreted as a sentence and split into space-separated words. The first (left-most) word is interpreted as a keyword, and the subsequent words as arguments for that keyword. In each sentence, text from the first word starting with the hash character (#) is interpreted as a human-readable comment and thus ignored by the program. All the supported keywords and corresponding arguments are documented on this page. The order of keywords generally doesn’t matter, with just two exceptions: ModeAndScheme must be the first keyword, and Scatterers must be the last. Two examples of input files are provided in the /test directory.

Citing TERMS

If you use TERMS, please cite the following user guide, as well as other publications listed below if relevant:


Schebarchov, D.; Fazel-Najafabadi, A.; Le Ru, E. C.; Auguié, B. Multiple Scattering of Light in Nanoparticle Assemblies: User Guide for the Terms Program. Journal of Quantitative Spectroscopy and Radiative Transfer 2022, 108131. https://doi.org/https://doi.org/10.1016/j.jqsrt.2022.108131.
Schebarchov, D.; Fazel-Najafabadi, A.; Le Ru, E. C.; Auguié, B. TERMS Website; 2021. https://doi.org/10.5281/zenodo.5703291.
Somerville, W. R. C.; Auguié, B.; Le Ru, E. C. SMARTIES: User-Friendly Codes for Fast and Accurate Calculations of Light Scattering by Spheroids. J. Quant. Spectrosc. Ra. 2016, 174, 39–55. https://doi.org/10.1016/j.jqsrt.2016.01.005.
Schebarchov, D.; Le Ru, E. C.; Grand, J.; Auguié, B. Mind the Gap: Testing the Rayleigh Hypothesis in T-Matrix Calculations with Adjacent Spheroids. Optics express 2019, 27 (24), 35750–35760. https://doi.org/10.1364/OE.27.035750.
Lee, S.; Hwang, H.; Lee, W.; Schebarchov, D.; Wy, Y.; Grand, J.; Augui’e, B.; Wi, D. H.; Cort’es, E.; Han, S. W. Core–Shell Bimetallic Nanoparticle Trimers for Efficient Light-to-Chemical Energy Conversion. ACS Energy Letters 2020, 5 (12), 3881–3890. https://doi.org/10.1021/acsenergylett.0c02110.
Fazel-Najafabadi, A.; Schuster, S.; Auguié, B. Orientation Averaging of Optical Chirality Near Nanoparticles and Aggregates. Physical Review B 2021, 103 (11), 115405. https://doi.org/10.1103/PhysRevB.103.115405.
Fazel-Najafabadi, A.; Auguié, B. Orientation Dependence of Optical Activity in Light Scattering by Nanoparticle Clusters. Mater. Adv. 2022, –. https://doi.org/10.1039/D1MA00869B.
Fazel-Najafabadi, A.; Auguié, B. Orientation-Averaged Light Scattering by Nanoparticle Clusters: Far-Field and Near-Field Benchmarks of Numerical Cubature Methods, 2022.