# AD Capabilities of the ADDA code for nanophotonics

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Maxim A. Yurkin,¹,* Dmitry A. Smunev,² Stefania A. Glukhova,³ Alexander A. Kichigin,⁴
Alexander E. Moskalensky,⁵,⁶ Konstantin G. Inzhevatkin,⁷ Danil V. Shershnev⁵,⁶

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¹Univ Rouen, INSA Rouen, CNRS, CORIA UMR 6614, France

⁴IMN & CENEM, FAU Erlangen-Nürnberg, Erlangen, Germany

⁶Novosibirsk State University, Russia

²Dartrace, Warsaw, Poland ³Victoria University of Wellington, New Zealand

⁵Sirius university of science and technology, Sochi, Russia

⁷JSC Upstream Solutions, Novosibirsk, Russia *e-mail: yurkin@gmail.com

## Discrete dipole approximation (DDA)

* Volume-integral equation in frequency domain (Lippmann-Schwinger)

* Discretization on a **regular cubic or cuboid grid**

* Analogous to a set of interacting dipoles

* Non-magnetic materials

## Arbitrary particle shape and composition

* 16 predefined particle shapes, any axisymmetric shape

* Arbitrary 3D geometry from file (including DDSCAT format)

* Automatic grid refinement

* Up to 255 domains

* Anisotropic refractive index (diagonal tensor)

* Spherical granules can be automatically added

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## Various scattering geometry/environment

* Non-absorbing homogeneous host medium or absorbing one (beta)

* Particle near a plane substrate (fast & robust)

* Arbitrary orientation or orientation averaging

* Incident beam: plane wave, Gaussian or Bessel beam, or any read from file

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## Wide variety of calculated quantities

* Scattering, absorption, and extinction cross sections

* Asymmetry parameter (or vector)

* Angle-resolved amplitude and Mueller matrices

* Radiation forces – total or for each voxel

* Electric fields in and near the particle

* Complete T-matrix (beta)

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## Quasi-classical simulations

* Emission (decay-rate) enhancement (LDOS, fluorescence, Raman scattering)

* Electron energy-loss spectroscopy (EELS) and cathodoluminescence, including Cherenkov radiation (beta: near substrate)

* Near-filed radiative heat transfer and Casimir forces (beta)

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## Parallel implementation

* MPI-based parallelization of a single DDA simulation

* Demonstrated computational grid of 32 Gvox (with 28 TB RAM)

* Also sequential execution and multi-core processors

* OpenCL version (for GPU)

## Fast and accurate

* Computational time is linear in number of voxels

* Optimized FFT-based 3D-convolution algorithm

* Efficient Krylov-subspace iterative solvers

* Modern DDA formulations: FCD and IGT – critical for high-contrast dielectrics

* Rectangular-cuboid voxels for highly oblate or prolate particles

* A special sparse mode is efficient for very porous particles

* Optimized calculations for many orientations (beta)

* Extremely efficient scan over refractive indices (beta)

## Examples

* Predictive design (color optimization) of colloidal photonic crystals
  Bleyer et al., Adv. Opt. Mater. 2403279 (2025)

$x_{PP} = 245$ nm

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Int.

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Opt.

$x_{PP} = 260$ nm

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Int.

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Opt.

$x_{PP} = 279$ nm

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Int.

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Opt.

* EELS maps of truncated Cu tetrahedra on carbon substrate
  Jeong et al., JACS 10.1021/jacs.5c12614 (2025)

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## Easy to use

* A standalone GUI (with 3D shape visualization)

* Powerful command line interface and internal help system

* A lot of information in wiki pages and manual

* Active discussion group to help users

* Checkpoint system for long simulations

* Highly scriptable with many input and output quantities

* Easy to compile on almost any platform, binaries for Windows

## Fully open-source development

* More than 10 contributors (and increasing)

* Large plans for further development (at issue tracker)

* Several development branches

* New contributors are welcome!

## Reliable

* Tested and trusted by the community (around 800 papers from 34 countries)

* Often compared with other methods

* Automatic testing during the development

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