**DIOGENeS**

DIscOntinuous GalErkin Nano Solver

Since 2012, the team is developing a software suite for the numerical simulation of light interaction with nanometer scale structures with applications to nanophotonics and nanoplasmonics.

In version V1.0 of this tool, the only component is a solver for the system of time-domain Maxwell equations in 3d coupled to local dispersion models.

This solver is based on a discontinuous Galerkin (DG) method formulated on a fully unstructured tetrahedral mesh or a hybrid structured/unstructured (cubic/tetrahedral) mesh.

Features of version V1.0:

- Time-domain Maxwell equations in mixed form
- Drude, Drude-Lorentz and generalized dispersion models
- Linear isotropic media
- Affine and curvilinear tetrahedral mesh
- Nodal DG schemes based on centered or upwind numerical fluxes
- Arbitrary high order nodal (Lagrange) interpolation of the field components within a mesh cell
- Explicit time-stepping schemes: 2nd and 4th order leap-frog, and optimized low storage Runge-Kutta schemes
- Silver-Muller absorbing boundary condition and PML

The software is not widely distributed currently. We are before all interested in setting up collaborations with potential users in order to improve the capabilities of this modeling tool for complex problems of practical interest relevant to nanophotonics and nanoplasmonics.
We plan to distribute freely a light version of the software by mid-2015.

Ongoing studies for version V1.1:

- Hydrodynamic Drude model for non-local dispersion effects
- DG formulation with local definition of the approximation order
- Linear anisotropic media
- New component dedicated to the frequency-domain Maxwell equations in mixed form

**Participants/contributors**

**Related publications**

S. Descombes, C. Durochat, S. Lanteri, L. Moya, C. Scheid and J. Viquerat

Recent advances on a DGTD method for time-domain electromagnetics

Photonics and Nanostructures - Fundamentals and Applications, Vol. 11, No. 4, pp. 291-302 (2013)

R. Léger, J. Viquerat, C. Durochat, C. Scheid and S. Lanteri

A parallel non-conforming multi-element DGTD method for the simulation of electromagnetic wave interaction with metallic nanoparticles

J. Comput. Appl. Math., Vol. 270, pp. 330–342 (2014)

J. Viquerat, M. Klemm, C. Scheid and S. Lanteri

Theoretical and numerical analysis of local dispersion models coupled to a discontinuous Galerkin time-domain method for Maxwell's equations

INRIA Research Report RR-8298

**Sample of results**

L-shaped waveguide formed of 50 nm diameter Au spheres in vacuum. The selected test problem involves an L-shaped waveguide inspired by [K.-Y. Jung and F. L. Teixeira and R. M. Reano, J. Lightwave Technol., Vol. 25, No. 9 (2007)] and [F. L. Teixeira, IEEE Trans. Antennas and Propag., Vol. 56, No. 8 (2008)]. This L-shaped waveguide is formed of seven 50 nm diameter Au spheres in vacuum, with a 75 nm center-to-center spacing while the whole computational domain consists of a 550 nm x 750 nm x 400 nm parallelepipedic domain. A Silver-Müller absorbing boundary condition is applied on the surface of this parallelepipedic domain. When excited by an optical regime source, the interest of this setting is the sub-wavelength energy guiding, from sphere to sphere, due to the surface plasmons coupling with each other. It follows that the geometry of the spheres should be correctly approximated in order to avoid non-physical energy concentration phenomena in spurious wedges of the mesh. Moreover, the vicinity of the spheres should be accurately resolved in order to capture the sub-wavelength phenomena of interest. Finally, the physical time window of the computation should be long enough for the phenomenon to settle.

This test problem has been simulated using a DGTD-P2 method applied on a fully tetrahedral mesh and a DGTD-P2Q2 method applied on a non-conforming cubic-tetrahedral mesh.

Scattering of a 20 nanometer radius gold nanosphere by a plane wave (the gold properties are described by a Drude dispersion model). Modulus of the electric field in the frequency domain: Mie solution (left figure) and DGTD-P2 solution (middle figure). Right figure: 1D plot of the electric field modulus for various orders of approximation (PhD thesis of Jonathan Viquerat).

INRIA, NACHOS project-team

2004 Route des Lucioles, B.P. 93

06902 Sophia Antipolis Cedex, France

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