# Home Page

### Welcome to the Nachos team homepage!

Nachos is a joint project-team between Inria, CNRS and the University of Nice/Sophia Antipolis

via the J.A. Dieudonné Mathematics Laboratory (UMR 7351).

## Job openings

Master internship

Numerical modeling of THz photoconductive antennas in a Discontinuous Galerkin Time-Domain framework

Duration: 6 months

Research and development engineer (fixed-term)

Exascale enabled finite element solvers for nanophotonics

Duration: 16 months

Research and development engineer (fixed-term)

High order finite element solvers for the design of nanophotonic devices

Duration: 12 months

## News - February 2019

Paper entitled "Optimization and uncertainty quantification of gradient index

metasurfaces" by N. Schmitt, N. Georg, G. Brière, D. Loukrezis, S. Héron, S. Lanteri, C. Klitis, M. Sorel, U. Römer, H. De Gersem, S. Vézian and P. Genevet

Opt. Mat. Express., Vol. 9, No. 2, pp. 892-910 (2019)

In this multidisciplinary work involving researchers in physics and applied mathematics, we present a computational methodology to optimize metasurface designs. We complement this computational methodology by quantifying the impact of fabrication uncertainties on the experimentally characterized components.

(a) Illustrative schematic of the angular deflection property of a phase gradient metasurface.

(b)-(c) The metasurface-based device works essentially as conventional echelette blazed grating, by replacing the periodic echelette with a subwavelength array of nanoridges.

(d) Typical broadband response of the transmission efficiency for an optimized metasurface obtained using two different electromagnetic simulation solvers, the Discontinuous Galerkin Time-Domain solver (DGTD) solver and the Rigorous Coupled Wave Analysis (RCWA) solver in orange dashed.

## News - November 2018

Paper entitled "The Multiscale Hybrid-Mixed method for the Maxwell equations in heterogeneous media" by S. Lanteri, D. Paredes, C. Scheid and F. Valentin

SIAM J. Multiscale Model. Simul., Vol. 16, No. 4, pp.1648–1683 (2018)

Simulating wave propagation in three-dimensional highly heterogeneous media or heterogeneous media with complex interfaces remains a challenging task. In many modern applications, this phenomena is associated with high frequency responses when compared to the size of the domain. Classical numerical methods, like finite difference or finite element methods, must use a very fine mesh to obtain high quality solutions, which results in huge computational resource requirements. The Multiscale Hybrid-Mixed (MHM) method implements the “divide-and-conquer” philosophy to obtain accurate solutions on coarse meshes. Based on a classical hybridization procedure, the MHM method yields a staggered algorithm , which is organized around two main ingredients: (1) a set of multiscale basis functions, which are constructed as the solution of local problems defined in each macro cell of the coarse mesh; (2) a global problem defined on the skeleton of the coarse mesh that gives rise to a classical finite element formulation leveraging the multiscale basis functions. In the context of electromagnetic wave propagation modelled by the system of time-domain Maxwell equations, the local problems are solved using a classical DGTD method.

Nanowaveguide problem: contour lines of

the amplitude of the electric field. Left: DGTD method with 5898,824 Dof - Middle: DGTD methid withg 4,608 DoF - Right: MHM-DGTD method with 9,216 DoF

## News - October 2018

Welcome to Théophile Chaumont-Frelet who has been awarded a Junior research scientist position in the team!

Kick-off of the EPEEC (European joint Effort toward a Highly Productive Programming Environment for Heterogeneous Exascale Computing) H2020 project

Welcome to Mahmoud Elsawy who joined the team as a postodtcoral fellow!

Paper entitled "Simulation of three-dimensional nanoscale light interaction with spatially dispersive metals using a high order curvilinear DGTD method" by N. Schmitt, C. Scheid, J. Viquerat and S. Lanteri

J. Comput. Phys., Vol. 373, pp. 210–229 (2018)

## News - September 2018

Congratulations to Nikolaï Schmitt who defended his doctoral thesis on September 27!

Paper entitled "Fitting experimental dispersion data with a simulated annealing method for nano-optics applications" by J. Viquerat

J. of Nanophotonics, Vol. 12, No. 3, 036014 (2018)

## News - March 2018

Kick-off meeting of the Math-Amsud PHOTOM - Photovoltaic Solar Devices

in Multiscale Computational Simulations - project

March 13-15, LNCC, Petrópolis, Brazil

New high order Hybridized Discontinuous Solver (HDG) for frequency-domain plasmonics in 3D - Work done in the context of the postdoctoral project of Mostafa Javadzadeh Moghtader

Scattering of a plane wave by a 50 nm gold nanosphere: magnitude of

**E**field at frequencies 1070 THz (left), 1185 THz (middle) and 1300 THz (right)

Scattering of a plane wave by a 50 nm gold nanosphere: scattering (left) and absorption (right) cross sections for calculations based on a HDG method with quadratic interpolation of the EM field components

## News - February 2018

Congratulations to Fréderic Valentin who has been awarded an Inria International Chair for the period 2018-2022! The research project that he will lead during this period aims at devising innovative multiscale numerical algorithms for the simulation of wave-matter interaction at the nanoscale. This topic is also at the heart of the Math-Amsud PHOTOM - Photovoltaic Solar Devices

in Multiscale Computational Simulations - project that has started in Januray 2018 for a duration of 2 years, and which involves researchers from Brazil, Chile and France.

Papers on reduced-order modeling based on Proper Orthogonal Decomposition for time-domain electromagnetics in the context of a collaborative work with researchers from UESTC, Chengdu, China.

K. Li, T.-Z. Huang, L. Li and S. Lanteri

A reduced-order DG formulation based on POD method for the time-domain Maxwell’s equations in dispersive media

J. Comput. Appl. Math., Vol. 336, pp. 249-266 (2018)

K. Li, T.-Z. Huang, L. Li, S. Lanteri, L. Xu and B. Li

A reduced-order discontinuous Galerkin method based on POD for electromagnetic simulation

IEEE Trans. Ant. Propag., Vol. 66, No. 1, pp. 242-254 (2018)

## News - May 2017

High order DGTD method based on exponential time integrators for modeling

3D transient multiscale electromagnetic problems

More details - Work done in the context of the PhD project of Hao Wang

H. Wang, L. Xu, B. Li, S. Descombes and S. Lanteri

A new family of exponential-based high order DGTD methods for modelling 3D transient multiscale electromagnetic problems

IEEE Trans. Ant. Propag., Vol. 65, No. 11, pp. 5960-5974 (2017)

## News - February 2017

Paper entitled "Analysis of a generalized dispersive model coupled to a DGTD method with application to nanophotonics" by S. Lanteri, C. Scheid and J. Viquerat

SIAM J. Sci. Comp., Vol. 39, No. 3, pp. A831–A859 (2017)

Simulation of light trapping in thin-film solar cells with textured layers

More details - Work done in the context of the PhD project of Alexis Gobé

## News - January 2017

First review meeting and workshop of the HPC4E project

January 30-February 2, 2017 - Inria Sophia Antipolis-Méditerranée

New DGTD solver for the 3D time-domain Maxwell equations coupled to a linearized non-local Drude model

More details - Work done in the context of the PhD project of Nikolai Schmitt