Théorie des ondes (TDO)

Exemple de mode diffus (gauche) et localisé (droit) dans un milieu désordonné corrélé

Figure de speckle au sein d'un milieu désordonné générée numériquement

Réseau désordonné hyperuniforme de points. Une fois habillé par des diffuseurs matériels, cet ensemble présente des propriétés optiques remarquables (transparence, absorption, localisation).

Responsable

Arthur GOETSCHY

Tél. : 01 80 96 39 46

Co-responsable

Romain PIERRAT

Tél. : 01 80 96 30 70

Membres permanents

Rémi CARMINATI

Tél. : 01 80 96 30 72

Marcel FILOCHE

Tél. : 01 80 96 30 82

Arthur GOETSCHY

Tél. : 01 80 96 39 46

Agnès MAUREL

Tél. : 01 80 96 30 71

Pierre MILLIEN

Tél. : 01 80 96 30 51

Romain PIERRAT

Tél. : 01 80 96 30 70

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Actualités

Localization structure of electronic states in the quantum Hall effect Seye, A., and M. Filoche Physical Review B 112, no. 14 (2025) Résumé: We investigate the localization of electronic states in the integer quantum Hall effect using a magnetic localization landscape (MLL) approach. By studying a continuum Schrödinger model with disordered electrostatic potential, we demonstrate that the MLL, defined via a modified landscape function incorporating magnetic effects, captures key features of quantum state localization. The MLL effective potential reveals the spatial confinement regions and provides predictions of eigenstate energies, particularly in regimes where traditional semiclassical approximations break down. Numerical simulations show that below a critical energy, states localize around minima of the effective potential, while above it they cluster around maxima—with edge effects becoming significant near boundaries. Bridging the gap between semiclassical intuition and full quantum models, the MLL offers a robust framework to understand transport and localization in disordered quantum Hall systems and extends the applicability of landscape theory to magnetic systems.
Radiant Field Theory: A Transport Approach to Shaped Wave Transmission through Disordered Media Gaspard, D., and A. Goetschy Physical Review Letters 135, no. 3, 033804 (2025) Résumé: We present a field-theoretic framework to characterize the distribution of transmission eigenvalues for coherent wave propagation through disordered media. The central outcome is a transport equation for a matrix-valued radiance, analogous to the classical radiative transport equation but capable of capturing coherent effects encoded in the transmission matrix. Unlike the Dorokhov-Mello-Pereyra-Kumar (DMPK) theory, our approach does not rely on the isotropy hypothesis, which presumes uniform angular scattering by material slices. As a result, it remains valid beyond the diffusive regime, accurately describing the transmission eigenvalue distribution in the quasiballistic regime as well. Moreover, the framework is more versatile than the DMPK theory, enabling straightforward incorporation of experimental realities such as absorption and incomplete channel control. These factors are frequently encountered in wave experiments on complex media but have lacked an ab initio theoretical treatment until now. We validate our predictions through numerical simulations based on the microscopic wave equation, confirming the accuracy and broad applicability of the theory.
Homogenized models of acoustic metainterfaces made of three-dimensional Helmholtz resonators Tachet, S., K. Pham, and A. Maurel Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences 481, no. 2316 (2025) Résumé: We investigate the behaviour of metainterfaces composed of three-dimensional subwavelength Helmholtz resonators (HRs), that are open at both ends and may have distinct neck geometries, using a homogenized model derived from a three-scale asymptotic approach. This model reduces such metainterfaces to homogenized boundary conditions that incorporate a resonant pressure field, providing a continuous representation of the discrete pressure field within the cavities that constitute the metasurface. Notable special cases include mirror-symmetric metainterfaces and metasurfaces that operate solely in reflection. The model, developed in the time domain, is validated and discussed in the harmonic regime through comparisons with direct numerical simulations.
Causality and Instability in Wave Propagation in Random Time-Varying Media Pierrat, R., J. Rocha, and R. Carminati Physical Review Letters 134, no. 23, 233801 (2025) Résumé: We develop a theoretical model to investigate wave propagation in media with random time-varying properties, where temporal fluctuations lead to complex scattering dynamics. Focusing on the ensemble-averaged field, we derive an exact expression for the average Green's function in the presence of finite temporal disorder, and extend the analysis to the thermodynamic limit. In contrast to spatial disorder, causality prevents recurrent scattering, allowing us to achieve a nonperturbative solution. We introduce an effective medium description providing a simple analysis of the propagation regimes. Our findings offer new insights into wave dynamics in temporally disordered media, with potential applications in time-varying metamaterials, dynamic sensing, and imaging in turbulent or chaotic environments.

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Présentation du thème

Nos activités théoriques (modélisation, approches analytiques et statistiques, simulations numériques) visent à comprendre les propriétés des ondes (optiques, acoustiques, électroniques) dans leurs interactions avec la matière et leur propagation. Ces activités couvrent 3 grandes thématiques : l’étude de systèmes complexes par nature (tissus biologiques, semi-conducteurs désordonnés, fibres multi-modes, cavités chaotiques, réseaux) ; le contrôle de la complexité des matériaux (désordre corrélé, résonance locales, milieux dépendant du temps) ; et le contrôle des ondes (spatial, spectral pour les ondes classiques, nature de l’état pour les ondes quantiques).

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Thèses, Notes scientifiques, Cours

Collaborations actives

Habib Ammari, Department of Mathematics, ETH Zurich
Geoffroy Aubry, Institut de Physique de Nice
Jean-Philippe Banon, Laboratoire Charles Fabry, Institut d’Optique Graduate School
Élie Bretin, Pôle de Mathématiques, INSA Lyon
Yaron Bromberg, Complex Photonics Lab, The Hebrew University of Jerusalem
CEA DAM
Hui Cao, Hui Cao Research Laboratory, Yale University
Nicolas Cherroret, Complex Quantum Systems, Laboratoire Kastler Brossel
Hilton de Aguiar, Optical imaging in biological and complex media, Laboratoire Kastler Brossel
Aristide Dogariu, Photonics Diagnostics of Random Media, University of Central Florida
Sylvain Gigan, Optical imaging in biological and complex media, Laboratoire Kastler Brossel
Wade Hsu, Optics in Complex Systems, USC
Ori Katz, Advanced Imaging Lab, The Hebrew University of Jerusalem
Fabrice Mortessagne, Institut de Physique de Nice
Sushil Mujumdar Nano-Optics & Mesoscopic Optics Laboratory, TIFR

Vincent Pagneux, LAUM, Le Mans
Philippe Petitjeans, PMMH, ESPCI Paris - PSL
Kim Pham, LMI, ENSTA Paris
Stefan Rotter, Nonlinear dynamics & Complex scattering, Vienna University of Technology
L’Oréal
Saint-Gobain Recherche
Riccardo Sapienza, Complex Nanophotonics, King’s College London
Frank Scheffold, Soft Matter Photonics, University of Fribourg
John Schotland, Department of Mathematics, Yale University
Laurent Seppecher, École Centrale de Lyon
Boris Shapiro, Technion
Simons collaboration on Localization of Waves
Ingve Simonsen, NTNU, Trondheim
Douglas Stone, Department of Applied Physics, Yale University
Nicolas Treps, Quantum Optics group, Laboratoire Kastler Brossel
Damien Vandembroucq, PMMH, ESPCI Paris - PSL
Silvia Vignolini, Max Planck Institute of colloids and interfaces, Potsdam
Kevin Vynck, Institut Lumière Matière, Lyon
Alexey Yamilov, METIS group, MST
Hasan Yılmaz, Bilkent University

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