Theory of Waves (TDO)

Example of diffuse (left) and localized (right) modes in a correlated disordered medium

Speckle pattern in a strongly scattering medium generated numerically

Disordered hyperuniform pattern of points. When dressed with material scatterers, this ensemble has remarkable optical properties (transparency, absorption, localisation).

Leader

Arthur GOETSCHY

Tel.: +33 (0)1 80 96 39 46

Co-leader

Romain PIERRAT

Tel.: +33 (0)1 80 96 30 70

Permanent staff

Rémi CARMINATI

Tel.: +33 (0)1 80 96 30 72

Marcel FILOCHE

Tel.: +33 (0)1 80 96 30 82

Arthur GOETSCHY

Tel.: +33 (0)1 80 96 39 46

Agnès MAUREL

Tel.: +33 (0)1 80 96 30 71

Pierre MILLIEN

Tel.: +33 (0)1 80 96 30 51

Romain PIERRAT

Tel.: +33 (0)1 80 96 30 70

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News

Floquet scattering of shallow water waves by a vertically oscillating plate Koukouraki, M., P. Petitjeans, A. Maurel, and V. Pagneux Wave Motion 136, 103530 (2025) Abstract: We report on the scattering of a plane wave from a vertically oscillating plate in the low frequency approximation by means of Floquet theory. In the case of a static plate, the scattering coefficients are evaluated via mode matching method for the full two-dimensional linearized water wave problem and are compared with the coefficients obtained from a reduced one-dimensional model in the shallow water approximation. The main part of the analysis is the extension of this 1D shallow water approximation to the case of a vertically oscillating plate, where time modulation is only encapsulated in the blockage coefficient. We show that the incident wave is scattered into Floquet sidebands and extract the scattering coefficients for each harmonic using a Floquet scattering formalism. Finally, considering a slowly oscillating plate, we propose a quasistatic approximation which appears to be particularly accurate.
Spectral width of maximum deposition eigenchannels in diffusive media Mcintosh, R. E., A. Goetschy, N. Bender, A. Yamilov, C. W. Hsu, H. Yllmaz, and H. Cao Physical Review B 111, no. 14 (2025) Abstract: The maximum deposition eigenchannel provides the largest possible power delivery to a target region inside a diffusive medium by optimizing the incident wavefront of a monochromatic beam. It originates from constructive interference of scattered waves, which is frequency sensitive. We investigate the spectral width of the maximum deposition eigenchannels over a range of target depths using numerical simulations of a 2D diffusive system. Compared to tight focusing into the system, power deposition to an extended region is more sensitive to frequency detuning. The spectral width of enhanced delivery to a large target displays a rather weak, nonmonotonic variation with target depth, in contrast to a sharp drop of focusing bandwidth with depth. While the maximum enhancement of power deposited within a diffusive system can exceed that of power transmitted through it, this comes at the cost of a narrower spectral width. We investigate the narrower deposition width in terms of the constructive interference of transmission eigenchannels within the target. We further observe that the spatial field distribution inside the target region decorrelates more slowly with spectral detuning than the power decay of the maximum deposition eigenchannel. Additionally, absorption increases the spectral width of deposition eigenchannels, but the depth dependence remains qualitatively identical to that without absorption. These findings hold for any diffusive waves, including electromagnetic waves, acoustic waves, pressure waves, mesoscopic electrons, and cold atoms.
Regular sloshing modes in irregular cavities using metabathymetry Anglart, A., A. Maurel, P. Petitjeans, and V. Pagneux Applied Physics Letters 125, no. 21 (2024) Abstract: We present a comprehensive investigation, combining numerical simulations and experimental measurements, into the manipulation of water waves and resonance characteristics within closed cavities utilizing anisotropic metamaterials. We engineer the anisotropic media with subwavelength-scale layered bathymetry through the application of coordinate transformation theory and the homogenization technique to a fully three-dimensional linear water wave problem. Experimental and numerical analyses of deformed cavities employing anisotropic metamaterial bathymetry demonstrate regular sloshing mode patterns and eigenfrequencies akin to those observed in rectangular reference cavities with flat bathymetry. Our study underscores the potential of water wave metamaterials for establishing robust anisotropic metabathymetry for the precise control of sloshing modes.
Experimental demonstration of negative refraction of water waves using metamaterials with hyperbolic dispersion Euvé, L.-P., K. Pham, P. Petitjeans, V. Pagneux, and A. Maurel Physical Review Fluids 9, no. 11 (2024)

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Presentation of the thematics

Our theoretical activities (modeling, analytical and statistical approaches, numerical simulations) aim to understand the properties of waves (optical, acoustic, electronic) in their interactions with matter and their propagation. These activities cover three major themes: the study of inherently complex systems (biological tissues, disordered semiconductors, multimode fibers, chaotic cavities, networks); the control of material complexity (correlated disorder, local resonances, time-dependent media); and wave control (spatial, spectral for classical waves, state nature for quantum waves).

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Theses, Scientific notes, Lecture notes

Active collaborations

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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Theory of Waves (TDO)

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