■ Topological insulators and negative index with hydro-elastic waves

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Description of the PhD project

Wave control, such as manipulation of their temporal and spatial evolution in a complex environment, has applications in many fields from medical imaging, telecommunications to seismology or solid state physics. Wave propagation has been quantitatively studied for almost two centuries but this research field has undergone remarkable developments during the past twenty years, especially in optics, microwaves or acoustics thanks to the progress of micro-fabrication. The medium plays a major role, and its properties (refractive index, sub-wavelength structure,...) allow for specific wave controls.
An important illustration is the recent development of topological insulators where wave propagation in the bulk is forbidden for symmetry reasons while they keep propagating modes on the edges. These modes are topologically protected as they propagate without losses even when defects are present. Similarly negative index media in which waves have a phase speed and a group speed of opposite sign allow for perfect focusing with sub-wavelength scale.
In this project, we offer to study these fundamental phenomena using a macroscopic bi-dimensional model system. We will use hydro-elastic waves that are obtained covering the air-water interface with an elastic lid. Their dispersion relation is set by the mechanical properties of the membrane and can be modulated at scales smaller than the wavelength. Moreover, they are perfectly adapted for model experiments as it is possible to measure with an excellent spatio-temporal resolution their propagation inside the medium. They are also interesting in a much more applied context as we are now collaborating with Ifremer (French Sea Institute) in order to create lenses and mirrors for water waves in a large test basin (20m x 50m) with the perspective to deploy such structures at sea.
These waves where recently introduced in the lab and we were able to create artificial crystals whose band structures are suitable to realise topological insulators by breaking temporal symmetry. Similarly, their dispersion relation allows to consider propagation regimes with negative index when the membrane is set under compression. The aim of this PhD project is to explore these phenomena at macroscopic scale and study their consequences of the propagation of hydro-elastic waves. Model experiments will shed a new light on fundamental phenomena as well as suggesting tracks for application into oceanic engineering.


Wave propagation, Fluid mechanics, Model experiments

Research unit

UMR7636 Physics & Mechanics of Heterogeneous Media

Description of the research Unit/subunit

PMMH laboratory (Physique et Mécanique des Milieux Hétérogènes - UMR 7636) develops scientific activities around several thematics (fluid mechanics, physics and mechanics, soft matter, interfaces and biophysics). Its activities are mainly experimental with a strong accent on model experiments.
The study of water waves has been introduced in the lab by P. Petitjeans and was further developed in PMMH after the recruitment of A. Eddi as CNRS researcher in 2013. With M. Fermigier, they try to shed a new light on the fundamental aspects of water wave propagation. They introduced several non-invasive real-time in-situ measurement techniques for water waves in order to monitor wave propagation in extended 2D fields. They develop new strategies to direct and mould wave propagation by tuning the water depth, using new temporal controls and more recently introducing hydro-elastic waves in the lab. These aspects are at the heart of the scientific projects led by A. Eddi and M. Fermigier, using internal collaborations (MecaWet team, directed by B. Roman and J. Bico, theoretical approaches with L. Tuckerman) or external collaborations (E. Fort, Institut Langevin, ESPCI).

Name of the supervisor
Marc Fermigier (marc.fermigier@espci.fr)

Name of the co-supervisor
Antonin Eddi (Antonin.Eddi@espci.fr)

3i Aspects of the proposal


This project aims at developing fundamental aspects of wave control using hydro-elastic waves. Nevertheless, it has a strong potential for innovative applications as the scientific team is currently collaborating with Ifremer (French Sea Institute) to probe the efficiency of hydro-elastic waves to manipulate oceanic waves. This application project has received funding from SATT Lutech for a 18 months post-doc in order to build and test an intermediate scale prototype. In this perspective, the development of new laboratory approaches to control hydro-elastic waves is crucial in order to ensure scientific perspectives. This CoFund PhD project will feed the potential applications and help designing large scale devices needed to protect harbours or harvest oceanic wave energy.


This project aims at linking fundamental aspects of wave propagation that have been developed in optics or solid state physics to applied technology. It targets potential applications at large scales that need the integration of concepts introduced in different fields of physics and their implementation in a practical fluid mechanics model experiments. The expected results will create the building blocks for larger scale prototypes that will be designed in collaboration with Ifremer. In that sense, this project bridges a gap between fundamental physics and industrial engineering at large scales.

International mobility

The team is currently collaborating with L. Deike (Assistant Professor, Princeton), who has experience with hydro-elastic waves and oceanic aspects of wave propagation. He was in our lab. last summer (1 month invitation with Chaire Joliot) and we exchange students on a regular basis. In this project, we expect the PhD student to visit (twice 3 months) his group to share knowledge and enforce our long-term collaboration.

Expected Profile of the candidate

Fluid Mechanics
Experimental laboratory work
Image analysis
Team working

Important dates

Call for applications : from February 1st to March 31st 2019
Eligibility check results : Mid April
3i Committee evaluation results : Mid May
Interviews from the shortlisted candidates with the Selection Committee : Late June-Early July
Final results : Mid July

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