Romain Pierrat’s research while affiliated with Langevin Institute, French Institute of Health and Medical Research and other places

We present a statistical study of the transmission and dwell-time matrices in disordered media composed of resonators, focusing on how frequency detuning influences their eigenvalue distributions. Our analysis reveals that the distribution of transmission eigenvalues undergoes a transition from a monomodal to a bimodal profile, and back to monomodal, as the frequency approaches the resonant frequency of the particles. Moreover, the distribution of dwell-time eigenvalues broadens significantly near resonance, with the longest lifetimes exceeding the median by several orders of magnitude. These results are explained by examining how frequency $\omega$ affects the transport mean free path of light, $\ell(\omega)$, and the energy transport velocity, $v_E(\omega)$, which in turn shape the observed distributions. We demonstrate the strong potential of wavefront shaping to enhance both transmission and energy storage in resonant disordered media. In the diffusive regime, where the system thickness L exceeds the mean free path, both transmission and dwell time can be enhanced by a factor $\varpropto L/\ell(\omega) \gg 1$ when using wavefronts associated with the largest eigenvalues instead of plane waves. In the localized regime, the enhancements become $\varpropto Ne^{2L/\xi}$ for transmission and $\varpropto N\xi /L$ for dwell time, where $\xi$ is the localization length and N is the number of controlled scattering channels. Finally, we show that employing high-Q resonators instead of low-Q ones increases energy storage within the medium by a factor of $\varpropto Q/k\ell(\omega)$, in both the diffusive and localized regimes.

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 our analysis to the thermodynamic limit. In contrast to spatial disorder, causality prevents recurrent scattering, allowing us to achieve a non-perturbative solution. We identify two distinct propagation regimes: one where the field oscillates with constant amplitude, and another where it grows exponentially at long times. 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.

Nonlinear disordered media uniquely combine multiple scattering and second-harmonic generation. Here, we investigate the statistical properties of the nonlinear light generated within such media. We report super-Rayleigh statistics of the second-harmonic speckle intensity, and demonstrate that it is caused by the mesoscopic correlations arising in extreme scattering conditions. The measured conductance is the lowest ever observed in an isotropically scattering 3D medium, with applications in broadband second-harmonic generation, wavefront shaping in nonlinear disordered media, and photonic computing.

When a solid metal is struck, its free surface can eject fast and fine particles. Despite the many diagnostics that have been implemented to measure the mass, size, velocity, or temperature of ejecta, these efforts provide only a partial picture of this phenomenon. Ejecta characterization, especially in constrained geometries, is an inherently ill-posed problem. In this context, Photon Doppler Velocimetry (PDV) has been a valuable diagnostic, measuring reliably particles and free surface velocities in the single scattering regime. Here, we present ejecta experiments in gas and how, in this context, PDV allows one to retrieve additional information on the ejecta, i.e., information on the particles’ size. We explain what governs ejecta transport in gas and how it can be simulated. To account for the multiple scattering of light in these ejecta, we use the Radiative Transfer Equation (RTE) that quantitatively describes PDV spectrograms, and their dependence not only on the velocity but also on the size distribution of the ejecta. We remind how spectrograms can be simulated by solving numerically this RTE and we show how to do so on hydrodynamic ejecta simulation results. Finally, we use this complex machinery in different ejecta transport scenarios to simulate the corresponding spectrograms. Comparing these to experimental results, we iteratively constrain the ejecta description at an unprecedented level. This work demonstrates our ability to recover particle size information from what is initially a velocity diagnostic, but more importantly it shows how, using existing simulation of ejecta, we capture through simulation the complexity of experimental spectrograms.

When a solid metal is struck, its free surface can eject fast and fine particles. Despite the many diagnostics that have been implemented to measure the mass, size, velocity or temperature of ejecta, these efforts provide only a partial picture of this phenomenon. Ejecta characterization, especially in constrained geometries, is an inherently ill-posed problem. In this context, Photon Doppler Velocimetry (PDV) has been a valuable diagnostic, measuring reliably particles and free surface velocities in the single scattering regime. Here we present ejecta experiments in gas and how, in this context, PDV allows one to retrieve additional information on the ejecta, i.e. information on the particles' size. We explain what governs ejecta transport in gas and how it can be simulated. To account for the multiple scattering of light in these ejecta, we use the Radiative Transfer Equation (RTE) that quantitatively describes PDV spectrograms, and their dependence on the velocity but also on the size distribution of the ejecta. We remind how spectrograms can be simulated by solving numerically this RTE and we show how to do so on hydrodynamic ejecta simulation results. Finally, we use this complex machinery in different ejecta transport scenarios to simulate the corresponding spectrograms. Comparing these to experimental results, we iteratively constrain the ejecta description at an unprecedented level. This work demonstrates our ability to recover particle size information from what is initially a velocity diagnostic, but more importantly it shows how, using existing simulation of ejecta, we capture through simulation the complexity of experimental spectrograms.

We theoretically study the propagation of light in one-dimensional space- and time-dependent disorder. The disorder is described by a fluctuating permittivity ε(x, t) exhibiting short-range correlations in space and time, without cross correlation between them. Depending on the illumination conditions, we show that the intensity of the average field decays exponentially in space or in time, with characteristic length or time defining the scattering mean-free path ℓ s and the scattering mean-free time τ s . In the weak scattering regime, we provide explicit expressions for ℓ s and τ s , that are checked against rigorous numerical simulations.

Upon impact, the free surface of a solid metal may eject a cloud of fast and fine particles. Photon Doppler Velocimetry (PDV) is one of the optical diagnostics used to characterize these ejecta. Although the technique provides a direct way to estimate the particle velocities in the single scattering regime, it has been shown that multiple scattering cannot be neglected in real ejecta. Here, we derive a model for PDV measurements starting from the first principles of wave scattering. We establish rigorously the relationship between the specific intensity and the measured signal, as well as the Radiative Transport Equation (RTE) that describes the evolution of the specific intensity upon scattering and absorption in dynamic ejecta, including the effects of inelastic scattering and inhomogeneities in the optical properties. We also establish rigorously the connection between the Monte Carlo scheme used for numerical simulations and the solution to the RTE. Using numerical simulations, we demonstrate the crucial contribution of multiple scattering to PDV spectrograms as well as the effect of statistical inhomogeneities in particle size distribution. These results could substantially impact the analysis of ejecta by PDV.

The optics of correlated disordered media is a conceptually rich research topic emerging at the interface between the physics of waves in complex media and nanophotonics. Inspired by photonic structures in nature and enabled by advances in nanofabrication processes, recent investigations have unveiled how the design of structural correlations down to the subwavelength scale could be exploited to control the scattering, transport, and localization of light in matter. From optical transparency to superdiffusive light transport to photonic gaps, the optics of correlated disordered media challenges our physical intuition and offers new perspectives for applications. This review examines the theoretical foundations, state-of-the-art experimental techniques, and major achievements in the study of light interaction with correlated disorder, covering a wide range of systems: from short-range correlated photonic liquids to Lévy glasses containing fractal heterogeneities to hyperuniform disordered photonic materials. The mechanisms underlying light scattering and transport phenomena are elucidated on the basis of rigorous theoretical arguments. Ongoing research on mesoscopic phenomena such as transport phase transitions and speckle statistics and the current development of disorder engineering for applications such as light-energy management and visual appearance design are overviewed. Finally, special efforts are made to identify the main theoretical and experimental challenges to address in the near future.

We report experimental and theoretical investigations of photon diffusion in a second-order-nonlinear disordered medium under conditions of strong nonlinearity. Experimentally, photons at the fundamental wavelength (λ=1064nm) are launched into the structure in the form of a cylindrical pellet, and the second-harmonic (λ=532nm) photons are temporally analyzed in transmission. For comparison, separate experiments are carried out with incident green light at λ=532nm. We observe that the second-harmonic light peaks earlier compared to the incident green photons. Next, the sideways spatial scattering of the fundamental as well as second-harmonic photons is recorded. The spatial diffusion profiles of second-harmonic photons are seen to peak deeper inside the medium in comparison to both the fundamental and incident green photons. In order to give more physical insights into the experimental results, a theoretical model is derived from first principles. It is based on the coupling of transport equations. Solved numerically using a Monte Carlo algorithm and experimentally estimated transport parameters at both wavelengths, it shows excellent semiquantitative agreement with the experiments for both fundamental and second-harmonic light.