Characterization and Exploitation of the Rotational Memory Effect in Multimode Fibers GutiérrezCuevas R., , Goetschy A., Bromberg Y., Pelc G., Ravn Andresen E., Bigot L., Quiquempois Y, Bsaibes M, Sillard P., Bigot M., Katz O., De Rosny J., and Popoff S. M. Physical Review X 14, no. 3, 031046 (2024)
Résumé: In an ideal perfectly straight multimode fiber with a circular core, the symmetry ensures that rotating the input wave front leads to a corresponding rotation of the output wave front. This invariant property, known as the rotational memory effect (RME), remains independent of the typically unknown output profile. The RME thus offers significant potential for imaging and telecommunication applications. However, in reallife fibers, this effect is degraded by intrinsic imperfections and external perturbations, and is challenging to observe because of its acute sensitivity to misalignments and aberrations in the optical setup. Building on a previously established method for precisely estimating fiber transmission properties, we demonstrate an accurate extraction of RME properties. Additionally, we introduce a comprehensive theoretical framework for both qualitative and quantitative analysis, which specifically links the angulardependent correlation of the RME to the core deformation’s geometrical properties and the fiber’s mode characteristics. Our theoretical predictions align well with experimental data and simulations for various amounts of fiber distorsion. Finally, we demonstrate the ability to engineer wave fronts with significantly enhanced correlation across all rotation angles. This work enables accurate characterization of distributed disorder from the fabrication process and facilitates calibrationfree imaging in multimode fibers.
Motsclés: multimode fiber; wavefront shaping; correlation; memory effect; imaging; telecommunications


Delivering broadband light deep inside diffusive media Mcintosh, R., A. Goetschy, N. Bender, A. Yamilov, C. W. Hsu, H. Yılmaz, and H. Cao Nature Photonics (2024)
Résumé: Wavefront shaping enables the targeted delivery of coherent light into randomscattering media, such as biological tissue, by the constructive interference of scattered waves. However, broadband waves have short coherence times, weakening the interference effect. Here we introduce a broadband deposition matrix that identifies a single input wavefront that maximizes the broadband energy delivered to an extended target deep inside a diffusive system. We experimentally demonstrate that longrange spatial and spectral correlations result in sixfold energy enhancement for targets containing 1,700 speckle grains and located at a depth of up to ten transport mean free paths, even when the coherence time is an order of magnitude shorter than the diffusion dwell time of light in the scattering sample. In the broadband (fast decoherence) limit, enhancement of energy delivery to extended targets becomes nearly independent of the target depth and dissipation. Our experiments, numerical simulations and analytic theory establish the fundamental limit for broadband energy delivery deep into a diffusive system, which has important consequences for practical applications.


Coherent backscattering of entangled photon pairs Safadi, M., O. Lib, H. C. Lin, C. W. Hsu, A. Goetschy, and Y. Bromberg Nature Physics (2023)
Résumé: Correlations between entangled photons are a key ingredient for testing fundamental aspects of quantum mechanics and an invaluable resource for quantum technologies. However, scattering from a dynamic medium typically scrambles and averages out such correlations. Here we show that multiply scattered entangled photons reflected from a dynamic complex medium remain partially correlated. In experiments and fullwave simulations we observe enhanced correlations, within an angular range determined by the transport mean free path, which prevail over disorder averaging. Theoretical analysis reveals that this enhancement arises from the interference between scattering trajectories, in which the photons leave the sample and are then virtually reinjected back into it. These paths are the quantum counterpart of the paths that lead to the coherent backscattering of classical light. This work points to opportunities for entanglement transport despite dynamic multiple scattering in complex systems.


Pseudogap and Anderson localization of light in correlated disordered media Monsarrat, R., R. Pierrat, A. Tourin, and A. Goetschy Physical Review Research 4, no. 3 (2022)
Résumé: Among the remarkable scattering properties of correlated disordered materials, the origin of pseudogaps and the formation of localized states are some of the most puzzling features. Fundamental differences between scalar and vector waves in both these aspects make their comprehension even more problematic. Here we present an indepth and comprehensive analysis of the ordertodisorder transition in 2D resonant systems. We show with exact ab initio numerical simulations in finitesize hyperuniform media that localization of 2D vector waves can occur in the presence of correlated disorder, in a regime of moderate density of scatterers. On the contrary, no signature of localization is found for white noise disorder. This is in striking contrast with scalar waves, which localize at high density whatever the amount of correlation. For correlated materials, localization is associated with the formation of pseudogap in the density of states. We develop two complementary models to explain these observations. The first one uses an effective photonic crystaltype framework and the second relies on a diagrammatic treatment of the multiple scattering sequences. We provide explicit theoretical evaluations of the density of states and localization length in good agreement with numerical simulations. In this way, we identify the microscopic processes at the origin of pseudogap formation and clarify the role of the density of states for wave localization in resonant correlated media. The generality of our framework makes possible to apply our predictions for a large variety of scattering systems including dielectric structures with high quality factor, cold atoms, artificial atoms, as well as microwave resonators.


Coherent enhancement of optical remission in diffusive media Bender, N., A. Goetschy, C. W. Hsu, H. Yilmaz, P. J. Palacios, A. Yamilov, and H. Cao Proceedings of the National Academy of Sciences of the United States of America 119, no. 41 (2022)
Résumé: Remitted waves are used for sensing and imaging in diverse diffusive media from the Earth's crust to the human brain. Separating the source and detector increases the penetration depth of light, but the signal strength decreases rapidly, leading to a poor signaltonoise ratio. Here, we show, experimentally and numerically, that wavefront shaping a laser beam incident on a diffusive sample enables an enhancement of remission by an order of magnitude at depths of up to 10 transport mean free paths. We develop a theoretical model which predicts the maximal remission enhancement. Our analysis reveals a significant improvement in the sensitivity of remitted waves to local changes of absorption deep inside diffusive media. This work illustrates the potential of coherent wavefront control for noninvasive diffuse wave imaging applications, such as diffuse optical tomography and functional nearinfrared spectroscopy.


Depthtargeted energy delivery deep inside scattering media Bender, N., A. Yamilov, A. Goetschy, H. Yılmaz, C. W. Hsu, and H. Cao Nature Physics (2022)


Full characterization of the transmission properties of a multiplane light converter Boucher, P., A. Goetschy, G. Sorelli, M. Walschaers, and N. Treps Physical Review Research 3, no. 2 (2021)
Résumé: Multiplane light conversion (MPLC) allows to perform arbitrary transformations on a finite set of spatial modes with no theoretical restriction to the quality of the transformation. Even though the number of shaped modes is in general small, the number of modes transmitted by an MPLC system is extremely large. In this paper, we aim to characterize the transmission properties of a multiplane light converter inside and outside the designmodes subspace. We report the construction of the full transmission matrix of such systems. By performing singular value decompositions, we individuate ways to evaluate their efficiency in performing the design transformation. Moreover, we develop an analytical random matrix model that suggests that in the regime of a large number of shaped modes an MPLC system behaves like a random scattering medium with limited number of controlled channels.


Optimizing Light Storage in Scattering Media with the DwellTime Operator Durand, M., S. M. Popoff, R. Carminati, and A. Goetschy Physical Review Letters 123, no. 24 (2019)
Résumé: © 2019 American Physical Society. We prove that optimal control of light energy storage in disordered media can be reached by wave front shaping. For this purpose, we build an operator for dwell times from the scattering matrix and characterize its full eigenvalue distribution both numerically and analytically in the diffusive regime, where the thickness L of the medium is much larger than the mean free path â.,". We show that the distribution has a finite support with a maximal dwell time larger than the most likely value by a factor (L/â.,")2≫1. This reveals that the highest dwelltime eigenstates deposit more energy than the open channels of the medium. Finally, we show that the dwelltime operator can be used to store energy in resonant targets buried in complex media, without any need for guide stars.


Angular Memory Effect of Transmission Eigenchannels Yllmaz, H., C. W. Hsu, A. Goetschy, S. Bittner, S. Rotter, A. Yamilov, and H. Cao Physical Review Letters 123, no. 20 (2019)
Résumé: © 2019 American Physical Society. The optical memory effect has emerged as a powerful tool for imaging through multiplescattering media; however, the finite angular range of the memory effect limits the field of view. Here, we demonstrate experimentally that selective coupling of incident light into a hightransmission channel increases the angular memoryeffect range. This enhancement is attributed to the robustness of the hightransmission channels against perturbations such as sample tilt or wave front tilt. Our work shows that the hightransmission channels provide an enhanced field of view for memoryeffectbased imaging through diffusive media.


Blind ghost imaging PaniaguaDiaz, A. M., I. Starshynov, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti Optica 6, no. 4, 460464 (2019)
Résumé: © 2019 Optical Society of America. Ghost imaging is an unconventional optical imaging technique that reconstructs the shape of an object by combining the measurement of two signals: one that interacted with the object, but without any spatial information; the other containing spatial information, but that never interacted with the object. Here we demonstrate that ghost imaging can be performed without ever knowing the patterns that illuminate the object, by instead using patterns correlated with them, no matter how weakly. As an experimental proof, we reconstruct the image of an object hidden behind a scattering layer using only the reflected light, which never interacts with the object.


NonGaussian Correlations between Reflected and Transmitted Intensity Patterns Emerging from Opaque Disordered Media Starshynov, I., A. M. PaniaguaDiaz, N. Fayard, A. Goetschy, R. Pierrat, R. Carminati, and J. Bertolotti Physical Review X 8, no. 2 (2018)
Résumé: © 2018 authors. Published by the American Physical Society. The propagation of monochromatic light through a scattering medium produces speckle patterns in reflection and transmission, and the apparent randomness of these patterns prevents direct imaging through thick turbid media. Yet, since elastic multiple scattering is fundamentally a linear and deterministic process, information is not lost but distributed among many degrees of freedom that can be resolved and manipulated. Here, we demonstrate experimentally that the reflected and transmitted speckle patterns are robustly correlated, and we unravel all the complex and unexpected features of this fundamentally nonGaussian and longrange correlation. In particular, we show that it is preserved even for opaque media with thickness much larger than the scattering mean free path, proving that information survives the multiple scattering process and can be recovered. The existence of correlations between the two sides of a scattering medium opens up new possibilities for the control of transmitted light without any feedback from the target side, but using only information gathered from the reflected speckle.


Mutual Information between Reflected and Transmitted Speckle Images Fayard, N., A. Goetschy, R. Pierrat, and R. Carminati Physical Review Letters 120, no. 7 (2018)
Résumé: © 2018 American Physical Society. We study theoretically the mutual information between reflected and transmitted speckle patterns produced by wave scattering from disordered media. The mutual information between the two speckle images recorded on an array of N detection points (pixels) takes the form of longrange intensity correlation loops that we evaluate explicitly as a function of the disorder strength and the Thouless number g. Our analysis, supported by extensive numerical simulations, reveals a competing effect of crosssample and surface spatial correlations. An optimal distance between pixels is proven to exist that enhances the mutual information by a factor Ng compared to the singlepixel scenario.


Correlationenhanced control of wave focusing in disordered media Hsu, C. W., S. F. Liew, A. Goetschy, H. Cao, and A. Douglas Stone Nature Physics 13, no. 5, 497502 (2017)
Résumé: A fundamental challenge in physics is controlling the propagation of waves in disordered media despite strong scattering from inhomogeneities. Spatial light modulators enable one to synthesize (shape) the incident wavefront, optimizing the multipath interference to achieve a specific behaviour such as focusing light to a target region. However, the extent of achievable control is not known when the target region is much larger than the wavelength and contains many speckles. Here we show that for targets containing more than g speckles, where g is the dimensionless conductance, the extent of transmission control is substantially enhanced by the longrange mesoscopic correlations among the speckles. Using a filtered random matrix ensemble appropriate for coherent diffusion in open geometries, we predict the full distributions of transmission eigenvalues as well as universal scaling laws for statistical properties, in excellent agreement with our experiment. This work provides a general framework for describing wavefrontshaping experiments in disordered systems.


LightMediated Cascaded Locking of Multiple NanoOptomechanical Oscillators GilSantos, E., M. Labousse, C. Baker, A. Goetschy, W. Hease, C. Gomez, A. Lemaître, G. Leo, C. Ciuti, and I. Favero Physical Review Letters 118, no. 6 (2017)
Résumé: © 2017 American Physical Society.Collective phenomena emerging from nonlinear interactions between multiple oscillators, such as synchronization and frequency locking, find applications in a wide variety of fields. Optomechanical resonators, which are intrinsically nonlinear, combine the scientific assets of mechanical devices with the possibility of long distance controlled interactions enabled by traveling light. Here we demonstrate lightmediated frequency locking of three distant nanooptomechanical oscillators positioned in a cascaded configuration. The oscillators, integrated on a chip along a common coupling waveguide, are optically driven with a single laser and oscillate at gigahertz frequency. Despite an initial mechanical frequency disorder of hundreds of kilohertz, the guided light locks them all with a clear transition in the optical output. The experimental results are described by Langevin equations, paving the way to scalable cascaded optomechanical configurations.


Coherent Control of Photocurrent in a Strongly Scattering Photoelectrochemical System Liew, S. F., S. M. Popoff, S. W. Sheehan, A. Goetschy, C. A. Schmuttenmaer, A. D. Stone, and H. Cao Acs Photonics 3, no. 3, 449455 (2016)
Motsclés: photoelectrochemical; dyesensitized solar cells; wavefront shaping; multiple scattering; multimode interference


Broadband Coherent Enhancement of Transmission and Absorption in Disordered Media Hsu, C. W., A. Goetschy, Y. Bromberg, A. D. Stone, and H. Cao Physical Review Letters 115, no. 22 (2015)
Résumé: © 2015 American Physical Society. Spatial modulation of the incident wave front has become a powerful method for controlling the diffusive transport of light in disordered media; however, such interferencebased control is intrinsically sensitive to frequency detuning. Here, we show analytically and numerically that certain wave fronts can exhibit strongly enhanced total transmission or absorption across bandwidths that are orders of magnitude broader than the spectral correlation width of the speckles. Such broadband enhancement is possible due to longrange correlations in coherent diffusion, which cause the spectral degrees of freedom to scale as the square root of the bandwidth rather than the bandwidth itself.


Coherent perfect absorption and coherent enhancement of absorption Douglas Stone, A., H. Cao, Y. D. Chong, L. Ge, S. Popoff, and A. Goetschy CLEO: QELS  Fundamental Science, CLEO_QELS 2015, 1551p (2015)
Résumé: Coherent illumination and wavefront shaping can be used to make a weakly absorbing cavity perfectly absorbing and to enhance strongly the absorption of a multiple scattering medium. © 2015 Optical Society of America.


Towards a random laser with cold atoms Guerin, W., N. Mercadier, F. Michaud, D. Brivio, L. S. FroufePérez, R. Carminati, V. Eremeev, A. Goetschy, S. E. Skipetrov, and R. Kaiser Journal of Optics A: Pure and Applied Optics 12, no. 2 (2010)
Résumé: Atoms can scatter light and they can also amplify it by stimulated emission. From this simple starting point, we examine the possibility of realizing a random laser in a cloud of lasercooled atoms. The answer is not obvious as both processes (elastic scattering and stimulated emission) seem to exclude one another: pumping atoms to make them behave as an amplifier drastically reduces their scattering crosssection. However, we show that even the simplest atom model allows the efficient combination of gain and scattering. Moreover, the supplementary degrees of freedom that atoms offer allow the use of several gain mechanisms, depending on the pumping scheme. We thus first study these different gain mechanisms and show experimentally that they can induce (standard) lasing. We then present how the constraint of combining scattering and gain can be quantified, which leads to an evaluation of the random laser threshold. The results are promising and we draw some prospects for a practical realization of a random laser with cold atoms. © 2010 IOP Publishing Ltd.
Motsclés: Cold atoms; Random laser; Cold atoms; Degrees of freedom; Lasercooled atoms; Practical realizations; Pumping schemes; Random lasers; Scattering cross section; Degrees of freedom (mechanics); Laser beams; Pumps; Scattering; Stimulated emission; Atoms

