Universal Statistics of Waves in a Random TimeVarying Medium Carminati, R., H. Chen, R. Pierrat, and B. Shapiro Physical Review Letters 127, no. 9 (2021)
Abstract: We study the propagation of waves in a medium in which the wave velocity fluctuates randomly in time. We prove that at long times, the statistical distribution of the wave energy is lognormal, with the average energy growing exponentially. For weak disorder, another regime preexists at shorter times, in which the energy follows a negative exponential distribution, with an average value growing linearly with time. The theory is in perfect agreement with numerical simulations, and applies to different kinds of waves. The existence of such universal statistics bridges the fields of wave propagation in timedisordered and spacedisordered media.


Quantitative Temperature Measurements in Gold Nanorods Using Digital Holography Lalisse, A., A. A. Mohtar, M. C. Nguyen, R. Carminati, J. Plain, and G. Tessier ACS Applied Materials and Interfaces (2021)
Abstract: © Temperature characterization and quantification at the nanoscale remain core challenges in applications based on photoinduced heating of nanoparticles. Here, we propose a new approach to obtain quantitative temperature measurements on individual nanoparticles by combining modulated photothermal stimulation and heterodyne digital holography. From fullfield reconstructed holograms, the temperature is determined with a precision of 0.3 K via a simple approach without requiring any calibration or fitting parameters. As an application, the dependence of temperature on the aspect ratio of gold nanoparticles is investigated. A good agreement with numerical simulation is observed.


Quantitative Measurement of the Thermal Contact Resistance between a Glass Microsphere and a Plate Doumouro, J., E. Perros, A. Dodu, N. Rahbany, D. Leprat, V. Krachmalnicoff, R. Carminati, W. Poirier, and Y. De Wilde Physical Review Applied 15, no. 1 (2021)
Abstract: © 2021 American Physical Society. Accurate measurements of the thermal resistance between microobjects made of insulating materials are complex because of their small size, low conductivity, and the presence of various illdefined gaps. We address this issue using a modified scanning thermal microscope operating in vacuum and in air. The sphereplate geometry is considered. Under controlled heating power, we measure the temperature on top of a glass microsphere glued to the probe as it approaches a glass plate at room temperature with nanometer accuracy. In vacuum, a jump is observed at contact. From this jump in temperature and the modeling of the thermal resistance of a sphere, the sphereplate contact resistance RK=(1.4±0.18)×107KW1 and effective radius r=36±4 nm are obtained. In air, the temperature on top of the sphere shows a decrease starting from a sphereplate distance of 200μm. A jump is also observed at contact, with a reduced amplitude. The sphereplate coupling out of contact can be described by the resistance shape factor of a sphere in front of a plate in air, placed in a circuit involving a series and a parallel resistance that are determined by fitting the approach curve. The contact resistance in air RK  =(1.2±0.46)×107KW1 is then estimated from the temperature jump. The method is quantitative without requiring any tedious multiplescale numerical simulation, and is versatile to describe the coupling between microobjects from large distances to contact in various environments.


Perfect depolarization in single scattering of light from uncorrelated surface and volume disorder Banon, J.P., I. Simonsen, and R. Carminati Optics Letters 45, no. 23, 6354 (2020)
Abstract: © 2020 Optical Society of America We demonstrate that single scattering of ppolarized waves from uncorrelated surface and volume disorder can lead to perfect depolarization. The degree of polarization vanishes in specific scattering directions that can be characterized based on simple geometric arguments. Depolarization results from a different polarization response of each source of disorder, which provides a clear physical interpretation of the depolarization mechanism.


Absorption of scalar waves in correlated disordered media and its maximization using stealth hyperuniformity Sheremet, A., R. Pierrat, and R. Carminati Physical Review A 101, no. 5, 053829 (2020)


Origin of transparency in scattering biomimetic collagen materials Salameh, C., F. Salviat, E. Bessot, M. Lama, J.M. Chassot, E. Moulongui, Y. Wang, M. Robin, A. Bardouil, M. Selmane, F. Artzner, A. Marcellan, C. Sanchez, M.M. GiraudGuille, M. Faustini, R. Carminati, and N. Nassif Proceedings of the National Academy of Sciences of the United States of America 117, no. 22, 1194711953 (2020)
Abstract: Living tissues, heterogeneous at the microscale, usually scatter light. Strong scattering is responsible for the whiteness of bones, teeth, and brain and is known to limit severely the performances of biomedical optical imaging. Transparency is also found within collagenbased extracellular tissues such as decalcified ivory, fish scales, or cornea. However, its physical origin is still poorly understood. Here, we unveil the presence of a gap of transparency in scattering fibrillar collagen matrices within a narrow range of concentration in the phase diagram. This precholesteric phase presents a threedimensional (3D) orientational order biomimetic of that in natural tissues. By quantitatively studying the relation between the 3D fibrillar network and the optical and mechanical properties of the macroscopic matrices, we show that transparency results from structural partial order inhibiting light scattering, while preserving mechanical stability, stiffness, and nonlinearity. The striking similarities between synthetic and natural materials provide insights for better understanding the occurring transparency.
Keywords: collagen; mechanical properties; photonic materials; selfassembly; transparency


Single scattering of polarized light by correlated surface and volume disorder Banon, J.P., I. Simonsen, and R. Carminati Physical Review A 101, no. 5 (2020)
Abstract: © 2020 American Physical Society. We study light scattering by systems combining randomly rough surface and volume dielectric fluctuations. We introduce a general model including correlations between surface and volume disorders, and we study the scattering properties within a singlescattering approach. We identify different regimes of surface and volume dominated scattering depending on length scales characterizing the surface and volume disorders. For uncorrelated disorders, we discuss the polarization response of each source of disorder, and show how polarimetric measurements can be used to separate the surface and volume contributions in the total measured diffusely scattered intensity. For correlated systems, we identify two configurations of volume disorder which, respectively, couple weakly or strongly to surface scattering via surfacevolume cross correlations. We illustrate these effects on different configurations exhibiting interference patterns in the diffusely scattered intensity, which may be of interest for the characterization of complex systems or for the design of optical components by engineering the degree of surfacevolume correlations.


Influence of the Local Scattering Environment on the Localization Precision of Single Particles Bouchet, D., R. Carminati, and A. P. Mosk Physical Review Letters 124, no. 13, 133903 (2020)
Abstract: We study the fundamental limit on the localization precision for a subwavelength scatterer embedded in a strongly scattering environment, using the external degrees of freedom provided by wavefront shaping. For a weakly scattering target, the localization precision improves with the value of the local density of states at the target position. For a strongly scattering target, the localization precision depends on the dressed polarizability that includes the backaction of the environment. This numerical study provides new insights for the control of the information content of scattered light by wavefront shaping, with potential applications in sensing, imaging, and nanoscale engineering.


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)
Abstract: © 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.


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)
Abstract: © 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.


Enhanced absorption of waves in stealth hyperuniform disordered media Bigourdan, F., R. Pierrat, and R. Carminati Optics Express 27, no. 6, 86668682 (2019)
Abstract: © 2019 Optical Society of America We study the propagation of waves in a set of absorbing subwavelength scatterers positioned on a stealth hyperuniform point pattern. We show that spatial correlations in the disorder substantially enhance absorption compared to a fully disordered structure with the same density of scatterers. The nonresonant nature of the mechanism provides broad angular and spectral robustness. These results demonstrate the possibility to design lowdensity materials with blackbodylike absorption.


Terahertz and Visible Probing of Particles Suspended in Air Prophete, C., H. Sik, E. Kling, R. Carminati, and J. De Rosny IEEE Transactions on Terahertz Science and Technology 9, no. 2, 120125 (2019)
Abstract: © 20112012 IEEE. The attenuation of air suspended particles is measured with a terahertz (THz) timedomain spectrometer. Simultaneously, the attenuation at a wavelength of 650 nm is probed with a laser diode. On the one hand, this dual measurement allows a direct assessment of the visibility evolution in the THz range compared to the visible range. On the other hand, this setup provides an estimation of the scattering strength and the density of particles. Using the Mie theory, the method is successfully applied to experimentally characterize the refractive index of sand grains and glass beads. The refractive indexes of sand grains and glass beads, average over the acquisitions, are 1.67 and 2.54, respectively. The estimation of the scattering properties of sand grains is crucial to evaluate the performance of THz systems to image through brownout clouds that are created by helicopter rotors when landing in arid areas.
Keywords: Propagation; refractive index; terahertz (THz) scattering; THz timedomain spectroscopy (THzTDS)


Quantum dipole emitters in structured environments: A scattering approach: Tutorial Bouchet, D., and R. Carminati Journal of the Optical Society of America A: Optics and Image Science, and Vision 36, no. 2, 186195 (2019)
Abstract: © 2019 Optical Society of America. We provide a simple semiclassical formalism to describe the coupling between one or several quantum emitters and a structured environment. Describing the emitter by an electric polarizability, and the surrounding medium by a Green function, we show that an intuitive scattering picture allows one to derive a coupling equation from which the eigenfrequencies of the coupled system can be extracted. The model covers a variety of regimes observed in light–matter interaction, including weak and strong coupling, coherent collective interactions, and incoherent energy transfer. It provides a unified description of many processes, showing that different interaction regimes are actually rooted on the same ground. It can also serve as a basis for the development of more refined models in a full quantum electrodynamics framework.


Cross density of states and mode connectivity: Probing wave localization in complex media CanaguierDurand, A., R. Pierrat, and R. Carminati Physical Review A 99, no. 1 (2019)
Abstract: © 2019 American Physical Society. We introduce the mode connectivity as a measure of the number of eigenmodes of a wave equation connecting two points at a given frequency. Based on numerical simulations of scattering of electromagnetic waves in disordered media, we show that the connectivity discriminates between the diffusive and the Anderson localized regimes. For practical measurements, the connectivity is encoded in the secondorder coherence function characterizing the intensity emitted by two incoherent classical or quantum dipole sources. The analysis applies to all processes in which spatially localized modes build up, and to all kinds of waves.


Modeling of an active terahertz imaging system in brownout conditions Prophète, C., R. Pierrat, H. Sik, E. Kling, R. Carminati, and J. De Rosny Applied Optics 57, no. 21, 60176026 (2018)
Abstract: © 2018 Optical Society of America. We present a theoretical evaluation of a subterahertz (subTHz) system to image through a scattering medium composed of scatterers of sizes close to the wavelength. We specifically study the case of sand grain clouds created by helicopter rotor airflow during landing in arid areas. The different powers received by one pixel of a matrix made of subTHz sensors are identified. Photometric and antennabased sensors are considered. Besides the thermal contribution to the noise, we focus our attention on the radiation backscattered by the brownout. It appears that a configuration where the source and the camera are distant is the most promising configuration and is realistic for embedded systems.


Photon echoes in strongly scattering media: A diagrammatic approach Pierrat, R., R. Carminati, and J. L. Le Gouët Physical Review A 97, no. 6 (2018)
Abstract: © 2018 American Physical Society. We study photon echo generation in disordered media with the help of multiple scattering theory based on diagrammatic approach and numerical simulations. We show that a strong correlation exists between the driving fields at the origin of the echo and the echo beam. Opening the way to a better understanding of nonlinear wave propagation in complex materials, this work supports recent experimental results with applications to the measurement of the optical dipole lifetime T2 in powders.


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)
Abstract: © 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.


OneShot Measurement of the ThreeDimensional Electromagnetic Field Scattered by a Subwavelength Aperture Tip Coupled to the Environment Rahbany, N., I. Izeddin, V. Krachmalnicoff, R. Carminati, G. Tessier, and Y. De Wilde ACS Photonics 5, no. 4, 15391545 (2018)
Abstract: © 2018 American Chemical Society. Nearfield scanning optical microscopy (NSOM) achieves subwavelength resolution by bringing a nanosized probe close to the surface of the sample. This extends the spectrum of spatial frequencies that can be detected with respect to a diffraction limited microscope. The interaction of the probe with the sample is expected to affect its radiation to the far field in a way that is often hard to predict. Here we address this question by proposing a general method based on fullfield offaxis digital holography microscopy which enables to study in detail the farfield radiation from a NSOM probe as a function of its environment. A first application is demonstrated by performing a threedimensional (3D) tomographic reconstruction of light scattered from the subwavelength aperture tip of a NSOM, in free space or coupled to transparent and plasmonic media. A single holographic image recorded in one shot in the far field contains information on both the amplitude and the phase of the scattered light. This is sufficient to reverse numerically the propagation of the electromagnetic field all the way to the aperture tip. Finite Difference Time Domain (FDTD) simulations are performed to compare the experimental results with a superposition of magnetic and electric dipole radiation.


Mutual Information between Reflected and Transmitted Speckle Images Fayard, N., A. Goetschy, R. Pierrat, and R. Carminati Physical Review Letters 120, no. 7 (2018)
Abstract: © 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.


Optimizing Hyperuniformity in SelfAssembled Bidisperse Emulsions Ricouvier, J., R. Pierrat, R. Carminati, P. Tabeling, and P. Yazhgur Physical Review Letters 119, no. 20 (2017)
Abstract: © 2017 American Physical Society. We study long range density fluctuations (hyperuniformity) in twodimensional jammed packings of bidisperse droplets. Taking advantage of microfluidics, we systematically span a large range of size and concentration ratios of the two droplet populations. We identify various defects increasing long range density fluctuations mainly due to organization of local particle environment. By choosing an appropriate bidispersity, we fabricate materials with a high level of hyperuniformity. Interesting transparency properties of these optimized materials are established based on numerical simulations.


Quantitative analysis of THz imaging systems in brownout conditions Prophete, C., R. Pierrat, H. Sik, E. Kling, R. Carminati, and J. De Rosny International Conference on Infrared, Millimeter, and Terahertz Waves, IRMMWTHz (2017)
Abstract: © 2017 IEEE. Brownout refers to dust cloud created by the rotor downwash of a helicopter. When it occurs, the visibility becomes limited, or even null. The pilot can be desorientated and accident may happen. No existing imaging systems can see through dust clouds, in realtime and with sufficient resolution. Using waves between 100GHz and 1THz seems to be a good solution to make a compact and suitable imaging system. After defining a brownout model, we establish theoretically the power balance of the involved sources of signal and noise. We compare a photometric detection system with one compounded of antennas.


Observation of mean path length invariance in lightscattering media Savo, R., R. Pierrat, U. Najar, R. Carminati, S. Rotter, and S. Gigan Science 358, no. 6364, 765768 (2017)
Abstract: © 2017, American Association for the Advancement of Science. All rights reserved. The microstructure of a medium strongly influences how light propagates through it. The amount of disorder it contains determines whether the medium is transparent or opaque. Theory predicts that exciting such a medium homogeneously and isotropically makes some of its optical properties depend only on the medium’s outer geometry. Here, we report an optical experiment demonstrating that the mean path length of light is invariant with respect to the microstructure of the medium it scatters through. Using colloidal solutions with varying concentration and particle size, the invariance of the mean path length is observed over nearly two orders of magnitude in scattering strength. Our results can be extended to a wide range of systems—however ordered, correlated, or disordered—and apply to all wavescattering problems.


Structure and dynamics of multicellular assemblies measured by coherent light scattering Brunel, B., C. Blanch, A. Gourrier, V. Petrolli, A. Delon, J. F. Joanny, R. Carminati, R. Pierrat, and G. Cappello New Journal of Physics 19, no. 7 (2017)
Abstract: © 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Determining the structure and the internal dynamics of tissues is essential to understand their functional organization. Microscopy allows for monitoring positions and trajectories of every single cell. Those data are useful to extract statistical observables, such as intercellular distance, tissue symm etry and anisotropy, and cell motility. However, this procedure requires a large and supervised computational effort. In addition, due to the large crosssection of cells, the light scattering limits the use of microscopy to relatively thin samples. As an alternative approach, we propose to take advantage of light scattering and to analyze the dynamical diffraction pattern produced by a living tissue illuminated with coherent light. In this article, we illustrate with a few examples that supracellular structures produce an exploitable diffraction signal. From the diffraction signal, we deduce the mean distance between cells, the anisotropy of the supracellular organization and, from its fluctuations, the mean speed of moving cells. This easy to implement technique considerably reduces analysis time, allowing real time monitoring.
Keywords: coherent optics; dynamic light scattering; multicellular structures


Spatial correlations of the spontaneous decay rate as a probe of dense and correlated disordered materials Leseur, O., R. Pierrat, and R. Carminati European Physical Journal: Special Topics 226, no. 7, 14231432 (2017)
Abstract: © 2017, The Author(s).We study theoretically and numerically a new kind of spatial correlation for waves in disordered media. We define CΓ as the correlation function of the fluorescent decay rate of an emitter at two different positions inside the medium. We show that the amplitude and the width of CΓ provide decoupled information on the structural correlation of the disordered medium and on the local environment of the emitter. This result may stimulate the emergence of new imaging and sensing modalities in complex media.


Causality, Nonlocality, and Negative Refraction Forcella, D., C. Prada, and R. Carminati Physical Review Letters 118, no. 13 (2017)
Abstract: © 2017 American Physical Society. American Physical Society.The importance of spatial nonlocality in the description of negative refraction in electromagnetic materials has been put forward recently. We develop a theory of negative refraction in homogeneous and isotropic media, based on first principles, and that includes nonlocality in its full generality. The theory shows that both dissipation and spatial nonlocality are necessary conditions for the existence of negative refraction. It also provides a sufficient condition in materials with weak spatial nonlocality. These fundamental results should have broad implications in the theoretical and practical analyses of negative refraction of electromagnetic and other kinds of waves.


Correlated blinking of fluorescent emitters mediated by single plasmons Bouchet, D., E. Lhuillier, S. Ithurria, A. Gulinatti, I. Rech, R. Carminati, Y. De Wilde, and V. Krachmalnicoff Physical Review A  Atomic, Molecular, and Optical Physics 95, no. 3 (2017)
Abstract: © 2017 American Physical Society.We observe timecorrelated emission between a single CdSe/CdS/ZnS quantum dot exhibiting singlephoton statistics and a fluorescent nanobead located micrometers apart. This is accomplished by coupling both emitters to a silver nanowire. Single plasmons are created on the latter from the quantum dot, and transfer energy to excite in turn the fluorescent nanobead. We demonstrate that the molecules inside the bead show the same blinking behavior as the quantum dot.


Temperature of a nanoparticle above a substrate under radiative heating and cooling Kallel, H., R. Carminati, and K. Joulain Physical Review B  Condensed Matter and Materials Physics 95, no. 11 (2017)
Abstract: © 2017 American Physical Society.Controlling the temperature in architectures involving nanoparticles and substrates is a key issue for applications involving micro and nanoscale heat transfer. We study the thermal behavior of a single nanoparticle interacting with a flat substrate under external monochromatic illumination, and with thermal radiation as the unique heat loss channel. We develop a model to compute the temperature of the nanoparticle, based on an effective dipolepolarizability approach. Using numerical simulations, we thoroughly investigate the impacts of various parameters affecting the nanoparticle temperature, such as the nanoparticletosubstrate gap distance, the incident light wavelength and polarization, or the material resonances. This study provides a tool for the thermal characterization and design of micro or nanoscale systems coupling substrates with nanoparticles or optical antennas.


Multiple scattering of polarized light in disordered media exhibiting shortrange structural correlations Vynck, K., R. Pierrat, and R. Carminati Physical Review A 94, no. 3 (2016)


Highdensity hyperuniform materials can be transparent Leseur, O., R. Pierrat, and R. Carminati Optica 3, no. 7, 763767 (2016)


Nearfield to farfield characterization of speckle patterns generated by disordered nanomaterials Parigi, V., E. Perros, G. Binard, C. Bourdillon, A. Maitre, R. Carminati, V. Krachmalnicoff, and Y. De Wilde Optics Express 24, no. 7, 70197027 (2016)


Quantum coherence of light emitted by two singlephoton sources in a structured environment CanaguierDurand, A., and R. Carminati Physical Review A  Atomic, Molecular, and Optical Physics 93, no. 3 (2016)
Abstract: © 2016 American Physical Society. We develop a theoretical framework for the analysis of the quantum coherence of light emitted by two independent singlephoton sources in an arbitrary environment. The theory provides design rules for the control of the degree of quantum coherence in terms of classical quantities widely used in nanophotonics. As an important example, we derive generalized conditions to generate superradiant and subradiant states of the emitters and demonstrate the ability of a structured environment to induce longrange quantum coherence. These results should have broad applications in quantum nanophotonics and for the sensing of fluorescent sources in complex environments.


LongRange PlasmonAssisted Energy Transfer between Fluorescent Emitters Bouchet, D., D. Cao, R. Carminati, Y. De Wilde, and V. Krachmalnicoff Physical Review Letters 116, no. 3 (2016)


Thermal emission by a subwavelength aperture Joulain, K., Y. Ezzahri, and R. Carminati Journal of Quantitative Spectroscopy and Radiative Transfer 173, 16 (2016)
Abstract: © 2015 Elsevier Ltd. We calculate, by means of fluctuational electrodynamics, the thermal emission of an aperture separating from the outside, vacuum or a material at temperature T. We show that thermal emission is very different whether the aperture size is large or small compared to the thermal wavelength. Subwavelength apertures separating vacuum from the outside have their thermal emission strongly decreased compared to classical blackbodies which have an aperture much larger than the wavelength. A simple expression of their emissivity can be calculated and their total emissive power scales as T8 instead of T4 for large apertures. Thermal emission of disk of materials with a size comparable to the wavelength is also discussed. It is shown in particular that emissivity of such a disk is increased when the material can support surface waves such as phonon polaritons.
Keywords: Fluctuational electrodynamics; Nanoscale Thermal emission; Phononpolaritons


Intensity correlations between reflected and transmitted speckle patterns Fayard, N., A. Cazé, R. Pierrat, and R. Carminati Physical Review A  Atomic, Molecular, and Optical Physics 92, no. 3 (2015)
Abstract: © 2015 American Physical Society. ©2015 American Physical Society. We study theoretically the spatial correlations between the intensities measured at the input and output planes of a disordered scattering medium. We show that at large optical thicknesses, a longrange spatial correlation persists and takes negative values. For small optical thicknesses, shortrange and longrange correlations coexist, with relative weights that depend on the optical thickness. These results may have direct implications for the control of wave transmission through complex media by wavefront shaping, thus finding applications in sensing, imaging, and information transfer.


Breakthroughs in photonics 2014: Random lasers Sebbah, P., and R. Carminati IEEE Photonics Journal 7, no. 3 (2015)
Abstract: © 2015 IEEE. Multiple scattering of light in a disordered medium with gain may provide for the necessary feedback to achieve lasing action without an optical cavity. In addition to the fundamental interest raised by this regime of lightmatter interaction in open cavity, the relatively simple design of these socalled "random lasers" and the possibility to control their emission open perspective of new applications in domains not yet covered by conventional lasers.
Keywords: Laser; random media


Linear and nonlinear Rabi oscillations of a twolevel system resonantly coupled to an Andersonlocalized mode Bachelard, N., R. Carminati, P. Sebbah, and C. Vanneste Physical Review A 91, no. 4 (2015)


Mapping the radiative and the apparent nonradiative local density of states in the near field of a metallic nanoantenna Cao, D., A. Cazé, M. Calabrese, R. Pierrat, N. Bardou, S. Collin, R. Carminati, V. Krachmalnicoff, and Y. De Wilde ACS Photonics 2, no. 2, 189193 (2015)
Abstract: © 2015 American Chemical Society. We present a novel method to extract the various contributions to the photonic local density of states from nearfield fluorescence maps. The approach is based on the simultaneous mapping of the fluorescence intensity and decay rate and on the rigorous application of the reciprocity theorem. It allows us to separate the contributions of the radiative and the apparent nonradiative local density of states to the change in the decay rate. The apparent nonradiative contribution accounts for losses due to radiation out of the detection solid angle and to absorption in the environment. Data analysis relies on a new analytical calculation, and does not require the use of numerical simulations. One of the most relevant applications of the method is the characterization of nanostructures aimed at maximizing the number of photons emitted in the detection solid angle, which is a crucial issue in modern nanophotonics.
Keywords: fluorescence microscopy; local density of states; nearfield scanning probe; plasmonic nanoantennas; radiative decay rate; reciprocity theorem


Electromagnetic field correlations in threedimensional speckles Dogariu, A. C., and R. Carminati Physics Reports 559, 129 (2015)
Abstract: © 2015. We describe recent developments in the characterization of threedimensional speckle fields produced by scattering of electromagnetic waves. In many practical situations the description of such fields requires approaches going beyond the Gaussian statistics approximation. Quantitative measures of spatial coherence and polarization can be defined from the fieldfield correlation matrix, known as the crossspectral density matrix in coherence theory. The complex degree of mutual polarization provides a measure of the similarity between polarization states at two different points. The degree of spatial coherence describes spatial coherence and averages out the polarization properties. We discuss their behavior in speckle fields produced by multiple scattering in disordered materials. A number of nonuniversal properties arise, that are related to the internal microscopic structure of the scattering medium. Nonuniversality affects observables quantities, such as spatial correlations in speckle patterns measured in the near field of the medium surface, statistics of the local density of states or the depolarization of the exciting electromagnetic field due to scattering. Specific microscopic scales are necessary to describe the nonuniversal behaviors, that characterize the scaledependent morphology of the scattering medium.
Keywords: Coherence; Polarization; Random fields; Speckle


Speckle fluctuations resolve the interdistance between incoherent point sources in complex media Carminati, R., G. A. Cwilich, L. S. FroufePérez, and J. J. Sáenz Physical Review A  Atomic, Molecular, and Optical Physics 91, no. 2 (2015)
Abstract: © 2015 American Physical Society. We study the fluctuations of the light emitted by two identical incoherent point sources in a disordered environment. The intensityintensity correlation function and the speckle contrast, obtained after proper temporal and configurational averaging, encode the relative distance between the two sources. This suggests the intriguing possibility that intensity measurements at only one point in a speckle pattern produced by two incoherent sources can provide information about the relative distance between the sources, with a precision that is not limited by diffraction. The theory also suggests an alternative approach to the Green'sfunction retrieval technique, where the correlations of the isotropic ambient noise detected by two receivers are replaced by a measurement at a single point of the noise due to two fluctuating incoherent sources.


Image transmission through a scattering medium: Inverse problem and sparsitybased imaging Gigan, S., S. M. Popoff, A. Liutkus, D. Martina, O. Katz, G. Chardon, R. Carminati, G. Lerosey, M. A. Fink., A. C. Boccara, I. Carron, and L. Daudet 2014 13th Workshop on Information Optics, WIO 2014 (2014)
Abstract: © 2014 IEEE. We demonstrate how to measure accurately the transmission matrix of a complex medium. With this information, we show how to focus light, recover an image, and even perform efficient reconstruction of a sparse object.


Probing twodimensional Anderson localization without statistics Leseur, O., R. Pierrat, J. J. Sáenz, and R. Carminati Physical Review A  Atomic, Molecular, and Optical Physics 90, no. 5 (2014)
Abstract: © 2014 American Physical Society. We investigate the possibility of using the independence of the transmitted speckle pattern on the illumination condition as a signature of Anderson localization in a single configuration of a twodimensional and open disordered medium. The analysis is based on exact numerical simulations of multiple light scattering. We introduce a similarity function that we propose as a reliable observable to probe Anderson localization without requiring any statistical averaging over an ensemble.


Invariance property of wave scattering through disordered media Pierrat, R., P. Ambichl, S. Gigan, A. Haber, R. Carminati, and S. Rotter Proceedings of the National Academy of Sciences of the United States of America 111, no. 50, 1776517770 (2014)
Abstract: A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the system's boundary geometry and is thus unaffected by the value of the mean free path. Here we show that this result is rooted on a much deeper level than that of a random walk, which allows us to extend the reach of this universal invariance property beyond the diffusion approximation. Specifically, we demonstrate that an equivalent invariance relation also holds for the scattering of waves in resonant structures as well as in ballistic, chaotic or in Anderson localized systems. Our work unifies a number of specific observations made in quite diverse fields of science ranging from the movement of ants to nuclear scattering theory. Potential experimental realizations using light fields in disordered media are discussed.
Keywords: Diffusion; Disordered media; Random walk; Time delay; Wave scattering


Electromagnetic density of states in complex plasmonic systems Carminati, R., A. Cazé, D. Cao, F. Peragut, V. Krachmalnicoff, R. Pierrat, and Y. De Wilde Surface Science Reports 70, no. 1, 141 (2015)
Abstract: © 2014 Elsevier B.V. All rights reserved. Nanostructured materials offer the possibility to tailor lightmatter interaction at scales below the wavelength. Metallic nanostructures benefit from the excitation of surface plasmons that permit light concentration at ultrasmall length scales and ultrafast time scales. The local density of states (LDOS) is a central concept that drives basic processes of lightmatter interaction such as spontaneous emission, thermal emission and absorption. We introduce theoretically the concept of LDOS, emphasizing the specificities of plasmonics. We connect the LDOS to real observables in nanophotonics, and show how the concept can be generalized to account for spatial coherence. We describe recent methods developed to probe or map the LDOS in complex nanostructures ranging from nanoantennas to disordered metal surfaces, based on dynamic fluorescence measurements or on the detection of thermal radiation.
Keywords: Cross density of states; Local density of states; Plasmonics; Spatial coherence; Spontaneous emission; Thermal radiation


Local control of the excitation of surface plasmon polaritons by nearfield magnetooptical Kerr effect Vincent, R., H. Marinchio, J. J. Saenz, and R. Carminati Physical Review B 90, no. 24 (2014)


Mapping and Quantifying Electric and Magnetic Dipole Luminescence at the Nanoscale Aigouy, L., A. Caze, P. Gredin, M. Mortier, and R. Carminati Physical Review Letters 113, no. 7 (2014)


Analysis of coherence properties of partially polarized light in 3D and application to disordered media Refregier, P., V. Wasik, K. Vynck, and R. Carminati Optics Letters 39, no. 8, 23622365 (2014)


Magnetooptical Kerr effect in resonant subwavelength nanowire gratings Marinchio, H., R. Carminati, A. GarcíaMartín, and J. J. Sáenz New Journal of Physics 16, no. 1, 015007015007 (2014)
Abstract: Periodic arrays of nanorods can present a resonant response at specific geometric conditions. We use a multiple scattering approach to analyze the optical response of subwavelength nanowire gratings made of arbitrary anisotropic materials. When the rods are made of magnetooptical dielectrics we show that there is a complex interplay between the geometric resonances of the grating and the magnetooptical Kerr effects (MOKE) response. As we will show, for a given polarization of the incident light, a resonant magnetooptical response can be obtained by tuning the incidence angle and grating parameters to operate near the resonance condition for the opposite polarization. Our results could be important to understand and optimize MOKE structures and devices based on resonant subwavelength gratings and could open new perspectives in sensing applications.


Extraordinary magnetoplasmonic effect in SPPMOKE configuration Vincent, R., H. Marinchio, J. J. Sáenz, and R. Carminati CLEO: QELS_Fundamental Science, CLEO:QELS FS 2013 (2013)
Abstract: An as yet unexploited Magneto Optical Kerr Effect (MOKE) at evanescent distance from a surface is introduced. In the case of a magnetic particlemetallic surface system, an extraordinary intensity is discovered and fully explained by the excitation of Surface Plasmon Polariton. © OSA 2013.
Keywords: Magnetooptical Kerr effects; Surface plasmon polaritons; Surface systems; Electromagnetic wave polarization; Surface plasmon resonance; Optical Kerr effect


Polarization and spatial coherence of electromagnetic waves in uncorrelated disordered media Vynck, K., R. Pierrat, and R. Carminati Physical Review A 89, no. 1, 013842 (2014)
Abstract: Spatial field correlation functions represent a key quantity for the description of mesoscopic phenomena in disordered media and the optical characterization of complex materials. Yet many aspects related to the vector nature of light waves have not been investigated so far. We study theoretically the polarization and coherence properties of electromagnetic waves produced by a dipole source in a threedimensional uncorrelated disordered medium. The spatial field correlation matrix is calculated analytically using a multiplescattering theory for polarized light. This allows us to provide a formal description of the light depolarization process in terms of “polarization eigenchannels” and to derive analytical formulas for the spatial coherence of multiply scattered light.


Surface plasmons: A probe for graphene electronics Carminati, R. Nature Nanotechnology (2013)


Strong coupling to twodimensional Anderson localized modes Cazé, A., R. Pierrat, and R. Carminati Physical Review Letters 111, no. 5 (2013)
Abstract: We use a scattering formalism to derive a condition of strong coupling between a resonant scatterer and an Anderson localized mode for electromagnetic waves in two dimensions. The strong coupling regime is demonstrated based on exact numerical simulations, in perfect agreement with theory. The strong coupling threshold can be expressed in terms of the Thouless conductance and the Purcell factor. This connects key concepts in transport theory and cavity quantum electrodynamics, and provides a practical tool for the design or analysis of experiments. © 2013 American Physical Society.


Towards a full characterization of a plasmonic nanostructure with a fluorescent nearfield probe Krachmalnicoff, V., D. Cao, A. Cazé, E. Castanié, R. Pierrat, N. Bardou, S. Collin, R. Carminati, and Y. De Wilde Optics Express 21, no. 9, 1153611545 (2013)
Abstract: We report on the experimental and theoretical study of the spatial fluctuations of the local density of states (EMLDOS) and of the fluorescence intensity in the nearfield of a gold nanoantenna. EMLDOS, fluorescence intensity and topography maps are acquired simultaneously by scanning a fluorescent nanosource grafted on the tip of an atomic force microscope at the surface of the sample. The results are in good quantitative agreement with numerical simulations. This work paves the way for a full nearfield characterization of an optical nanoantenna. © 2013 Optical Society of America.
Keywords: Atomic force microscope (AFM); Fluorescence intensities; Local density of state; Nearfield characterizations; Optical nano antennas; Plasmonic nanostructures; Quantitative agreement; Spatial fluctuation; Atomic force microscopy; Nanostructures; Surface topography; Fluorescence


Subwavelength focusing inside an open disordered medium by time reversal at a single point antenna Pierrat, R., C. Vandenbem, M. Fink, and R. Carminati Physical Review A  Atomic, Molecular, and Optical Physics 87, no. 4 (2013)
Abstract: We study theoretically light focusing at subwavelength scale inside a disordered strongly scattering open medium. We show that broadband time reversal at a single point antenna, in conjunction with nearfield interactions and multiple scattering, produces spatial focusing with a quality comparable to that obtained in an ideal closed cavity. This provides different perspectives for superresolved optical imaging and coherent control of single nanosources or absorbers in complex media. © 2013 American Physical Society.
Keywords: Closed cavity; Coherent control; Disordered medium; Near field interactions; Optical imaging; Spatial focusing; Subwavelength focusing; Subwavelength scale; Antennas; Focusing


Spatial coherence in complex photonic and plasmonic systems Cazé, A., R. Pierrat, and R. Carminati Physical Review Letters 110, no. 6 (2013)
Abstract: The concept of cross density of states characterizes the intrinsic spatial coherence of complex photonic or plasmonic systems, independently of the illumination conditions. Using this tool and the associated intrinsic coherence length, we demonstrate unambiguously the spatial squeezing of eigenmodes on disordered fractal metallic films, thus clarifying a basic issue in plasmonics. © 2013 American Physical Society.
Keywords: Coherence lengths; Density of state; Eigen modes; Illumination conditions; Plasmonic; Plasmonics; Spatial coherence; Atomic physics; Physics; Plasmons


Recovering fluorophore location and orientation from lifetimes Irishina, N., M. Moscoso, and R. Carminati Optics Express 21, no. 1, 421430 (2013)
Abstract: In this paper, we study the possibility of using lifetime data to estimate the position and orientation of a fluorescent dipole source within a disordered medium. The vector FoldyLax equations are employed to calculate the interaction between the fluorescent source and the scatterers that are modeled as pointscatterers. The numerical experiments demonstrate that if good prior knowledge about the positions of the scatterers is available, the position and orientation of the dipole source can be retrieved from its lifetime data with precision. If there is uncertainty about the positions of the scatterers, the dipole source position can be estimated within the same level of uncertainty. © 2013 Optical Society of America.
Keywords: Dipole sources; Disordered medium; Lifetime data; Numerical experiments; Prior knowledge; Fluorescence; Uncertainty analysis; Scattering


Dressed polarizability and absorption of a dipole nanoantenna in an arbitrary environment Castanié, E., R. Vincent, R. Pierrat, and R. Carminati AIP Conference Proceedings 1475, 116118 (2012)
Abstract: In this work, we show how the absporption crosssection of a dipole nanoantenna is modified by the local environment. In particular, we clarify the key role of the Local Density of States (LDOS) and show the analogy that exists with quantum emitters. This link with the LDOS shows that it is possible to probe the LDOS inside a structured environment with a nanoparticle. Conversely, we can design nanostructures to control the level of absorption in a nanoparticle, a strong limitation for applications in nanophotonics. The theoretical results are illustrated numerically in the simple case of a silver particle near a perfect mirror. © 2012 American Institute of Physics.
Keywords: absorption; local density of states; nanoantenna


Radiative and nonradiative local density of states on disordered plasmonic films Cazé, A., R. Pierrat, and R. Carminati Photonics and Nanostructures  Fundamentals and Applications 10, no. 4, 339344 (2012)
Abstract: We present numerical calculations of the local density of optical states (LDOS) in the near field of disordered plasmonic films. The calculations are based on an integral volume method, that takes into account polarization and retardation effects, and allows us to discriminate radiative and nonradiative contributions to the LDOS. At short distance, the LDOS fluctuations are dominated by nonradiative channels, showing that changes in the spontaneous dynamics of dipole emitters are driven by nonradiative coupling to plasmon modes. Maps of radiative and nonradiative LDOS exhibit strong fluctuations, but with substantially different spatial distributions. © 2012 Elsevier B.V. All rights reserved.
Keywords: Disordered systems; Fractals; Local density of states; Metallic films; Numerical simulations; Plasmons; Disordered system; Local density; Local density of state; Near fields; Nonradiative; Nonradiative channels; Numerical calculation; Optical state; Plasmon modes; Plasmonic; Retardation effect; Volume method; Computer simulation; Electrical engineering; Fractals; Hardware; Metallic films; Plasmons


Distance dependence of the local density of states in the near field of a disordered plasmonic film Castanié, E., V. Krachmalnicoff, A. Cazé, R. Pierrat, Y. De Wilde, and R. Carminati Optics Letters 37, no. 14, 30063008 (2012)
Abstract: We measure the statistical distribution of the photonic local density of states in the near field of a semicontinuous gold film. By varying the distance between the measurement plane and the film, we show that nearfield confined modes play a major role in the width of the distribution. Numerical simulations in good agreement with experiments allow us to point out the influence of nonradiative decay channels at short distance. © 2012 Optical Society of America.
Keywords: Confined modes; Gold film; Local density of state; Measurement planes; Near fields; Nearfield; Nonradiative decay channels; Plasmonic; Semicontinuous; Statistical distribution; Optics; Optoelectronic devices


Light scattering by a magnetooptical nanoparticle in front of a flat surface: Perturbative approach Marinchio, H., J. J. Sáenz, and R. Carminati Physical Review B  Condensed Matter and Materials Physics 85, no. 24 (2012)
Abstract: We develop a perturbative formalism for the interaction of a magnetooptical nanoparticle with a flat surface made of a dielectric or metallic material. The formalism leads to a simple interpretation of the interplay between the purely dielectric and the magnetooptical responses, in terms of excitation of (and radiation by) two orthogonal electric dipoles. We analyze two different routes for the enhancement of the magnetooptical response with respect to the purely dielectric contribution, both based on the nanoparticlesurface interaction. The enhancement is discussed in terms of relevant magnetooptical signals, such as changes in reflectivity, polarization (Kerr) rotation, and ellipticity. © 2012 American Physical Society.


Absorption by an optical dipole antenna in a structured environment Castanié, E., R. Vincent, R. Pierrat, and R. Carminati International Journal of Optics 2012 (2012)
Abstract: We compute generalized absorption and extinction crosssections of an optical dipole nanoantenna in a structured environment. The expressions explicitly show the influence of radiation reaction and the local density of states on the intrinsic absorption properties of the antenna. Engineering the environment could allow to modify the overall absorption as well as the frequency and the linewidth of a resonant antenna. Conversely, a dipole antenna can be used to probe the photonic environment, in a similar way as a quantum emitter. Copyright © 2012 E. Castanié et al.


Source location from fluorescence lifetime in disordered media Irishina, N., M. Moscoso, and R. Carminati Optics Letters 37, no. 5, 951953 (2012)
Abstract: We show that the source location problem can be solved in a scattering medium using the fluorescence lifetime and realistic a priori information. The intrinsic illposedness of the problem is reduced when the level of scattering increases. This work is a proof of principle demonstrating the high potential of quantitative lifetime imaging in complex media. © 2012 Optical Society of America.
Keywords: Complex media; Disordered media; Fluorescence lifetimes; High potential; Illposedness; Lifetime imaging; Priori information; Proof of principles; Scattering medium; Source location; Source location problem; Optics; Optoelectronic devices; Fluorescence


Timedomain radiation and absorption by subwavelength sources Bossy, E., and R. Carminati EuroPhysics Letters 97, no. 3, 34001 (2012)
Abstract: Radiation by elementary sources is a basic problem in wave physics. We show that the timedomain energy flux radiated from electromagnetic and acoustic subwalength sources exhibits remarkable features. In particular, a subtle tradeoff between source emission and absorption underlies the mechanism of radiation. This behavior should be observed for any kind of classical waves, thus having broad potential implications. We discuss the implication for subwavelength focusing by time reversal with active sources. Copyright © EPLA, 2012.


CramerRao analysis of steadystate and timedomain fluorescence diffuse optical imaging Boffety, M., M. Allain, A. Sentenac, M. Massonneau, and R. Carminati Biomedical Optics Express 2, no. 6, 16261636 (2011)
Abstract: Using a CramerRao analysis, we study the theoretical performances of a time and spatially resolved fDOT imaging system for jointly estimating the position and the concentration of a pointwide fluorescent volume in a diffusive sample. We show that the fluorescence lifetime is a critical parameter for the precision of the technique. A time resolved fDOT system that does not use spatial information is also considered. In certain cases, a simple steadystate configuration may be as efficient as this time resolved fDOT system. © 2011 Optical Society of America.
Keywords: Critical parameter; Diffuse optical imaging; Fluorescence lifetimes; Spatial informations; Spatially resolved; Theoretical performance; Time domain; Timeresolved; Fluorescence; Time domain analysis


Nearfield correlations and fluctuations in multiple scattering of light Carminati, R. AIP Conference Proceedings 1398, 1920 (2011)
Abstract: The analysis of the photonic properties of disordered media structured at a submicron scale combines nanophotonics with light transport in the multiple scattering regime. We show that nearfield interactions are fundamental in the analysis of speckle patterns observed at subwavelength distance from boundaries, or produced by nanosources immersed inside the scattering medium, as well as for the description of fluctuations of the local density of optical states. © 2011 American Institute of Physics.
Keywords: Disordered media; local density of states; multiple scattering; near field; speckle correlations


Luminescence diffuse optical tomography on a reflectance imaging setup Boffety, M., M. Allain, A. Sentenac, M. Massonneau, and R. Carminati 2011 Conference on Lasers and ElectroOptics Europe and 12th European Quantum Electronics Conference, CLEO EUROPE/EQEC 2011 (2011)
Abstract: Luminescence diffuse optical tomography has become a valuable tool in optical molecular imaging. As an actor of this recent field, the French company Quidd has developed a luminescence reflectance imaging system for small animal in vivo imaging. In previous studies, we have determined the potential and the limits of such approaches for the determination of the depth of fluorophores/bioluminescent substrates in tissues [1,2]. In the present work, we demonstrate the first reconstructions on test samples. For this study, we use a prototype of the Quidd Optical System (QOS) as well as calibrated phantom (cf. Fig. 1) and source. The optical detection setup is composed of a cooled CCD camera with a telecentric lens. The camera can be translated along the z and x axes and rotated with an angular amplitude of 120. The phantom is a diffusive epoxy resin hemisphere whose optical properties are given in Fig. 1 for 635 nm. An optical fiber inserted inside the phantomand connected to an hallogen lamp with a 635 nm filter is used to modelized a pointlike isotropic bioluminescent source. The output measured power of the fiber is 5 mW. The lighttransport (forward) model relies on the diffusion equation and the inverse problem is solved using a leastsquares criterion. The optimization method [3] is easy and fast to implement, and does not use an explicit Tikhonov regularization. Our aim is to localize the bioluminescent pointlike source inside the phantom, and to reconstruct its power. Three experiments were performed for three positions of the fiber. In each case, a single reflectance image was taken with the camera right above the phantom. The results given by the algorithm are gathered in the following figure: the sources are located with submillimiter precision and their power is estimated with a fairly good accuracy © 2011 IEEE.
Keywords: Angular amplitude; Cooled CCD; Diffuse optical tomography; Diffusion equations; French companies; InVivo imaging; Least Square; Optical detection; Optical molecular imaging; Optimization method; Reflectance images; Reflectance imaging; Small Animal; Test samples; Tikhonov regularization; Bioluminescence; CCD cameras; Electron optics; Epoxy resins; Inverse problems; Lenses; Light; Optical fibers; Optical systems; Optical tomography; Optics; Partial differential equations; Quantum electronics; Re


Intrinsic precision limit in steadystate and timedomain fluorescence diffuse optical imaging Boffety, M., M. Allain, A. Sentenac, M. Massonneau, and R. Carminati 2011 Conference on Lasers and ElectroOptics Europe and 12th European Quantum Electronics Conference, CLEO EUROPE/EQEC 2011 (2011)
Abstract: The precision limit for the considered setups are depicted below. For TD and ITD fDOT, we note that (i) the accuracy of the depth estimation decreases with the depth of the fluorescent volume and (ii) this accuracy substatially depends on the fluorescence lifetime . The longer the lifetime, the poorer the precision limit. Moreover, for realistic lifetime, the CW and the ITD setups in reflection geometry achieve comparable precision limits. © 2011 IEEE.
Keywords: Depth Estimation; Diffuse optical imaging; Fluorescence lifetimes; Precision limits; Reflection geometry; Time domain; Electron optics; Optics; Quantum electronics; Fluorescence


Enhanced lightmatter interaction at the nanoscale using localized plasmon modes on disordered metallic films Carminati, R., E. Castanié, V. Krachmalnicoff, A. Cazé, R. Pierrat, and Y. De Wilde 2011 Conference on Lasers and ElectroOptics Europe and 12th European Quantum Electronics Conference, CLEO EUROPE/EQEC 2011 (2011)
Abstract: Disordered semicontinuous metallic films are a particularly striking example of complex photonic systems. They exhibit peculiar optical properties that cannot be explained from the behavior of bulk metals or ensembles of isolated nanoparticles [1]. The interplay between surfaceplasmon excitations and scattering by multiscale (fractal) metallic clusters leads to spatial localization of the electromagnetic field in subwavelength areas (hot spots). A feature of these hotspots modes is the expected coexistence of both localized and delocalized modes at the same frequency [2,3], a situation referred to as inhomogeneous localization. © 2011 IEEE.
Keywords: Bulk metals; Hot spot; Hotspots; Lightmatter interactions; Metallic clusters; Multiscales; Nano scale; Photonic systems; Plasmon modes; Semicontinuous; Spatial localization; Subwavelength; Surface plasmon excitation; Electromagnetic fields; Electron optics; Metallic films; Optical properties; Optics; Quantum electronics; Plasmons


Transmission matrix in optics: Taking advantage of transmission channels for image transmission in disordered materials Popoff, S. M., G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan 2011 Conference on Lasers and ElectroOptics Europe and 12th European Quantum Electronics Conference, CLEO EUROPE/EQEC 2011 (2011)
Abstract: Recently, a method has been proposed by I. Vellekoop et al. [1] to focus light through a multiple scattering material, using a spatial light modulator as a tool to shape the incoming beam to obtain a maximal interference on a speckle spot of the output speckle pattern. The result is a bright, diffraction limited, spot which can be several hundred times brighter than the rest of the speckle. © 2011 IEEE.
Keywords: Diffraction limited; Disordered materials; Spatial light modulators; Speckle patterns; Transmission channels; Transmission matrix; Electron optics; Light modulators; Optics; Quantum electronics; Speckle; Light


Longtail statistics of the purcell factor in disordered media driven by nearfield interactions Sapienza, R., P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. Van Hulst Physical Review Letters 106, no. 16 (2011)
Abstract: In this Letter, we study the Purcell effect in a 3D disordered dielectric medium through fluorescence decay rates of nanosized light sources. We report distributions of Purcell factor with nonGaussian longtailed statistics and an enhancement of up to 8 times the average value. We attribute this large enhancement to strong fluctuations of the local density of states induced by nearfield scattering sustained by more than one particle. Our findings go beyond standard diagrammatic and singlescattering models and can be explained only by taking into account the full nearfield interaction. © 2011 American Physical Society.
Keywords: Average values; Disordered dielectrics; Disordered media; Fluorescence decays; Local density of state; Nanosized; Near field interactions; Nearfield scattering; NonGaussian; Purcell effect; Purcell factor; Singlescattering model; Light sources; Dielectric materials


Magnetooptical control of Förster energy transfer Vincent, R., and R. Carminati Physical Review B  Condensed Matter and Materials Physics 83, no. 16 (2011)
Abstract: We introduce a general framework to study dipoledipole energy transfer between an emitter and an absorber in a nanostructured environment. The theory allows us to address Förster resonant energy transfer (FRET) between a donor and an acceptor in the presence of a nanoparticle with an anisotropic electromagnetic response. In the particular case of a magnetooptical anisotropy, we compute the generalized FRET rate and discuss the orders of magnitude. The distance dependence, the FRET efficiency, and the sensitivity to the orientation of the transition dipoles orientation differ from standard FRET and can be controlled using the static magnetic field as an external parameter. © 2011 American Physical Society.


Magnetooptical control of förster energy transfer Vincent, R., and R. Carminati AIP Conference Proceedings 1291, 9396 (2010)
Abstract: We study dipoledipole energy transfer between an emitter and an absorber in the presence of a nanoparticle with an anisotropic dielectric response. We demonstrate that the presence of the nanoparticle modifies the Förster Resonant Energy Transfer (FRET), and we present a general framework to deal with systems involving a donoracceptor couple and a nanostructure. In the particular case of a magnetooptical nanoparticle, for which the anisotropy can be tuned by an external magnetic field, we compute the generalized FRET rate and discuss the orders of magnitude. We show that the distance dependence can be different from the R 6 law of standard FRET. © 2010 American Institute of Physics.
Keywords: Fluorescence; FRET; Magnetooptics; Nanoparticle; Quenching.; Single molecule


Nearfield interactions and fluctuations of the local density of states in a strongly scattering environment Pierrat, R., A. Cazé, and R. Carminati AIP Conference Proceedings 1291, 8587 (2010)
Abstract: We study the local density of states (LDOS) statistics near a dipole emitter embedded in a strongly scattering medium. We perform numerical simulations that emphasize the fact that LDOS fluctuations are strongly affected by the local environment of the emitter and is very sensitive to nearfield interactions and correlation of disorder. © 2010 American Institute of Physics.
Keywords: Local density of states; Nearfield; Strongly scattering medium


Fluctuations of the local density of states probe localized surface plasmons on disordered metal films Krachmalnicoff, V., E. Castanié, Y. De Wilde, and R. Carminati Physical Review Letters 105, no. 18 (2010)
Abstract: We measure the statistical distribution of the local density of optical states (LDOS) on disordered semicontinuous metal films. We show that LDOS fluctuations exhibit a maximum in a regime where fractal clusters dominate the film surface. These large fluctuations are a signature of surfaceplasmon localization on the nanometer scale. © 2010 The American Physical Society.
Keywords: Disordered metals; Film surfaces; Fractal clusters; Local density; Local density of state; Localized surface plasmon; Nanometer scale; Optical state; Semicontinuous metal films; Statistical distribution; Surfaceplasmon; Metallic films; Plasmons; Optical data storage


Nearfield interactions and nonuniversality in speckle patterns produced by a point source in a disordered medium Cazé, A., R. Pierrat, and R. Carminati Physical Review A  Atomic, Molecular, and Optical Physics 82, no. 4 (2010)
Abstract: A point source in a disordered scattering medium generates a speckle pattern with nonuniversal features, giving rise to the socalled C0 correlation. We analyze theoretically the relationship between the C0 correlation and the statistical fluctuations of the local density of states, based on simple arguments of energy conservation. This derivation leads to a clear physical interpretation of the C0 correlation. Using exact numerical simulations, we show that C0 is essentially a correlation resulting from nearfield interactions. These interactions are responsible for the nonuniversality of C0 that confers to this correlation a huge potential for sensing and imaging at the subwavelength scale in complex media. © 2010 The American Physical Society.
Keywords: Complex media; Disordered medium; Local density of state; Near field interactions; Nonuniversality; Numerical simulation; Physical interpretation; Point sources; Scattering medium; Sensing and imaging; Speckle patterns; Statistical fluctuations; Subwavelength scale; Ferroelectric materials; Speckle; Correlation methods


Measuring and exploiting the transmission matrix in optics Popoff, S. M., G. Lerosey, R. Carminati, M. Fink, A. C. Boceara, and S. Gigan Lasers and ElectroOptics/Quantum Electronics and Laser Science Conference: 2010 Laser Science to Photonic Applications, CLEO/QELS 2010 (2010)
Abstract: We introduce a method to measure the transmission matrix of a complex medium. This matrix exhibits statistical properties in good agreement with random matrix theory and allows light focusing and imaging through the random medium. ©2010 IEEE.
Keywords: Complex medium; Light focusing; matrix; Random matrix theory; Random medium; Statistical properties; Transmission matrix


Theory of infrared nanospectroscopy by photothermal induced resonance Dazzi, A., F. Glotin, and R. Carminati Journal of Applied Physics 107, no. 12 (2010)
Abstract: We present a theoretical investigation of the physics involved in a recently developed spectromicroscopy technique, called photothermal induced resonance (PTIR). With this technique, one measures the local infrared absorption spectrum of a sample shined with a tunable infrared laser pulse, and detects the induced photothermal expansion with the tip of an atomic force microscope (AFM). Simple physical assumptions allow us to describe analytically the heating and expansion of the sample, the excitation of the vibration modes of the AFM cantilever, and the detected signal. We show that the signal depends on the thermal expansion velocity rather than on the absolute displacement of the tip, and we investigate the influence of the laser pulse length. Eventually, we express the PTIR signal in terms of relevant parameters, and prove its proportionality to the sample absorbance. This analytical approach complement our experimental results and validates the PTIR method as a technique of choice for infrared spectroscopy of nanoscopic samples, getting around optical artifacts like reflectance perturbation. © 2010 American Institute of Physics.
Keywords: Absolute displacement; Absorbances; AFM cantilevers; Analytical approach; Atomic force microscopes; Photothermal; Photothermal expansion; Physical assumptions; Spectromicroscopy; Theoretical investigations; Tunable infrared laser; Vibration modes; Absorption spectroscopy; Atomic force microscopy; Atomic spectroscopy; Infrared lasers; Infrared spectroscopy; Laser pulses; Photolithography; Pulsed laser applications; Resonance; Vibration analysis; Thermal expansion


Spontaneous decay rate of a dipole emitter in a strongly scattering disordered environment Pierrat, R., and R. Carminati Physical Review A  Atomic, Molecular, and Optical Physics 81, no. 6 (2010)
Abstract: We study the statistics of the fluorescence decay rate of a dipole emitter embedded in a strongly scattering medium. In the multiplescattering regime, the probability of observing a decrease in the decay rate is substantial, as predicted by exact numerical simulations. The decrease originates from a reduction of the local density of optical states and is due to collective interactions and interferences. In the strongscattering regime, signatures of recurrent scattering are visible in the behavior of the average decay rate. © 2010 The American Physical Society.
Keywords: Decay rate; Fluorescence decays; Local density; Numerical simulation; Optical state; Scattering medium; Scattering regime; Spontaneous decay rates; Computer simulation; Decay (organic); Optical waveguides; Scattering


Subwavelength spatial correlations in nearfield speckle patterns Carminati, R. Physical Review A  Atomic, Molecular, and Optical Physics 81, no. 5 (2010)
Abstract: At subwavelength distance from the exit surface of a disordered medium, speckle patterns generated by multiple scattering of waves exhibit nonuniversal nearfield correlations. A calculation of the field spatial correlation function shows that the correlation length is driven by the microscopic structure of the medium. The averaged speckle spot size can be smaller than the wavelength, even for nonresonant dielectric media. © 2010 The American Physical Society.
Keywords: Correlation lengths; Disordered medium; Microscopic structures; Nearfield; Nearfield speckles; Nonresonant dielectrics; Spatial correlation functions; Spatial correlations; Speckle patterns; Spot sizes; Subwavelength; Speckle


Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media Popoff, S. M., G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan Physical Review Letters 104, no. 10 (2010)
Abstract: We introduce a method to experimentally measure the monochromatic transmission matrix of a complex medium in optics. This method is based on a spatial phase modulator together with a fullfield interferometric measurement on a camera. We determine the transmission matrix of a thick random scattering sample. We show that this matrix exhibits statistical properties in good agreement with random matrix theory and allows light focusing and imaging through the random medium. This method might give important insight into the mesoscopic properties of a complex medium. © 2010 The American Physical Society.
Keywords: Complex medium; Disordered media; Fullfield; Interferometric measurement; matrix; Mesoscopic properties; Random matrix theory; Random medium; Random scattering; Spatial phase modulator; Statistical properties; Transmission matrix; Light; Light propagation; Light transmission


Controlling the quantum yield of a dipole emitter with coupled plasmonic modes Vandenbem, C., D. Brayer, L. S. FroufePérez, and R. Carminati Physical Review B  Condensed Matter and Materials Physics 81, no. 8 (2010)
Abstract: We study theoretically the possibility of controlling the quantum yield of a single dipole emitter using coupled plasmonic modes. Plasmon hybridization offers spectral and spatial degrees of freedom that can be used to tune the spontaneous decay rate and the apparent quantum yield with high sensitivity. We demonstrate this concept on simple structures that could be implemented experimentally. © 2010 The American Physical Society.


Radiative corrections to the polarizability tensor of an electrically small anisotropic dielectric particle Albaladejo, S., R. GómezMedina, L. S. FroufePérez, H. Marinchio, R. Carminati, J. F. Torrado, G. Armelles, A. GarcíaMartín, and J. J. Sáenz Optics Express 18, no. 4, 35563567 (2010)
Abstract: Radiative corrections to the polarizability tensor of isotropic particles are fundamental to understand the energy balance between absorption and scattering processes. Equivalent radiative corrections for anisotropic particles are not well known. Assuming that the polarization within the particle is uniform, we derived a closedform expression for the polarizability tensor which includes radiative corrections. In the absence of absorption, this expression of the polarizability tensor is consistent with the optical theorem. An analogous result for infinitely long cylinders was also derived. Magneto optical Kerr effects in nonabsorbing nanoparticles with magnetooptical activity arise as a consequence of radiative corrections to the electrostatic polarizability tensor. © 2010 Optical Society of America.
Keywords: Anisotropic dielectrics; Anisotropic particles; Closedform expression; Isotropic particles; Magnetooptical activity; Magnetooptical Kerr effects; Optical theorem; Polarizability tensor; Radiative corrections; Scattering process; Absorption; Anisotropy; Gene expression; High energy physics; Kerr magnetooptical effect; Magnetic field effects; Magnetos; Tensors; Optical Kerr effect; anisotropy; article; computer simulation; electromagnetic field; impedance; particle size; radiation dose; radiati


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)
Abstract: 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.
Keywords: 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


Fluorescence quenching by a metal nanoparticle in the extreme nearfield regime Castanié, E., M. Boffety, and R. Carminati Optics Letters 35, no. 3, 291293 (2010)
Abstract: We study the spontaneous decay rate of a dipóle emitter close to a metallic nanoparticle in the extreme nearfield regime. The metal is modeled using a nonlocal dielectric function that accounts for the microscopic length scales of the free electron gas. We describe quantitatively the crossover between the macroscopic and microscopic regimes and the enhanced nonradiative decay due to microscopic interactions. Our theory is in agreement with results previously established in the asymptotic near and farfield regimes. © 2010 Optical Society of America.
Keywords: Dielectric functions; Farfield; Fluorescence quenching; Free electron gas; Metal nanoparticles; Metallic nanoparticles; Microscopic interaction; Microscopic length scale; Nearfield; Nonlocal; Nonradiative decays; Spontaneous decay rates; Decay (organic); Electron gas; Nanoparticles


Fluorescence signal of a single emitter coupled to a nanoparticle through a plasmonic film Vandenbem, C., L. S. FroufePérez, and R. Carminati Journal of Optics A: Pure and Applied Optics 11, no. 11 (2009)
Abstract: We study theoretically the detection of the fluorescence intensity emitted by a single emitter coupled to a nanoparticle through a metallic thin film. The coupling results from the overlap of the surface plasmon modes propagating on each interface of the film. We show that the distance between the nanoparticle and the film can be used to tune the apparent quantum yield and the radiation pattern with nanometerscale sensitivity. Such a system is appealing from the experimental point of view since it involves simple structures that can be controlled using current scanning nearfield optical techniques. It could be used to improve the detection sensitivity of molecules embedded in substrates, or to design sensitive biological or chemical plasmonic sensors. © 2009 IOP Publishing Ltd.
Keywords: Fluorescence; Molecular imaging; Plasmons; Quenching; Single molecule; Detection sensitivity; Fluorescence intensities; Fluorescence molecular; Fluorescence signals; Metallic thin films; Molecular imaging; Nanometerscale; Nearfield; Optical technique; Plasmonic sensors; Radiation patterns; Simple structures; Single emitter; Single molecule; Surface plasmon modes; Fluorescence; Molecules; Optical data storage; Plasmons; Quenching; Nanoparticles


Single molecule fluorescence quenching by metallic nanoparticles: Crossover between macroscopic and microscopic interactions Castanié, E., M. Boffety, and R. Carminati AIP Conference Proceedings 1176, 4951 (2009)
Abstract: We study the spontaneous decay rate of a single molecule close to a metallic nanopartiele in the extreme nearfield regime. The electrodynamic response of the metal is modelled using a noulocal dielectric constant, that accounts for the relevant microscopic length scales. We describe quantitatively the crossover between the macroscopic and microscopic regimes. In the case of silver, for a nanoparlielc with radius 25 nm. the transition occurs for a distance between the emitter and the metal surface on the order of 10 nm. We show that below this distance, the nonradiative decay rate and the quenching efficiency are enhanced due to the nonlocal interaction. © 2009 American Institute of Physics.
Keywords: Fluorescence; Nanoparticle; Quenching; Single molecule


Threshold of a random laser with cold atoms FroufePérez, L. S., W. Guerin, R. Carminati, and R. Kaiser Physical Review Letters 102, no. 17 (2009)
Abstract: We address the problem of achieving an optical random laser with a cloud of cold atoms, in which gain and scattering are provided by the same atoms. The lasing threshold can be defined using the onresonance optical thickness b0 as a single critical parameter. We predict the threshold quantitatively, as well as power and frequency of the emitted light, using two different light transport models and the atomic polarizability of a strongly pumped twolevel atom. We find a critical b0 on the order of 300, which is within reach of stateoftheart coldatom experiments. Interestingly, we find that random lasing can already occur in a regime of relatively low scattering. © 2009 The American Physical Society.
Keywords: Atomic polarizability; Cold atoms; Critical parameter; Emitted light; Lasing threshold; Light transport model; Optical thickness; Random lasers; Random lasing; Twolevel atom; Laser beams; Atoms


Density of states and extinction mean free path of waves in random media: Dispersion relations and sum rules Carminati, R., and J. J. Sáenz Physical Review Letters 102, no. 9 (2009)
Abstract: We establish a fundamental relationship between the averaged local density of states and the extinction mean free path of waves propagating in random media. From the principle of causality and the KramersKronig relations, we show that both quantities are connected by dispersion relations and are constrained by a frequency sum rule. The results should be helpful in the analysis of wave transport through complex media and in the design of materials with specific transport properties. © 2009 The American Physical Society.
Keywords: Transport properties; Complex medias; Density of state; Dispersion relations; KramersKronig relations; Local density of state; Mean free paths; Random medias; Sum rules; Wave transports; Quantum theory


Analysis of the depth resolution limit of luminescence diffuse optical imaging Boffety, M., M. Allain, A. Sentenac, M. Massonneau, and R. Carminati Optics Letters 33, no. 20, 22902292 (2008)
Abstract: We introduce a methodology to determine quantitatively the depth resolution limit in luminescence diffuse optical imaging. The approach is based on a CramerRao statistical analysis, a noise model, and calculations of photon transport in tissues. We illustrate the method in the case of luminescence imaging in a brainskull model, showing its potential applications in molecular imaging on small animals. © 2008 Optical Society of America.
Keywords: Light emission; Luminescence; Optical image storage; Optical variables measurement; Depth resolutions; Diffuse optical imaging; Luminescence imaging; Molecular imaging; Noise models; Photon transports; Potential applications; Skull models; Small animals; Statistical analysis; Light sources


Controlling the fluorescence lifetime of a single emitter on the nanoscale using a plasmonic superlens FroufePérez, L. S., and R. Carminati Physical Review B  Condensed Matter and Materials Physics 78, no. 12 (2008)
Abstract: Coupling a single dipole emitter to a metallic nanoparticle through the optical modes of a planar superlens made of lefthanded material can lead to substantial modifications of its spontaneous decay rate. We provide a quantitative study based on exact numerical simulation and show that such a scheme could allow the detection, the localization, and the control of the emitter dynamics with nanometerscale sensitivity, as well as the determination of its transition dipole orientation. © 2008 The American Physical Society.


Lifetime fluctuations of a single emitter in a disordered nanoscopic system: The influence of the transition dipole orientation FroufePérez, L. S., and R. Carminati Physica Status Solidi (A) Applications and Materials Science 205, no. 6, 12581265 (2008)
Abstract: We study the fluctuations of the fluorescence decay rate of a single emitter in a random cluster of nanoparticles, in a regime dominated by nearfield scattering. Configurational changes of the environment induce statistical changes of the decay rate. Two regimes are considered which differ in terms of transition dipole orientation. In one regime, the orientation of the transition dipole is assumed to remain constant while the configuration of the cluster changes randomly. In another regime, the orientation of the transition dipole is assumed unknown and continuously averaged over the three directions of space. Using exact numerical simulations and a simple analytical model, we show that the statistical distributions of the spontaneous decay rate are substantially different in both regimes. In both cases, the decay rate fluctuations are strongly dependent on the level of absorption at the nanoscale. We discuss the impact of this result in terms of imaging in complex media. © 2008 WILEYVCH Verlag GmbH & Co. KGaA.
Keywords: Analytical models; Complex medias; Decay rates; Fluorescence decay rates; Imaging; Nanoscale; Nanoscopic systems; Nearfield; Numerical simulations; Random clusters; Spontaneous decay rates; Statistical distributions; Three directions; Transition dipoles; Absorption; Computer simulation; Molecular vibrations; Nanotechnology; Optical waveguides; Statistical methods; Decay (organic)


Theory of the time reversal cavity for electromagnetic fields Carminati, R., R. Pierrat, J. De Rosny, and M. Fink Optics Letters 32, no. 21, 31073109 (2007)
Abstract: We derive a general expression of the electric dyadic Green function in a timereversal cavity, based on vector diffraction theory in the frequency domain. Our theory gives a rigorous framework to timereversal experiments using electromagnetic waves and suggests a methodology to design structures generating subwavelength focusing after time reversal. © 2007 Optical Society of America.
Keywords: Diffraction; Electromagnetic waves; Frequency domain analysis; Green's function; Microcavities; Time reversal cavity; Electromagnetic fields


Thermal radiation scanning tunnelling microscopy De Wilde, Y., F. Formanek, R. Carminati, B. Gralak, P.A. Lemoine, K. Joulain, J.P. Mulet, Y. Chen, and J.J. Greffet Nature 444, no. 7120, 740743 (2006)
Abstract: In standard nearfield scanning optical microscopy (NSOM), a subwavelength probe acts as an optical 'stethoscope' to map the near field produced at the sample surface by external illumination. This technique has been applied using visible, infrared, terahertz and gigahertz radiation to illuminate the sample, providing a resolution well beyond the diffraction limit. NSOM is well suited to study surface waves such as surface plasmons or surfacephonon polaritons. Using an aperture NSOM with visible laser illumination, a nearfield interference pattern around a corral structure has been observed, whose features were similar to the scanning tunnelling microscope image of the electronic waves in a quantum corral. Here we describe an infrared NSOM that operates without any external illumination: it is a nearfield analogue of a nightvision camera, making use of the thermal infrared evanescent fields emitted by the surface, and behaves as an optical scanning tunnelling microscope. We therefore term this instrument a 'thermal radiation scanning tunnelling microscope' (TRSTM). We show the first TRSTM images of thermally excited surface plasmons, and demonstrate spatial coherence effects in nearfield thermal emission. ©2006 Nature Publishing Group.
Keywords: diffraction; scanning tunnelling microscopy; temperature effect; article; illumination; infrared radiation; microscope; near field scanning optical microscopy; priority journal; radiation; scanning tunneling microscopy; signal detection; surface plasmon resonance; thermal radiation scanning tunneling microscopy


Modal representation of spatial coherence in dissipative and resonant photonic systems Sauvan, C., J. P. Hugonin, R. Carminati, and P. Lalanne Physical Review A 89, no. 4 (2014)

