Optical Speckle Field Research Articles

Optimized Stokes imaging for highly resolved optical speckle fields, Part III: topological analysis of polarimetric state distributions with optimized data representations

In this last article of a three-paper series focusing on Stokes polarimetry of optical speckle fields resolved at the individual speckle grain scale, experimental results are provided on test samples of varying nature and polarization properties, and are analyzed extensively. For this purpose, a review of the classical ways of displaying Stokes polarimetric information is provided. Then, some original alternative graphical representations are introduced that ensure optimal readability and interpretability of the Stokes imaging data in the context of speckle field polarimetry, and it is shown how they can be adapted to various observation scales. Finally, these tools are implemented in order to provide a topological analysis of the distribution of the states of polarization across a speckle pattern, and in the vicinity of polarimetric singularities of the field.

Optimized Stokes imaging for highly resolved optical speckle fields, Part I: optimized experimental setup

In this first article of a three-part series focusing on the Stokes polarimetry of optical speckle fields resolved at the individual speckle grain scale, a review of the state-of-the-art techniques for such experimental investigations is provided. An optimized experimental setup is then extensively described, which allows polarimetric Stokes measurements on such complex interference patterns to be carried out at each location of the speckle field without disturbing the wavefront. Specific calibration procedures are also described to provide an estimation of the reliable polarimetric properties of light across a resolved speckle field.

Optimized Stokes imaging for highly resolved optical speckle fields, Part II: optimal acquisition and estimation strategies

In this second paper of a three-paper series focusing on Stokes polarimetry of optical speckle fields resolved at the individual speckle grain scale, a theoretical study based on numerical simulations is presented in order to establish the optimum sensing, estimation, and processing strategies that guarantee the best precision, accuracy, and robustness for Stokes polarimetry in this specific context. In particular, it is demonstrated that the so-called state of polarization analysis by full projection on the Poincaré space (SOPAFP) approach can be optimized in order to ensure best estimation performance. These numerical simulations also make it possible to establish that the SOPAFP approach provides better results in terms of robustness to residual experimental imperfections of the setup when compared to classical Stokes polarimetry approaches.

Solving classification tasks by a receptron based on nonlinear optical speckle fields

Among several approaches to tackle the problem of energy consumption in modern computing systems, two solutions are currently investigated: one consists of artificial neural networks (ANNs) based on photonic technologies, the other is a different paradigm compared to ANNs and it is based on random networks of non-linear nanoscale junctions resulting from the assembling of nanoparticles or nanowires as substrates for neuromorphic computing. These networks show the presence of emergent complexity and collective phenomena in analogy with biological neural networks characterized by self-organization, redundancy, and non-linearity. Starting from this background, we propose and formalize a generalization of the perceptron model to describe a classification device based on a network of interacting units where the input weights are non-linearly dependent. We show that this model, called “receptron”, provides substantial advantages compared to the perceptron as, for example, the solution of non-linearly separable Boolean functions with a single device. The receptron model is used as a starting point for the implementation of an all-optical device that exploits the non-linearity of optical speckle fields produced by a solid scatterer. By encoding these speckle fields we generated a large variety of target Boolean functions. We demonstrate that by properly setting the model parameters, different classes of functions with different multiplicity can be solved efficiently. The optical implementation of the receptron scheme opens the way for the fabrication of a completely new class of optical devices for neuromorphic data processing based on a very simple hardware.

Fickian yet non-Gaussian diffusion of a quasi-2D colloidal system in an optical speckle field: experiment and simulations

We investigate a quasi-2D suspension of Brownian particles in an optical speckle field produced by holographic manipulation of a laser wavefront. This system was developed to study, in a systematic and controllable way, a distinctive instance of diffusion, called Fickian yet Non Gaussian diffusion (FnGD), observed, during the last decade, for colloidal particles in a variety of complex and biological fluids. Our setup generates an optical speckle field that behaves like a disordered set of optical traps. First, we describe the experimental setup and the dynamics of the particles, focusing on mean square displacements, displacement distributions and kurtosis. Then, we present Brownian Dynamics simulations of point-like particles in a complex energy landscape, mimicking that generated by the optical speckle field. We show that our simulations can capture the salient features of the experimental results, including the emergence of FnGD, also covering times longer than the ones so far achieved in experiments. Some deviations are observed at long time only, with the Gaussian restoring being slower in simulations than in experiments. Overall, the introduced numerical model might be exploited to guide the design of upcoming experiments targeted, for example, to fully monitor the recovery of Gaussianity.

Imaging of the skin microvascularization using spatially depolarized dynamic speckle.

.SignificanceWe propose a technique devoted to real-time high-resolution imaging of skin microvascularization.AimThe process utilizes the temporal variation of the spatially depolarized optical speckle field generated by moving red blood cells when illuminated with fully polarized coherent light.ApproachPolarimetric filtering prevents the contribution of surface scattering from reaching the camera and thus favors the detection of multiscattered photons from the deeper layers of the skin.ResultsFull-field images reveal the microvasculature with a spatial resolution of . The acquisition speed allows for real-time applications.ConclusionsWe demonstrate the ability of this method to determine in 1 s a stable and reliable microvascular activity, enabling numerous clinical applications that require quantitative measurements.

Generation of Non-Rayleigh Nondiffracting Speckles.

Optical speckle fields with both non-Rayleigh statistics and nondiffracting characteristics in propagation are an important light source for many applications. However, tailoring either non-Rayleigh statistical speckles or nondiffracting speckles are only investigated independently in previous studies. Here, we report the first observation of optical speckles that remain diffraction-free over a long axial distance while keeping non-Rayleigh statistics simultaneously. We further show the enhancement of Anderson localization of light with the non-Rayleigh nondiffracting speckles. The work presented here provides a versatile framework for customizing optical fields with desired speckle patterns for applications in the fields of solid-state physics, cold atoms, and optical imaging.

Random object optical field diagnostics by using carbon nanoparticles.

We propose a new approach of using carbon nanoparticles for correlation optical diagnostics of а complex scalar optical field created by scattering and diffraction of radiation off a rough surface. This surface is simulated and we generate a diffraction pattern of the amplitude and phase distribution in the far field. Carbon nanoparticles of a certain size and concentration are obtained by the bottom-up methods of hydrothermal synthesis of citric acid and urea followed by centrifugation. The optical properties of carbon nanoparticles, such as luminescence and absorption in the visible spectrum that essentially differs for different wavelengths, as well as particle size of about dozen nanometers, are the determining criteria for using these particles as probes for the optical speckle field. Luminescence made it possible to register the coordinate position of carbon nanoparticles in real time. The algorithm for reconstruction of the scalar optical field intensity distribution through the analysis of the nanoparticle positions is here displayed. The skeleton of the optical speckle field is analyzed by Hilbert transform to restore the phase. Special attention is paid to the restoration of the speckle field's phase singularities.

Carbon Nanoparticles. Production, properties, perspectives of use

The paper is devoted to the study of the optical properties of carbon nanoparticles synthesized by the method developed during our experimental studies. The optimal conditions for the creation of carbon nanostructures with predetermined properties are defined. Nanoparticles of the size of about 100 nm were obtained, the maximum of absorption of which is localized at wavelengths in the violet-blue region of the spectrum, while the maximum of luminescence – in the green region of the spectrum. The assumption is made about the possibility of using the obtained particles for correlation diagnostics of optical speckle fields.

In vivo measurement of organelle motility in human retinal pigment epithelial cells.

Retinal pigment epithelial (RPE) cells are well known to play a central role in the progression of numerous retinal diseases. Changes in the structure and function of these cells thus may serve as sensitive biomarkers of disease onset. While in vivo studies have focused on structural changes, functional ones may better capture cell health owing to their more direct connection to cell physiology. In this study, we developed a method based on adaptive optics optical coherence tomography (AO-OCT) and speckle field dynamics for characterizing organelle motility in individual RPE cells. We quantified the dynamics in terms of an exponential decay time constant, the time required for the speckle field to decorrelate. Using seven normal subjects, we found the RPE speckle field to decorrelate in about 5 s. This result has two fundamental implications for future clinical use. First, it establishes a path for generating a normative baseline to which motility of diseased RPE cells can be compared. Second, it predicts an AO-OCT image acquisition time that is 36 times faster than used in our earlier report for individuating RPE cells, thus a major improvement in clinical efficacy.

Few-boson localization in a continuum with speckle disorder

The disorder-induced localization of few bosons interacting via a contact potential is investigated through the analysis of the level-spacing statistics familiar from random matrix theory. The model we consider is defined in a continuum and describes one-dimensional bosonic atoms exposed to the spatially correlated disorder due to an optical speckle field. % First, we identify the speckle-field intensity required to observe, in the single-particle case, the Poisson level-spacing statistics, which is characteristic of localized quantum systems, in a computationally and experimentally feasible system size. Then, we analyze the two-body and the three-body systems, exploring a broad interaction range, from the noninteracting limit up to moderately strong interactions. Our main result is that the contact potential does not induce a shift towards the Wigner-Dyson level-spacing statistics, which would indicate the emergence of an ergodic chaotic state, indicating that localization can occur also in interacting few-body systems in a continuum. We also analyze how the ground-state energy evolves as a function of the interaction strength

Supervised machine learning of ultracold atoms with speckle disorder

We analyze how accurately supervised machine learning techniques can predict the lowest energy levels of one-dimensional noninteracting ultracold atoms subject to the correlated disorder due to an optical speckle field. Deep neural networks with different numbers of hidden layers and neurons per layer are trained on large sets of instances of the speckle field, whose energy levels have been preventively determined via a high-order finite difference technique. The Fourier components of the speckle field are used as the feature vector to represent the speckle-field instances. A comprehensive analysis of the details that determine the possible success of supervised machine learning tasks, namely the depth and the width of the neural network, the size of the training set, and the magnitude of the regularization parameter, is presented. It is found that ground state energies of previously unseen instances can be predicted with an essentially negligible error given a computationally feasible number of training instances. First and second excited state energies can be predicted too, albeit with slightly lower accuracy and using more layers of hidden neurons. We also find that a three-layer neural network is remarkably resilient to Gaussian noise added to the training-set data (up to 10% noise level), suggesting that cold-atom quantum simulators could be used to train artificial neural networks.

Measurement of Spectral Functions of Ultracold Atoms in Disordered Potentials.

We report on the measurement of the spectral functions of noninteracting ultracold atoms in a three-dimensional disordered potential resulting from an optical speckle field. Varying the disorder strength by 2 orders of magnitude, we observe the crossover from the "quantum" perturbative regime of low disorder to the "classical" regime at higher disorder strength, and find an excellent agreement with numerical simulations. The method relies on the use of state-dependent disorder and the controlled transfer of atoms to create well-defined energy states. This opens new avenues for experimental investigations of three-dimensional Anderson localization.

Structuring Stokes correlation functions using vector-vortex beam

Higher order statistical correlations of the optical vector speckle field, formed due to scattering of a vector-vortex beam, are explored. Here, we report on the experimental construction of the Stokes parameters covariance matrix, consisting of all possible spatial Stokes parameters correlation functions. We also propose and experimentally realize a new Stokes correlation functions called Stokes field auto correlation functions. It is observed that the Stokes correlation functions of the vector-vortex beam will be reflected in the respective Stokes correlation functions of the corresponding vector speckle field. The major advantage of proposing Stokes correlation functions is that the Stokes correlation function can be easily tuned by manipulating the polarization of vector-vortex beam used to generate vector speckle field and to get the phase information directly from the intensity measurements. Moreover, this approach leads to a complete experimental Stokes characterization of a broad range of random fields.

Simulation of polarized optical speckle fields: effects of the observation scale on polarimetry

In this paper, we propose the simulation of polarized speckle fields using the Stokes formalism, which allows the description of partially polarized electromagnetic waves. We define a unique parameter which determines the partial decorrelation of the involved fields, allowing to simulate the polarized speckles produced by all types of scatterers, from simple to multiple scatterers. We validate this model by comparison with experimental measurements. We use that simulation model to study the impact of the imaging device parameters on polarimetric measurements: first we emphasize a limit of resolution on retardance measurements, then we study the spatial depolarization, which appears when an observer is measuring any space-variant polarization map.

Polarized vortices in optical speckle field: observation of rare polarization singularities.

Using a recent method able to characterize the polarimetry of a random field with high polarimetric and spatial accuracy even near places of destructive interference, we study polarized optical vortices at a scale below the transverse correlation width of a speckle field. We perform high accuracy polarimetric measurements of known singularities described with an half-integer topological index and we study rare integer index singularities which have, to our knowledge, never been observed in a speckle field.

All-digital wavefront sensing for structured light beams.

We present a new all-digital technique to extract the wavefront of a structured light beam. Our method employs non-homogeneous polarization optics together with dynamic, digital holograms written to a spatial light modulator to measure the phase relationship between orthogonal polarization states in real-time, thereby accessing the wavefront information. Importantly, we show how this can be applied to measuring the wavefront of propagating light fields, over extended distances, without any moving components. We illustrate the versatility of the tool by measuring propagating optical vortices, Bessel, Airy and speckle fields. The comparison of the extracted and programmed wavefronts yields excellent agreement.

Nonlinear propagation of an optical speckle field

We provide a theoretical explanation of the results on the intensity distributions and correlation functions obtained from a random beam speckle field in nonlinear bulk waveguides reported in the recent publication Y. Bromberg et.al., Nat. Photonics \textbf{4}, 721 (2010). We study both focusing and defocusing case and in the limit of small speckle size (short correlated disordered beam) provide analytical asymptotes for the intensity probability distributions at the output facet. Additionally we provide a simple relation between the speckle sizes at the input and output of a focusing nonlinear waveguide. The results are of practical significance for the nonlinear Hanbury Brown and Twiss interferometry both in optical waveguides and Bose-Einstein condensates.

A Gaussian transition of an optical speckle field studied by the minimal spanning tree method

We propose to study the Gaussian transition of an optical speckle field using the Minimal Spanning Tree method. We perform an analysis of the spatial intensity distribution and show that the maxima of intensity evolve from a cluster distribution in the strongly non Gaussian regime, to a gradient distribution around the transition and then approach the random distribution area when we tend to the Gaussian regime. In the generated minimal spanning trees, we observe that the standard deviation of the edges length exhibits a maximum around the Gaussian transition when about 4 correlation cells of the surface roughness are illuminated.

Strongly Interacting Bosons in a Disordered Optical Lattice

We experimentally probe the properties of the disordered Bose-Hubbard model using an atomic Bose-Einstein condensate trapped in a 3D disordered optical lattice. Controllable disorder is introduced using a fine-grained optical speckle field with features comparable in size to the lattice spacing along every lattice direction. A precision measurement of the disordering potential is used to compute the single-particle parameters of the system. To constrain theories of the disordered Bose Hubbard model, we have measured the change in condensate fraction as a function of disorder strength for several different ratios of tunneling to interaction energy. We observe disorder-induced, reversible suppression of condensate fraction for superfluid and coexisting superfluid-Mott-insulator phases.