Transport Mean Free Path Research Articles

Enhancing color saturation in photonic glasses through optimized absorption

Photonic glasses, isotropically assembled nanoparticles with short-range correlation, can produce angle independent structural colors. They show broader reflectance spectra and lower saturated colors, compared to photonic crystals. Low color saturation creates barriers for photonic glasses to be used for coatings, cosmetics, and colors. Broadband absorbing materials are commonly used to absorb incoherently scattered light to enhance the saturation. However, there is limited understanding on how the absorption quantitatively affects the colors of photonic glasses. To this end, we here use a validated Monte Carlo-based multiple scattering model to investigate how absorption impacts the reflectance spectra in photonic glasses. We show that the color saturation can be maximized with an optimal level of absorption regardless of sample thickness or refractive index contrast between particles and matrix. We quantitatively demonstrate that the multiple scattering is largely reduced with the optimal absorption level and the reflectance is dominantly contributed by the single scattering. The optimal absorption occurs when the sample absorption mean free path is comparable to the transport mean free path, which offers a guidance on how much absorbing material is needed for creating highly saturated photonic glasses. This work will not only pave ways for pushing applications of angle-independent structural colors, but also improve our understanding of light scattering and absorption in short-range correlated disordered systems.

Effect of skin color on optical properties and the implications for medical optical technologies: a review.

Skin color affects light penetration leading to differences in its absorption and scattering properties. COVID-19 highlighted the importance of understanding of the interaction of light with different skin types, e.g., pulse oximetry (PO) unreliably determined oxygen saturation levels in people from Black and ethnic minority backgrounds. Furthermore, with increased use of other medical wearables using light to provide disease information and photodynamic therapies to treat skin cancers, a thorough understanding of the effect skin color has on light is important for reducing healthcare disparities. The aim of this work is to perform a thorough review on the effect of skin color on optical properties and the implication of variation on optical medical technologies. Published in vivo optical coefficients associated with different skin colors were collated and their effects on optical penetration depth and transport mean free path (TMFP) assessed. Variation among reported values is significant. We show that absorption coefficients for dark skin are to 74% greater than for light skin in the 400 to 1000nm spectrum. Beyond 600nm, the TMFP for light skin is greater than for dark skin. Maximum transmission for all skin types was beyond 940nm in this spectrum. There are significant losses of light with increasing skin depth; in this spectrum, depending upon Fitzpatrick skin type (FST), on average 14% to 18% of light is lost by a depth of 0.1mm compared with 90% to 97% of the remaining light being lost by a depth of 1.93mm. Current published data suggest that at wavelengths beyond 940nm light transmission is greatest for all FSTs. Data beyond 1000nm are minimal and further study is required. It is possible that the amount of light transmitted through skin for all skin colors will converge with increasing wavelength enabling optical medical technologies to become independent of skin color.

Overlapping speckle correlation algorithm for high-resolution imaging and tracking of objects in unknown scattering media

Optical imaging in scattering media is important to many fields but remains challenging. Recent methods have focused on imaging through thin scattering layers or thicker scattering media with prior knowledge of the sample, but this still limits practical applications. Here, we report an imaging method named ‘speckle kinetography’ that enables high-resolution imaging in unknown scattering media with thicknesses up to about 6 transport mean free paths. Speckle kinetography non-invasively records a series of incoherent speckle images accompanied by object motion and the inherently retained object information is extracted through an overlapping speckle correlation algorithm to construct the object’s autocorrelation for imaging. Under single-colour light-emitting diode, white light, and fluorescence illumination, we experimentally demonstrate 1 μm resolution imaging and tracking of objects moving in scattering samples, while reducing the requirements for prior knowledge. We anticipate this method will enable imaging in currently inaccessible scenarios.

Optimized virtual optical waveguides enhance light throughput in scattering media

Ultrasonically-sculpted gradient-index optical waveguides enable non-invasive light confinement inside scattering media. The confinement level strongly depends on ultrasound parameters (e.g., amplitude, frequency), and medium optical properties (e.g., extinction coefficient). We develop a physically-accurate simulator, and use it to quantify these dependencies for a radially-symmetric virtual optical waveguide. Our analysis provides insights for optimizing virtual optical waveguides for given applications. We leverage these insights to configure virtual optical waveguides that improve light confinement fourfold compared to previous configurations at five mean free paths. We show that virtual optical waveguides enhance light throughput by 50% compared to an ideal external lens, in a medium with bladder-like optical properties at one transport mean free path. We corroborate these simulation findings with real experiments: we demonstrate, for the first time, that virtual optical waveguides recycle scattered light, and enhance light throughput by 15% compared to an external lens at five transport mean free paths.

Numerical calculation method for the mean free path of single-mode semiconductor nanosheets with surface roughness

A numerical calculation method is proposed to compute the transport mean free path of single-mode semiconductor nanosheets with surface roughness, where the mean free path is extracted from the statistical average of the logarithm of the dimensionless resistance. The present method requires only a computationally less demanding coherent transmission probability, and is applicable to wider channel length ranges from the quasi-ballistic to the localization regime. The channel thickness, T w, dependence of the mean free path calculated by the proposed method within the effective mass approximation shows the well-known T W 6 dependence for thicker T w, while it becomes weaker for thinner T w.

Scan-free time-of-flight-based three-dimensional imaging through a scattering layer.

Reconstructing an object's three-dimensional shape behind a scattering layer with a single exposure is of great significance in real-life applications. However, due to the little information captured by a single exposure while strongly perturbed by the scattering layer and encoded by free-space propagation, existing methods cannot achieve scan-free three-dimensional reconstruction through the scattering layer in macroscopic scenarios using a short acquisition time of seconds. In this paper, we proposed a scan-free time-of-flight-based three-dimensional reconstruction method based on explicitly modeling and inverting the time-of-flight-based scattering light propagation in a non-confocal imaging system. The non-confocal time-of-flight-based scattering imaging model is developed to map the three-dimensional object shape information to the time-resolved measurements, by encoding the three-dimensional object shape into the free-space propagation result and then convolving with the scattering blur kernel derived from the diffusion equation. To solve the inverse problem, a three-dimensional shape reconstruction algorithm consisting of the deconvolution and diffractive wave propagation is developed to invert the effects caused by the scattering diffusion and the free-space propagation, which reshapes the temporal and spatial distribution of scattered signal photons and recovers the object shape information. Experiments on a real scattering imaging system are conducted to demonstrate the effectiveness of the proposed method. The single exposure used in the experiment only takes 3.5s, which is more than 200 times faster than confocal scanning methods. Experimental results show that the proposed method outperforms existing methods in terms of three-dimensional reconstruction accuracy and imaging limit subjectively and objectively. Even though the signal photons captured by a single exposure are too highly scattered and attenuated to present any valid information in time gating, the proposed method can reconstruct three-dimensional objects located behind the scattering layer of 9.6 transport mean free paths (TMFPs), corresponding to the round-trip scattering length of 19.2 TMFPs.

Weak Localization of Light in a Magneto-Active Medium

The interference contribution to the optical conductance (total transmittance) of a sample of a disordered Faraday medium is calculated. The suppression of wave interference in a magnetic field is shown to be due to helicity-flip scattering events. The magnetic field does not destroy the interference of waves with a given helicity, but suppresses it if the helicity changes along different parts of the wave trajectory. This leads to a decrease in the interference contribution to the conductance with increasing the magnetic field. A similar phenomenon, negative magnetoresistance, is known as a consequence of weak localization of electrons in metals with impurities. It is found that, as the magnetic field increases, the change in the interference correction to the optical conductance tends to a certain limiting value, which depends on the ratio of the transport mean free path to the helicity-flip scattering mean free path. We also discuss the possibility of controlling the transition to the regime of strong “Anderson” localization in the quasi-one-dimensional case by means of the field.

Relevance and utility of the in-vivo and ex-vivo optical properties of the skin reported in the literature: a review [Invited

Imaging non-invasively into the human body is currently limited by cost (MRI and CT scan), image resolution (ultrasound), exposure to ionising radiation (CT scan and X-ray), and the requirement for exogenous contrast agents (CT scan and PET scan). Optical imaging has the potential to overcome all these issues but is currently limited by imaging depth due to the scattering and absorption properties of human tissue. Skin is the first barrier encountered by light when imaging non-invasively, and therefore a clear understanding of the way that light interacts with skin is required for progress on optical medical imaging to be made. Here we present a thorough review of the optical properties of human skin measured in-vivo and compare these to the previously collated ex-vivo measurements. Both in-vivo and ex-vivo published data show high inter- and intra-publication variability making definitive answers regarding optical properties at given wavelengths challenging. Overall, variability is highest for ex-vivo absorption measurements with differences of up to 77-fold compared with 9.6-fold for the in-vivo absorption case. The impact of this variation on optical penetration depth and transport mean free path is presented and potential causes of these inconsistencies are discussed. We propose a set of experimental controls and reporting requirements for future measurements. We conclude that a robust in-vivo dataset, measured across a broad spectrum of wavelengths, is required for the development of future technologies that significantly increase the depth of optical imaging.

Analysis of relative error in perturbation Monte Carlo simulations of radiative transport.

Perturbation and differential Monte Carlo (pMC/dMC) methods, used in conjunction with nonlinear optimization methods, have been successfully applied to solve inverse problems in diffuse optics. Application of pMC to systems over a large range of optical properties requires optimal "placement" of baseline conventional Monte Carlo (cMC) simulations to minimize the pMC variance. The inability to predict the growth in pMC solution uncertainty with perturbation size limits the application of pMC, especially for multispectral datasets where the variation of optical properties can be substantial. We aim to predict the variation of pMC variance with perturbation size without explicit computation of perturbed photon weights. Our proposed method can be used to determine the range of optical properties over which pMC predictions provide sufficient accuracy. This method can be used to specify the optical properties for the reference cMC simulations that pMC utilizes to provide accurate predictions over a desired optical property range. We utilize a conventional error propagation methodology to calculate changes in pMC relative error for Monte Carlo simulations. We demonstrate this methodology for spatially resolved diffuse reflectance measurements with ±20% scattering perturbations. We examine the performance of our method for reference simulations spanning a broad range of optical properties relevant for diffuse optical imaging of biological tissues. Our predictions are computed using the variance, covariance, and skewness of the photon weight, path length, and collision distributions generated by the reference simulation. We find that our methodology performs best when used in conjunction with reference cMC simulations that utilize Russian Roulette (RR) method. Specifically, we demonstrate that for a proximal detector placed immediately adjacent to the source, we can estimate the pMC relative error within 5% of the true value for scattering perturbations in the range of . For a distal detector placed at transport mean free paths relative to the source, our method provides relative error estimates within 20% for scattering perturbations in the range of . Moreover, reference simulations performed at lower values showed better performance for both proximal and distal detectors. These findings indicate that reference simulations utilizing continuous absorption weighting (CAW) with the Russian Roulette method and executed using optical properties with a low ratio spanning the desired range of values, are highly advantageous for the deployment of pMC to obtain radiative transport estimates over a wide range of optical properties.

Collagen fiber anisotropy characterization by polarized photoacoustic imaging for just-in-time quantitative evaluation of burn severity

Just-in-time burn severity assessment plays a vital role in burn treatment and care. However, it is still difficult to quantitatively and promptly evaluate burn severity by existing medical imaging methods via initial burn depth measurement since burn wounds are usually dynamically developed. As an elastic skeleton of skin, the degree of conformational changes of collagen fibers caused by overheating can reflect the burn severity in a timelier manner. Herein, the polarized photoacoustic technique (PPAT) for just-in-time quantitative evaluation of burn severity via collagen fiber anisotropy assessment is proposed. First, phantom experiments demonstrate the ability of PPAT for deep imaging in a transport mean free path and accurately quantify changes in microstructural order by thermal damage. Then, the Pearson correlation coefficient of the PPAT in assessing burn severity is shown to be up to 0.95, validated by burn skin samples. The PPAT provides a just-in-time quantitative strategy for burn severity evaluation.

Information transport and limits of optical imaging in the highly diffusive regime

Noninvasive imaging through the human body or dense fog at optical wavelengths requires the collection of highly scattered photons, which corrupt imaging information and restrict most diffuse imaging techniques to $<$ 10 transport mean free path (TMFP) lengths. An information theoretical analysis of numerical simulations including practical considerations shows imaging information exists at the single-photon detection limit beyond 200 TMFP lengths. Information can be enhanced through increasing the collection of light, optimizing detector placement, and resolving measurements in the space-time domain.

Transmissive multifocal laser speckle contrast imaging through thick tissue

Laser speckle contrast imaging (LSCI) is a powerful tool for monitoring blood flow changes in tissue or vessels in vivo, but its applications are limited by shallow penetration depth under reflective imaging configuration. The traditional LSCI setup has been used in transmissive imaging for depth extension up to [Formula: see text]–[Formula: see text] ([Formula: see text] is the transport mean free path), but the blood flow estimation is biased due to the depth uncertainty in large depth of field (DOF) images. In this study, we propose a transmissive multifocal LSCI for depth-resolved blood flow in thick tissue, further extending the transmissive LSCI for tissue thickness up to [Formula: see text]. The limited-DOF imaging system is applied to the multifocal acquisition, and the depth of the vessel is estimated using a robust visibility parameter [Formula: see text] in the coherent domain. The accuracy and linearity of depth estimation are tested by Monte Carlo simulations. Based on the proposed method, the model of contrast analysis resolving the depth information is established and verified in a phantom experiment. We demonstrated its effectiveness in acquiring depth-resolved vessel structures and flow dynamics in in vivo imaging of chick embryos.

TiO2–SiO2 Self-Standing Materials bearing Hierarchical Porosity: MUB-200(x) Series toward 3D-Efficient VOC Photoabatement Properties

Three-dimensional photoactive self-standing porous materials have been synthesized through the integration of soft chemistry and colloids (emulsions, lyotrope mesophases, and P25 titania nanoparticles). Final multiscale porous ceramics bear 700-1000 m2 g-1 of micromesoporosity depending on the P25 nanoparticle contents. The applied thermal treatment does not affect the P25 anatase/rutile allotropic phase ratio. Photonic investigations correlated with the foams' morphologies suggest that the larger amount of TiO2 that is introduced, the larger the walls' density and the smaller the mean size of the void macroscopic diameters, with both effects inducing a reduction of the photon transport mean free path (lt) with the P25 content increase. A light penetration depth in the range of 6 mm is reached, thus depicting real 3D photonic scavenger behavior. The 3D photocatalytic properties of the MUB-200(x) series, studied in a dynamic "flow-through" configuration, show that the highest photoactivity (concentration of acetone ablated and concentration of CO2 formed) is obtained with the highest monolith height (volume) while providing an average of 75% mineralization. These experimental results validate the fact that these materials, bearing 3D photoactivity, are paving the path for air purification operating with self-standing porous monolith-type materials, which are much easier to handle than powders. As such, the photocatalytic systems can now be advantageously miniaturized, thereby offering indoor air treatment within vehicles/homes while drastically limiting the associated encumbrance. This volumetric counterintuitive acting mode for light-induced reactions may find other relevant advanced applications for photoinduced water splitting, solar fuel, and dye-sensitized solar cells while both optimizing photon scavenging and opening the path for the miniaturization of the processes where encumbrance or a foot-print penalty would be advantageously circumvented.

Coherent backscattering of entangled photon pairs

Correlations between entangled photons are a key ingredient for testing fundamental aspects of quantum mechanics and an invaluable resource for quantum technologies. However, scattering from a dynamic medium typically scrambles and averages out such correlations. Here we show that multiply scattered entangled photons reflected from a dynamic complex medium remain partially correlated. In experiments and full-wave simulations we observe enhanced correlations, within an angular range determined by the transport mean free path, which prevail over disorder averaging. Theoretical analysis reveals that this enhancement arises from the interference between scattering trajectories, in which the photons leave the sample and are then virtually reinjected back into it. These paths are the quantum counterpart of the paths that lead to the coherent backscattering of classical light. This work points to opportunities for entanglement transport despite dynamic multiple scattering in complex systems. Dynamic and disordered media destroy the correlations that underlie many quantum measurement protocols and applications. However, coherently backscattered photons can remain partially correlated due to interference between scattering trajectories.

Effect of scatterer interactions on photon transport in diffusing wave spectroscopy.

We calculate the effect of particle size, concentration, and interactions on the photon transport mean-free path l^{*} that characterizes the multiple light scattering in diffusing wave spectroscopy (DWS). For scatterers of sufficient size, such that the first peak of the suspension structure factor S(q_{max}) remains in the range of accessible scattering vectors, neither repulsive nor attractive interactions between scatterers contribute strongly to l^{*}; its values are bounded by those for hard spheres and scatterers without interactions. However, for scatterers smaller than the wavelength of light, crowding induced by attraction or repulsion can lead to nonmonotonic behavior in l^{*} with increasing scatterer concentration. The effect is strongest for repulsive particles.

Propagation of 2-D SH waves in random media: Insights from ab initio numerical simulations and transport theory

Increasing the frequency range of physics-based predictions of earthquake ground motions requires to account for small-scale heterogeneities, which can only be described in a stochastic way. Although many studies have addressed the impact of random heterogeneities on ground motion intensity parameters obtained by numerical simulation, very few have verified the accuracy of their numerical solutions or controlled the scattering regime they were simulating. Here we present a comprehensive analysis ofSHwave propagation in 2D random media which covers a broad range of propagation regimes from ballistic to diffusive. The coherent and incoherent parts of the wavefield are examined independently. The random media consist in correlated density and velocity fluctuations described by a von Kármán autocorrelation function with a Hurst coefficient of 0.25 and a correlation lengtha= 500 m. The Birch correlation coefficient which relates density to velocity fluctuations takes 4 possible values between 0.5 and 1, and the standard deviation of the perturbations is either 5% or 10%. Spectral element simulations of SH wave propagation excited by a plane wave are performed for normalized wavenumbers (ka) up to 5. Analysis of the decay of the coherent wave amplitude, obtained through different averaging procedures, allows for a direct measure of the scattering attenuation, which we successfully compare with the predictions of the Dyson mean field theory. We also present the comparison between the energy envelopes measured from the synthetics and their theoretical counterpart provided by the radiative transfer theory and the diffusion approximation. Excellent agreement is found between numerical simulations and theoretical predictions of radiative transfer theory for the mean intensity. The numerical study highlights the difference of attenuation length between the mean field and the mean intensity. In the forward scattering regime, the peak intensity appears to decay exponentially over a length scale known as the transport mean free path. Furthermore, the fluctuations of intensity in the ballistic peak exhibit a transition from Log-normal to Exponential statistics. This transition occurs for a propagation distance of the order of the mean free path, which offers an alternative method of estimating this parameter.

Coherent enhancement of optical remission in diffusive media

Remitted waves are used for sensing and imaging in diverse diffusive media from the Earth's crust to the human brain. Separating the source and detector increases the penetration depth of light, but the signal strength decreases rapidly, leading to a poor signal-to-noise ratio. Here, we show, experimentally and numerically, that wavefront shaping a laser beam incident on a diffusive sample enables an enhancement of remission by an order of magnitude at depths of up to 10 transport mean free paths. We develop a theoretical model which predicts the maximal remission enhancement. Our analysis reveals a significant improvement in the sensitivity of remitted waves to local changes of absorption deep inside diffusive media. This work illustrates the potential of coherent wavefront control for noninvasive diffuse wave imaging applications, such as diffuse optical tomography and functional near-infrared spectroscopy.

Scattering of hot charge carriers in solid solutions of dielectric crystals with substitutional disorder

The spatial distribution of the components that make up the substitutional solid solution is non-uniform. The randomness of substitution leads to the formation of a random potential acting on secondary electrons in the conduction band and holes in the valence band. The random potential is one of the factors that significantly affect the migration, localization, and recombination of a given charge carriers. The influence of another factor, the energy structure of the conduction band, was considered for a substitutional solid solution of the AxB1−xC type in the model of multiple parabolic branches of the electron dispersion law. The transport mean free paths for the cases of elastic scattering of electrons by potential fluctuations and inelastic scattering of electrons by LA and LO phonons were calculated. It was shown that the presence of several parabolic branches of the electron dispersion law in the conduction band in all cases leads to a significant reduction in transport mean free paths compared to the model of one parabolic branch of the electron dispersion law in the conduction band.

Impact of compositional disorder on electron migration in lutetium–yttrium oxyorthosilicate scintillator

A general description of the dynamics of nonequilibrium carriers in multicomponent activated scintillation materials with a compositional disorder of the crystalline matrix is developed and applied for studying the excitation transfer and timing properties of lutetium–yttrium oxyorthosilicate (LYSO). The energy structure, the density of states, and the effective potential of LSO and YSO crystals have been calculated by using the Quantum Espresso package. An analytical form of the potential fluctuations due to compositional disorder is suggested in the pseudopotential approximation. The spatial distribution of lutetium and yttrium cations in the LYSO crystal has been simulated by the Monte Carlo method using the thermodynamic approach for three qualitatively different cases of cation distribution: uniform, heterogeneous neighboring, and clustered. The impact of the compositional disorder on electron migration is found to be qualitatively different in four typical regions of electron energy. The density of localized states in LYSO calculated using the coherent potential approximation (CPA) and the quasiclassical approach is comparable to the density of secondary carriers expected in an ionization track and might have significant influence on the migration of thermalized carriers. The transport mean free path of nonlocalized electrons limited by elastic scattering on pseudopotential fluctuations is shown to be substantially longer than that due to longitudinal optical phonon emission in the low-energy region (calculated using CPA) and the high-energy region (calculated using the Born approximation). The scattering on pseudopotential fluctuations is important for intermediate-energy electrons due to a substantial influence of the core potential fluctuations on high-energy branches.

Particle sizing in non-dilute dispersions using diffusing wave spectroscopy with multiple optical path lengths

Non-dilute dispersed phase systems, such as foams, emulsions, and suspensions, are an important class of final formulations and chemical process intermediates in a variety of industries. The utility of these systems hinges on their stability over the lifetime of use, and therefore an accurate assessment of chemical and physical dynamics, asformulated, is required. We describe a unified treatment of diffusing wave spectroscopy (DWS) data using a range of optical path length with a goniometric instrument. DWS correlation data from multiple angles and robust Monte Carlo simulations are used to determine accurate values of the photon transport mean free path length. The variance on each correlation function is used to determine the physical time range that the mean squared displacement can be analyzed. Using standard solid particle suspensions of polystyrene and SiO2, we determine the average particle size with accuracy comparable to dynamic light scattering.