Transport Mean Free Path Research Articles

Dichroism-sensitive photoacoustic computed tomography.

Photoacoustic computed tomography (PACT), a fast-developing modality for deep tissue imaging, images the spatial distribution of optical absorption. PACT usually treats the absorption coefficient as a scalar. However, the absorption coefficients of many biological tissues exhibit an anisotropic property, known as dichroism or diattenuation, which depends on molecular conformation and structural alignment. Here we present a novel imaging method called dichroism-sensitive PACT (DS-PACT), which measures both the amplitude of tissue's dichroism and the orientation of the optic axis of uniaxial dichroic tissue. By modulating the polarization of linearly polarized light and measuring the alternating signals through lock-in detection, DS-PACT can boost dichroic signals from biological tissues. To validate the proposed approach, we experimentally demonstrated the performance of DS-PACT by imaging plastic polarizers and ex vivo bovine tendons deep inside scattering media. We successfully detected the orientation of the optic axis of uniaxial dichroic materials, even at a depth of 4.5 transport mean free paths. We anticipate that the proposed method will extend the capability of PACT to imaging tissue absorption anisotropy.

The anomalous depolarization anisotropy in the central backscattering area for turbid medium with Mie scatterers

It is generally recognized that circularly polarized light is preferentially maintained over linearly polarized light in turbid medium with Mie scatterers. However, in this work, the anomalous depolarization anisotropy is reported in the backscattering area near the point of illumination. Both experimental and Monte Carlo simulations show preferential retention of linear polarization states compared to circular polarization states in a specific backscattering area. Further analysis indicates that the anomalous depolarization behavior in the specific area is induced by lateral scattering events, which own low circular polarization memory. In addition, it is also found that the size of the anomalous depolarization area is related to the transport mean free path of the turbid medium.

Achieving a strongly negative scattering asymmetry factor in random media composed of dual-dipolar particles

Understanding radiative transfer in random media like micro/nanoporous and particulate materials, allows people to manipulate the scattering and absorption of radiation, as well as opens new possibilities in applications such as imaging through turbid media, photovoltaics and radiative cooling. A strong-backscattering phase function, i.e., a negative scattering asymmetry parameter $g$, is of great interest which can possibly achieve unusual radiative transport phenomena, for instance, Anderson localization of light. Based on the multipole expansion of Foldy-Lax equations and quasicrystalline approximation (QCA), we have rigorously derived analytical expressions for effective propagation constant and scattering phase function for a random system containing dual-dipolar particles, by taking the effect of structural correlations into account. Here we demonstrate that by utilizing structural correlations and the second Kerker condition for a disordered medium composed of randomly distributed silicon nanoparticles, a strongly negative scattering asymmetry factor ($g\sim-0.5$) for multiple light scattering can be realized in the near-infrared. As concentration of scattering particles rises, the backscattering is also enhanced. Moreover, we show that in this circumstance, transport mean free path is largely reduced and even smaller than that predicted by independent scattering approximation. We further explored the dependent scattering effects, including the modification of electric and magnetic dipole excitations and far-field interference effect, both induced by the structural correlations, for volume fraction of particles up to $f_v\sim0.25$. Our results have profound implications in harnessing micro/nanoscale radiative transfer through random media.

Bio‐inspired Highly Scattering Networks via Polymer Phase Separation

AbstractA common strategy to optimize whiteness in living organisms consists in using 3D random networks with dense and polydisperse scattering elements constituted by relatively low refractive index materials. Inspired by these natural architectures, a fast and scalable method to produce highly scattering porous polymer films via phase separation is developed. By varying the molecular weight of the polymer, the morphology of the porous films is modified, and therefore their scattering properties are tuned. The achieved transport mean free paths are in the micrometer range, improving the scattering strength of analogous low refractive index systems, e.g., standard white paper, by an order of magnitude. The produced porous films show a broadband reflectivity of ≈75% while only 4 µm thick. In addition, the films are flexible and can be readily index‐matched with water (i.e., they become transparent when wet), allowing for various applications such as coatings with tunable transmittance and responsive paints.

Effective Radiative Cooling by Paint-Format Microsphere-Based Photonic Random Media

We demonstrate that photonic media, when properly randomized to minimize the photon transport mean free path, can be used to coat a black substrate and reduce its temperature by radiative cooling. Even under strong solar radiation, the substrate temperature could reach substantially below that of the ambient air. Our random media that consist of silica microspheres considerably outperform commercially available solar-reflective white paint for daytime cooling. We have achieved the outstanding cooling performance through a systematic study on light scattering, which reveals that the structural parameters of the random media for maximum scattering are significantly different from those of the commercial paint. We have created the random media to maximize optical scattering in the solar spectrum and to enhance thermal emission in the atmospheric transparency window. In contrast to previous studies, our random media do not require expensive processing steps or materials, such as silver, and can be applied to ...

Optimized diffusion approximation.

We show that the diffusion approximation (DA) to the radiative transport equation, which is commonly used in biomedical optics to describe propagation of light in tissues, contains a previously unexplored adjustable parameter. This parameter is related to the rate of exponential decay of the reduced intensity. In conventional theories, there are two distinct choices for this parameter. However, neither of these choices is optimal. When the optimal value for the parameter is used, the resulting DA becomes much more accurate near the medium boundaries, e.g.,at the depth of up to a few ℓ*, where ℓ* is the transport mean free path (typically, about 1mm in tissues). We refer to the new adjustable parameter as the reduced extinction coefficient. The proposed technique can reduce the relative error of the predicted diffuse density of the optical energy from about 30% to less than 1%. The optimized DA can still be inaccurate very close to an interface or in some other physical situations. Still, the proposed development extends the applicability range of the DA significantly. This result can be useful, for instance, in tomographic imaging of relatively shallow (up to a few ℓ* deep) layers of tissues in the reflection geometry.

Time-resolved study of optical properties and microscopic dynamics during the drying of TiO2 films by spectral diffusing wave spectroscopy.

We present a combined experimental, theoretical, and numerical study of photon transport and microscopic dynamics in rigid and drying turbid thin films. Our setup is based in multispeckle diffusing wave spectroscopy and is adapted for frequency sweep of the illuminating source. We apply our approach to simultaneously monitor the changes in optical properties and microscopic dynamics of turbid thin films of rutile TiO2 powder dispersed in ethanol during the full drying process. Accordingly, we introduce an extension of the photon diffusion model for spectral speckle intensity correlations to account for system microscopic dynamics. We find that our results are well described by the model, where parameters required as the time-dependent sample thickness and transport mean free path are obtained from experiments. Furthermore, our findings are validated by numerical simulations of speckle dynamics based on the copula scheme. We consider that our scheme could be useful in time-resolved physical characterization of time-evolving turbid thin systems.

Polydispersed Powders (Nd3+:YVO4) for Ultra Efficient Random Lasers

AbstractRandom lasers hold the potential for cheap, coherent light sources that can be miniaturized and molded into any shape with several other added benefits such as speckle‐free imaging; however, they require improvements specifically in terms of efficiency. This paper details for the first time a strategy for increasing the efficiency of a random laser that consists in using smaller particles, trapped between large particles to serve as absorption and gain centers whereas the large particles control mainly the light diffusion into the sample. Measurements of backscattering cone, sample absorption, reflection, and laser emission are used to determine the samples' transport mean free path, fill fractions, laser efficiency, and the average photon path lengths inside the scattering medium for backscattered pump photons. A record slope efficiency of 50% is reached by optimizing pump photon diffusion and absorption in a powder pellet composed by a polydispersed particle size distribution (smaller particles between bigger ones) from a grinded and sieved 1.33 mol% yttrium vanadate doped with neodymium crystal with mean particle size of 54 µm.

Interplay of Stimulated Emission and Fluorescence Resonance Energy Transfer in Electrospun Light-Emitting Fibers

Concomitant amplified spontaneous emission (ASE) and F\"orster resonance energy transfer (FRET) are investigated in electrospun light-emitting fibers. Upon dye-doping with a proper FRET couple system, free-standing fibrous mats exhibit tunable FRET efficiency and, more importantly, tailorable threshold conditions for stimulated emission. In addition, effective scattering of light is found in the fibrous material by measuring the transport mean free path of photons by coherent backscattering experiments. The interplay of ASE and FRET leads to high control in designing optical properties from electrospun fibers, including the occurrence of simultaneous stimulated emission from both donor and acceptor components. All tunable-optical properties are highly interesting in view of applying electrospun light-emitting materials in lightening, display, and sensing technologies.

Diffusing-wave spectroscopy in a standard dynamic light scattering setup.

Diffusing-wave spectroscopy (DWS) extends dynamic light scattering measurements to samples with strong multiple scattering. DWS treats the transport of photons through turbid samples as a diffusion process, thereby making it possible to extract the dynamics of scatterers from measured correlation functions. The analysis of DWS data requires knowledge of the path length distribution of photons traveling through the sample. While for flat sample cells this path length distribution can be readily calculated and expressed in analytical form; no such expression is available for cylindrical sample cells. DWS measurements have therefore typically relied on dedicated setups that use flat sample cells. Here we show how DWS measurements, in particular DWS-based microrheology measurements, can be performed in standard dynamic light scattering setups that use cylindrical sample cells. To do so we perform simple random-walk simulations that yield numerical predictions of the path length distribution as a function of both the transport mean free path and the detection angle. This information is used in experiments to extract the mean-square displacement of tracer particles in the material, as well as the corresponding frequency-dependent viscoelastic response. An important advantage of our approach is that by performing measurements at different detection angles, the average path length through the sample can be varied. For measurements performed on a single sample cell, this gives access to a wider range of length and time scales than obtained in a conventional DWS setup. Such angle-dependent measurements also offer an important consistency check, as for all detection angles the DWS analysis should yield the same tracer dynamics, even though the respective path length distributions are very different. We validate our approach by performing measurements both on aqueous suspensions of tracer particles and on solidlike gelatin samples, for which we find our DWS-based microrheology data to be in good agreement with rheological measurements performed on the same samples.

Improved diffusing wave spectroscopy based on the automatized determination of the optical transport and absorption mean free path

Diffusing wave spectroscopy (DWS) can be employed as an optical rheology tool with numerous applications for studying the structure, dynamics and linear viscoelastic properties of complex fluids, foams, glasses and gels. To carry out DWS measurements, one first needs to quantify the static optical properties of the sample under investigation, i.e. the transport mean free path $l^\ast$ and the absorption length $l_a$. In the absence of absorption this can be done by comparing the diffuse optical transmission to a calibration sample whose $l^\ast$ is known. Performing this comparison however is cumbersome, time consuming and prone to mistakes by the operator. Moreover, already weak absorption can lead to significant errors. In this paper, we demonstrate the implementation of an automatized approach, based on which the DWS measurement procedure can be simplified significantly. By comparison with a comprehensive set of calibration measurements we cover the entire parameter space relating measured count rates (CR$_t$, CR$_b$) to ($l^\ast$, $l_a$). Based on this approach we can determine $l^\ast$ and $l_a$ of an unknown sample accurately thus making the additional measurement of a calibration sample obsolete. We illustrate the use of this approach by monitoring the coarsening of a commercially available shaving foam with DWS.

Resonant transport and near-field effects in photonic glasses

A fundamental quantity in multiple scattering is the transport mean free path the inverse of which describes the scattering strength of a sample. In this paper, we emphasize the importance of an appropriate description of the effective refractive index $n_{\mathrm{eff}}$ in multiple light scattering to accurately describe the light transport in dense photonic glasses. Using $n_{\mathrm{eff}}$ as calculated by the energy-density coherent potential approximation we are able to predict the transport mean free path of monodisperse photonic glasses. This model without any fit parameter is in qualitative agreement with numerical simulations and in fair quantitative agreement with spectrally resolved coherent backscattering measurements on new specially synthesized polystyrene photonic glasses. These materials exhibit resonant light scattering perturbed by strong near-field coupling, all captured within the model. Our model might be used to maximize the scattering strength of high index photonic glasses, which are a key in the search for Anderson localization of light in three dimensions.

Biomineral Amorphous Lasers through Light‐Scattering Surfaces Assembled by Electrospun Fiber Templates

AbstractNew materials aim at exploiting the great control of living organisms over molecular architectures and minerals. Optical biomimetics has been widely developed by microengineering, leading to photonic components with order resembling those found in plants and animals. These systems, however, are realized by complicated and adverse processes. Here we show how biomineralization might enable the one‐step generation of components for amorphous photonics, in which light is made to travel through disordered scattering systems, and particularly of active devices such as random lasers, by using electrospun fiber templates. The amount of bio‐enzymatically produced silica is related to light‐scattering capacity and the resulting organosilica surfaces exhibit a transport mean free path for light as low as 3 μm, and lasing with linewidth below 0.2 nm. The resulting, complex optical material is characterized and modelled to elucidate scattered fields and lasing performance. Tightly‐controlled nanofabrication of direct biological inspiration establishes a new concept for the additive manufacturing of engineered light‐diffusing materials and photonic components, not addressed by existing technologies.

Electromagnetic energy stored in inhomogeneous scattering systems.

We analytically study the time-averaged electromagnetic energy stored inside scatterers containing inclusions of arbitrary shapes. Assuming the low density of inclusions, we derive the expression for the energy-transport velocity through disordered media without relying on the radiative transfer equation. Moreover, this expression is independent of the shape of scatterers. In addition, we obtain a relation between the dwell and absorption times associated with inclusions by considering the relationship between the internal energy and absorption cross-section. An approximation for the electromagnetic energy stored inside a disordered medium in terms of the transport mean free path and the packing fraction is also derived. This expression suggests that the enhanced electromagnetic energy within the host medium is achieved for inclusions exhibiting negative scattering asymmetry parameters. As a result, disordered media with enhanced backscattering is expected to exhibit large quality factors.

Theoretical basis of the amplitude source location method for volcano‐seismic signals

AbstractThe source location method using high‐frequency seismic amplitudes based on the assumption of isotropic radiation of S waves has been used successfully to locate seismic events and tremor at volcanoes. This amplitude source location (ASL) method overcomes the limitations of traditional hypocenter determination methods that use onset arrival times and has great potential to improve volcano‐seismic monitoring and the investigation of source processes of volcano‐seismic signals. However, theoretical justification of the basic assumption used in the ASL method has not been provided in previous studies. In this study, we tested the ASL method by using seismic waveforms simulated with a finite difference method in realistic heterogeneous volcanic structures with intrinsic attenuation and topography. Our results showed that ASL determinations were successful when using waveforms characterized by multiple scattering that can be approximated by the diffusion model. We found that the energy solution of the diffusion model provided an amplitude‐distance relation that is similar to that used in the ASL method. Our results suggest that the ASL method is applicable to high‐frequency seismograms in highly heterogeneous media with transport mean free paths of 103 m or smaller and strong intrinsic attenuation. These medium parameters are consistent with those estimated at various volcanoes. Our study validates the basic assumption of the ASL method and justifies its use to locate the sources of high‐frequency seismic signals observed at volcanoes.

Influence of liquid crystalline phases on the tunability of a random laser.

In this paper, we report the temperature behavior of an optimized disordered photonic system-based liquid crystal by means of heat capacity and refractive index measurements. The scattering system is formed by a porous borosilicate glass random matrix (about 60%) infiltrated with a smectogenic liquid crystal (about 16%) and a small amount of laser dye (0.1%). The rest of the scattering system is about 24% air, giving rise to a high refractive index contrast scattering system. Such a system has the functionality to change the refractive index contrast with temperature due to the liquid crystal temperature behavior. The system, optically pumped by the second harmonic of a Q-switched Nd:YAG pulsed laser working at 532 nm, exhibits random laser action, the threshold of which depends upon the liquid crystalline mesophase. Temperatures of existence of the smectic-B phase correspond to the most optimized random laser. In such a mesophase, the transport mean free path has been determined as about 16 μm in a coherent backscattering experiment.

Coherent multiple light scattering in Faraday active materials

Wave propagation in multiple scattering media shows various kinds of coherent phenomena such as coherent backscattering [1, 2] or Anderson localization [3], both of which are intimately connected to the concept of reciprocity. Manipulating reciprocity in such media is a powerful tool to study these phenomena in experiments [4]. Here we discuss the manipulation of reciprocity in reflection and transmission geometry for the case of light propagation in magneto-optical media. We show new experiments on coherent backscattering and speckle correlations in strongly scattering samples containing Faraday active materials (CeF3) with transport mean free path in the μm range, at low temperatures (T < 10 K) and high fields (B = 18 T). Under such conditions we observe the effect of a Faraday rotation saturation in multiple scattering measurements.

Bio-inspired, large scale, highly-scattering films for nanoparticle-alternative white surfaces

Inspired by the white beetle of the genus Cyphochilus, we fabricate ultra-thin, porous PMMA films by foaming with CO2 saturation. Optimising pore diameter and fraction in terms of broad-band reflectance results in very thin films with exceptional whiteness. Already films with 60 µm-thick scattering layer feature a whiteness with a reflectance of 90%. Even 9 µm thin scattering layers appear white with a reflectance above 57%. The transport mean free path in the artificial films is between 3.5 µm and 4 µm being close to the evolutionary optimised natural prototype. The bio-inspired white films do not lose their whiteness during further shaping, allowing for various applications.

Design and Realization of a Novel Optically Disordered Material: A Demonstration of a Mie Glass

Herein, a diffusive material presenting optical disorder is introduced, which represents an example of a Mie glass. Comprising spherical crystalline TiO2 nanoparticles randomly dispersed in a mesoporous TiO2 matrix, it is proved that the scattering of light in this inhomogeneous solid can be predicted in an unprecedented manner from single‐particle considerations employing Mie theory. To that aim, a study of the dependence of the key parameters employed is performed to describe light propagation in random media, i.e., the scattering mean free path and the transport mean free path, as a function of the size and concentration of the spherical inclusions based on a comparison between experimental results and analytical calculations. It is also demonstrated that Mie glasses enable enhanced fluorescence intensity due to a combined absorptance enhancement of the excitation light combined with an improved outcoupling of the emitted light. The method offers the possibility to perform a deterministic design for the realization of a light diffuser with tailor‐made scattering properties.

Characterization of the Lung Parenchyma Using Ultrasound Multiple Scattering

The purpose of the study described here was to showcase the application of ultrasound to quantitative characterization of the micro-architecture of the lung parenchyma to predict the extent of pulmonary edema. The lung parenchyma is a highly complex and diffusive medium for which ultrasound techniques have remained qualitative. The approach presented here is based on ultrasound multiple scattering and exploits the complexity of ultrasound propagation in the lung structure. The experimental setup consisted of a linear transducer array with an 8-MHz central frequency placed in contact with the lung surface. The diffusion constant D and transport mean free path L* of the lung parenchyma were estimated by separating the incoherent and coherent intensities in the near field and measuring the growth of the incoherent diffusive halo over time. Significant differences were observed between the L* values obtained in healthy and edematous rat lungs in vivo. In the control rat lung, L* was found to be 332 μm (±48.8 μm), whereas in the edematous lung, it was 1040 μm (±90 μm). The reproducibility of the measurements of L* and D was tested in vivo and in phantoms made of melamine sponge with varying air volume fractions. Two-dimensional finite difference time domain numerical simulations were carried out on rabbit lung histology images with varying degrees of lung collapse. Significant correlations were observed between air volume fraction and L* in simulation (r = −0.9542, p < 0.0117) and sponge phantom (r = −0.9932, p < 0.0068) experiments. Ex vivo measurements of a rat lung in which edema was simulated by adding phosphate-buffered saline revealed a linear relationship between the fluid volume fraction and L*. These results illustrate the potential of methods based on ultrasound multiple scattering for the quantitative characterization of the lung parenchyma.