Random Media Research Articles

Fluorescence amplification in laser-pumped random media: Fundamental limitations

Experimental data on the narrowing of fluorescence spectra of laser-pumped random media are interpreted within the framework of a probabilistic model of incoherent amplification of the stimulated component of fluorescence. R6G- and DCM-doped layers of dense-packed anatase and anatase-rutile particles and suspensions of DCM crystallites were examined under pulse-periodic laser pumping with various pump intensities at the wavelength of 532 nm. It was shown that, in the case of quasi-stationary fluorescence response at high pump intensities, amplification of stochastically propagating partial components of fluorescence field at various wavelengths is governed by the pump-independent factor of fluorescence amplification and the average number of stimulated emission acts in the pumped system. Analysis of the experimental data has shown that, despite certain simplifying assumptions, the considered model reasonably describes evolution of the fluorescence spectra of random fluorescent media with the increase in the pump intensity. A procedure of recovery of the fluorescence amplification factor from the sets of fluorescence spectra obtained at various pump intensities is considered. Features of the spectral shapes of the recovered amplification factors caused by the influence of the scattering matrices in pumped media are discussed.

Statistical theory of fluids confined in quenched disordered porous media.

We develop a theory to calculate structural correlations and thermodynamic properties of a fluid confined in a random porous solid medium (matrix). We used density functional formalism to derive an annealed averaged expression for the density profile and excess free energy of fluid arising due to random fields of a particular realization of the matrix. After performing the second average over the quenched-disordered variables, the excess free energy is organized to give one- and two-body potentials for fluid particles. The average over disorder reduces the system to an effective one-component system of fluid in which particles feel one-body (external) potential and interact via effective pair potential. The effective pair potential is a sum of the bare (the one in the pure fluid) and the matrix-induced potential. The resulting partition function involves only fluid variables. Equations are derived for fluid-fluid and fluid-matrix correlation functions and for free energy, pressure, and chemical potential of the fluid. The theory is applied to a model system of hard spheres and results for the effective pair potential, correlation functions, and thermodynamic properties are reported. The effective pair potential is found to be attractive at the contact and develops a repulsive peak before decaying to zero. Results for pair correlation function and structure factor are compared with simulation results for several fluid densities at two matrix densities. In all the cases, a very good agreement has been found.

Multiple scattering of coherent light in a random medium containing optical turbulence and randomly distributed particles

Multiple scattering of coherent light in a random medium containing optical turbulence and randomly distributed particles

Experimental Study of Fast Orthogonal Frequency Division Multiplexing Transmission over a Random Media Channel for Optical Wireless Communications

In this paper, a 4 amplitude shift keying (4-ASK) fast orthogonal frequency division multiplexing (FOFDM) scheme was experimentally investigated over a turbulent air–water channel for optical wireless communications. The experiment results showed that the 4-ASK-FOFDM modulated signals were not sensitive to weak atmospheric turbulence, and the bit-error rate (BER) was lower than the 7% forward error correction (FEC) limit of 3.8 × 10−3. Under the condition of the same spectra efficiency, the 4-ASK-FOFDM scheme just had a tiny performance penalty compared to the 16-QAM-OFDM scheme. Consequently, the 4-ASK-FOFDM scheme is a promising alternative to the conventional 16-QAM-OFDM scheme in optical wireless communications.

Scintillating and decorrelating signals for different propagation paths in a random medium

Randomness in the medium of propagation affects the signal received at a distance from a source resulting in amplitude and phase fluctuations as well as reduced coherence between different paths of propagation. A method is described and validated for incorporating such fluctuations and decorrelations in sound signals in a single approach. Here, simplified conditions are used of open space, with or without a single reflecting surface, assuming fluctuations as for plane waves in homogeneous and isotropic temperature turbulence. Validating results are shown for Gaussian and von Karman turbulence models and exemplifying sound clips are provided as supplementary material.

A computational method for calculating the electrical and thermal conductivity of random composites

In the present work, for the first time, the electrical–thermal conductivity of a composite random material is correlated with the number of conductive paths, the mean path length, and the mean effective path width measured in a representative surface element (RSE) by Monte Carlo sampling. This work is organized in two parts. The theoretical calculation takes place in the first part for the correlation of conductive paths by adopting three approaches (incremental with respect to accuracy and complexity) based on: (i) one-component straight paths; (ii) one-component non-straight paths; (iii) multi-component non-straight paths. In the second part, a novel numerical methodology for the calculation of the conductance of the RSE through the conductive paths, mean path length and the mean effective path is developed for the general model of multi-component non-straight line paths based on Ohm’s law. In addition, a methodology that reduces the calculated conductivity from the microscale to the macroscale is proposed, that takes into account the probability of percolation for finite sizes and the average value of the conductivity from the samples in which percolation occurs. After the necessary consistency steps and verification of the method and its implementation on random binary material systems, it is further applied to solve synthetic continuous percolation problems at the microscale and macroscale. The results and the accuracy of the calculations are in close agreement with existing models. The electrical Direct Current (DC) and thermal conductivity follow the same scaling relation and the proposed methodology can be applied at the same stage without additional cost. In a random binary medium the simulations showed that a scaling law of conductivity is followed by an exponent value close to 1.3. In addition, the number of conductive paths, the average length of the paths, and the effective width follow scaling laws with exponents 1.44±0.01 , −0.25±0.01 and −0.39±0.01, respectively.

Adaptive Spatial Scheduling for Event Traffic in LoRaWAN Networks.

Low-Power Wide-Area Networks constitute a leading, emerging Internet-of-Things technology, with important applications in environmental and industrial monitoring and disaster prevention and management. In such sensor networks, external detectable events can trigger synchronized alarm report transmissions. In LoRaWANs, and more generally in networks with a random access-based medium access algorithm, this can lead to a cascade of frame collisions, temporarily resulting in degraded performance and diminished system operational capacity, despite LoRaWANs' physical layer interference and collision reduction techniques. In this paper, a novel scheduling algorithm is proposed that can increase system reliability in the case of such events. The new adaptive spatial scheduling algorithm is based on learning automata, as well as previous developments in scheduling over LoRaWANs, and it leverages network feedback information and traffic spatial correlation to increase network performance while maintaining high reliability. The proposed algorithm is investigated via an extensive simulation under a variety of network conditions and compared with a previously proposed scheduler for event-triggered traffic. The results show a decrease of up to 30% in average frame delay compared to the previous approach and an order of magnitude lower delay compared to the baseline algorithm. These findings highlight the importance of using spatial information in adaptive schemes for improving network performance, especially in location-sensitive applications.

Peridynamic Models for Random Media Found by Coarse Graining

Peridynamic Models for Random Media Found by Coarse Graining

Slope Design in Surface Mining with a Total Probability Methodology [Diseño de Taludes en Minería Superficial con una Metodología de Probabilidad Total

The main goal of this research is to propose a methodology for the design of optimal slopes in surface mining, by applying the probability of total failure in the process of determining the geometry of the berm-bench of rock slopes. The rock mass is characterized by being a discontinuous, anisotropic and random medium. Therefore, to design slopes, a deterministic value or Safety Factor that represents the reliability of the design is not sufficient, and the inherent uncertainty of the geotechnical properties must be considered. The stability of slopes at bench level is a function of the quality of the rock mass and is controlled by the strength of the intact rock, the structural rocks, or a combination of both. When the slope has a defined structural control, planar, wedge or toppling failure modes are formed; These, depending on the stability conditions and generates rockfall events. Therefore, it is necessary to apply an effective method to establish the optimal geometry of the bench. The purpose of the berm-bench is to retain and mitigate the risk of rockfall and contain spill from upper slopes due to inherent instabilities, to provide a safe environment for personnel and equipment working near the slopes. The proposed methodology considers the variability of the dip, dip direction, persistence, and friction of the discontinuities. The procedure begins with the collection and analysis of the geotechnical information of the rock mass, which defines geotechnical domains, design sectors and main families of discontinuities; then, statistical analysis and kinematic evaluation are carried out and the conceptual berm width is determined; finally, the kinetic and probability of total failure analysis is carried out, validating the design geometry. The research focused on a domain with 04 sectors of geotechnical design. The results show that the applicable design bench face angle is between 53° and 71°, which corresponds to a berm width of 9.3m to 8.6m and a geometric interramp angle between 36° and 48° respectively. Likewise, probabilities of total planar failure of up to 31% and total wedge of 41% were obtained according to the geotechnical peculiarities of each sector. It was proven that, in the sectors with a greater probability of failure, a lower bench face angle and a greater catch bench of the design berm are considered acceptable designs, due to a greater probability of crest loss. Finally, in the sectors with a lower probability of failure, a greater interramp angle is considered an acceptable design. In conclusion, through the applied methodology it has been demonstrated that the results of the berm-bench design process meet the acceptability criteria of the Probability of Failure. Therefore, the developed method, which considers the variability of the parameters of the rock mass discontinuities, allows designing safe and reliable slopes validated through an acceptable level of probability.

Terahertz bistatic three-dimensional computational imaging of hidden objects through random media

Random media pose limitations on the imaging capability of photoelectric detection devices. Currently, imaging techniques employed through random media primarily operate within the laser wavelength range, leaving the imaging potential of terahertz waves unexplored. In this study, we present an approach for terahertz bistatic three-dimensional imaging (TBTCI) of hidden objects through random media. By deducing the field distribution of bistatic terahertz time-domain spectroscopy system, and proposing an explicit point spread function of the random media, we conducted three-dimensional imaging of hidden objects obscured by the random media. Our proposed method exhibits promising applications in imaging scenarios with millimeter-wave radar, including non-invasive testing and biological imaging.

High-throughput speckle spectrometers based on multifractal scattering media

We present compact integrated speckle spectrometers based on monofractal and multifractal scattering media in a silicon-on-insulator platform. Through both numerical and experimental studies we demonstrate enhanced optical throughput, and hence signal-to-noise ratio, for a number of random structures with tailored multifractal geometries without affecting the spectral decay of the speckle correlation functions. Moreover, we show that the developed multifractal media outperform traditional scattering spectrometers based on uniform random distributions of scattering centers. Our findings establish the potential of low-density random media with multifractal correlations for integrated on-chip applications beyond what is possible with uncorrelated random disorder.

Random laser emission from dye-doped gain media with optically trapped scattering particles

In this study, an optical trapping technique is employed to manipulate the scatterer distribution within a random laser medium. By focusing the trapping beams into small regions within the three-dimensional scattering medium, the scattering particles around them are concentrated in those regions, resulting in an inhomogeneous scatterer distribution. The experimental results show that optical trapping increases the maximum spike intensity in the emission spectrum. Furthermore, the spectral spike intensity depends on the power of the trap spots. The relationship between the maximum and average spike intensities in the emission spectra exhibits a characteristic observed in other random lasers with inhomogeneous scatterer distributions.

Random medium modeling and underwater acoustic field simulation

The von Karman random medium model is established based on the small scale random medium theory in this paper. Combined with the finite element theory, the numerical simulation of the sound field under this model is realized by using the spectral-element method, and the characteristics of the sound field are compared with those under the uniform medium underwater environment. The results show that the correlation length reflects the variation of the heterogeneous size, and the scattering wave generated by random disturbance may provide a more reasonable explanation for the amplitude and energy anomalies in some trial data.

Recovery of polarization entanglement in partially coherent photonic qubits.

Partially coherent photonic qubits, owing to their robustness in propagation through random media compared to fully coherent qubits, find applications in free-space communication, quantum imaging, and quantum sensing. However, the reduction of spatial coherence degrades entanglement in qubits, adversely affecting entanglement-based applications. We report the recovery of entanglement in the partially coherent photonic qubits generated using a spontaneous parametric downconversion process despite retaining their multimode nature. This study utilizes an electron multiplying charge-coupled device (EMCCD) to perform coincidence measurements, eliminating the need for raster scanning of single-pixel detectors, which simplifies optical alignment, enhances precision, and reduces time consumption. We demonstrate that the size of apertures used to select biphotons substantially impacts the visibility and S-parameter of polarization-entangled partially coherent qubits. The entanglement is recovered with partial spatial coherence properties by choosing small sizes of the apertures in the captured image plane. This study could help in the advancement of free-space quantum communication, quantum imaging, and quantum metrology.

Probing the large deviations for the beta random walk in random medium.

We consider a discrete-time random walk on a one-dimensional lattice with space- and time-dependent random jump probabilities, known as the beta random walk. We are interested in the probability that, for a given realization of the jump probabilities (a sample), a walker starting at the origin at time t=0 is at position beyond ξsqrt[T/2] at time T. This probability fluctuates from sample to sample and we study the large-deviation rate function, which characterizes the tails of its distribution at large time T≫1. It is argued that, up to a simple rescaling, this rate function is identical to the one recently obtained exactly by two of the authors for the continuum version of the model. That continuum model also appears in the macroscopic fluctuation theory of a class of lattice gases, e.g., in the so-called KMP model of heat transfer. An extensive numerical simulation of the beta random walk, based on an importance sampling algorithm, is found in good agreement with the detailed analytical predictions. A first-order transition in the tilted measure, predicted to occur in the continuum model, is also observed in the numerics.

Universal Crosstalk of Twisted Light in Random Media.

Structured light offers wider bandwidths and higher security for communication. However, propagation through complex random media, such as the Earth's atmosphere, typically induces intermodal crosstalk. We show numerically and experimentally that coupling of photonic orbital angular momentum modes is governed by a universal function of a single parameter: the ratio between the random medium's and the beam's transverse correlation lengths, even in the regime of pronounced intensity fluctuations.

Coherent full microwave scattering formulation for random layered media.

We present a fully coherent, analytic model of the backscattering intensity in all H H,H V,V H, and V V channels, for the volume scattering of radiation from a layer of finite thickness, such as a vegetation layer over bare soil. We aim for a simple, not numerically intensive, model that could be used either as a forward model in a Bayesian estimation scheme, or else as a preliminary means to identify key features of a concrete problem, for its further analysis by more sophisticated theoretical and numerical approaches.

Isotropic gap formation, localization, and waveguiding in mesoscale Yukawa-potential amorphous structures

Amorphous photonic structures are mesoscopic optical structures described by electrical permittivity distributions with underlying spatial randomness. They offer a unique platform for studying a broad set of electromagnetic phenomena, including transverse Anderson localization, enhanced wave transport, and suppressed diffusion in random media. Despite this, at a more practical level, there is insufficient work on both understanding the nature of optical transport and the conditions conducive to vector-wave localization in these planar structures, as well as their potential applications to photonic nanodevices. In this study, we fill this gap by investigating experimentally and theoretically the characteristics of optical transport in a class of amorphous photonic structures and by demonstrating their use to some basic waveguiding nanostructures. We demonstrate that these 2-D structures have unique isotropic and asymmetric band gaps for in-plane propagation, controlled from first principles by varying the scattering strength and whose properties are elucidated by establishing an analogy between photon and carrier transport in amorphous semiconductors. We further observe Urbach band tails in these random structures and uncover their relation to frequency- and disorder-dependent Anderson-like localized modes through the modified Ioffe-Regel criterion and their mean free path - localization length character. Finally, we illustrate that our amorphous structures can serve as a versatile platform in which photonic devices such as disorder-localized waveguides can be readily implemented.

A modification to the extended Rytov theory

This paper proposes a heuristic modification to the extended Rytov theory of strong scintillation [Andrews L, Phillips R. Laser beam propagation through random media. 2nd ed., Washington, USA: SPIE Press; 2005, Andrews LC, Al-Habash MA, Hopen CY, et al. Theory of optical scintillation: Gaussian-beam wave model. Waves Random Media. 2001;11(3):271–291]. This is done by dividing the large and small scales in the extended Rytov theory into further sub-scales. Expressions for the induced irradiance variance, and log-irradiance, due to each sub-scale are presented. The modified theory is used to derive and justify recent results in irradiance fluctuation modeling and hence answer a question initially proposed in [Shishter YM, Young RC, Ali FH. Irradiance probability density function for turbulence induced fading in free space optics. JOSA A. 2022;39(7):1267–1274, Shishter YM, Young RC, Ali FH. General statistical model of irradiance fluctuations in free space optics. JOSA A. 2023;40(1):53–63]. Plots of the irradiance pdf under the modified theory are in support of the theory. The validity of the theory presented would result in modifications to the classical scintillation analysis of waves in random media, with applications to the design of optical systems. Moreover, it is observed that the mathematical framework developed also follows from the assumption of variations in the turbulence along a horizontal path. The work presented in this paper suggests the need of further theoretical and experimental investigations into the effect of variations in atmospheric turbulence characteristics along horizontal paths in the received signal irradiance distribution.

A machine learning based-method to generate random circle-packed porous media with the desired porosity and permeability

The generation of digital porous media facilitates the fabrication of artificial porous media and the analysis of their properties. The past random digital porous medium generation methods are unable to generate a porous medium with a specified permeability. In this work, a new method is proposed to generate a random circle-packed digital porous medium with a specified porosity and permeability. Firstly, the process of generating the random circle-packed digital porous medium with a specified porosity is detailed. Secondly, the permeability of the digital porous medium is calculated by the multi-relaxation time lattice Boltzmann method. A total of 3,000 digital porous medium samples are generated, and their microstructure data and permeabilities are prepared for the training of a convolutional neural network (CNN) model, which is then applied to effectively predict the permeability of a digital porous medium. Finally, our method is elaborated and the choice of target permeability in this method is discussed. Our approach has the potential to be applied to the generation of other types of porous media.