Two-dimensional Random Media Research Articles

Depinning and flow of a vortex line in a uniaxial random medium

We study numerically and analytically the dynamics of a single directed elastic string driven through a three-dimensional disordered medium. In the quasistatic limit the string is super-rough in the direction of the driving force, with roughness exponent ${\ensuremath{\zeta}}_{\ensuremath{\parallel}}=1.25\ifmmode\pm\else\textpm\fi{}0.01$, dynamic exponent ${z}_{\ensuremath{\parallel}}=1.43\ifmmode\pm\else\textpm\fi{}0.01$, correlation-length exponent $\ensuremath{\nu}=1.33\ifmmode\pm\else\textpm\fi{}0.02$, depinning exponent $\ensuremath{\beta}=0.24\ifmmode\pm\else\textpm\fi{}0.01$, and avalanche-size exponent ${\ensuremath{\tau}}_{\ensuremath{\parallel}}=1.09\ifmmode\pm\else\textpm\fi{}0.03$. In the transverse direction we find ${\ensuremath{\zeta}}_{\ensuremath{\perp}}=0.5\ifmmode\pm\else\textpm\fi{}0.01, {z}_{\ensuremath{\perp}}=2.27\ifmmode\pm\else\textpm\fi{}0.05$, and ${\ensuremath{\tau}}_{\ensuremath{\perp}}=1.17\ifmmode\pm\else\textpm\fi{}0.06$. Our results show that transverse fluctuations do not alter the critical exponents in the driving direction, as predicted by the planar approximation (PA) proposed by Ertas and Kardar (EK) [Phys. Rev. B 53, 3520 (1996)]. We check the PA for the measured force-force correlator, comparing to the functional renormalization-group and numerical simulations. Both random-bond (RB) and random-field (RF) disorder yield a single universality class, indistinguishable from the one of an elastic string in a two-dimensional random medium. While relations ${z}_{\ensuremath{\perp}}={z}_{\ensuremath{\parallel}}+1/\ensuremath{\nu}$ and $\ensuremath{\nu}=1/(2\ensuremath{-}{\ensuremath{\zeta}}_{\ensuremath{\parallel}})$ of EK are satisfied, the transversal movement is that of a Brownian, with a clock set locally by the forward movement. This implies ${\ensuremath{\zeta}}_{\ensuremath{\perp}}=(2\ensuremath{-}d)/2$, distinct from EK. Finally, at small driving velocities the distribution of local parallel displacements has a negative skewness, while in the transverse direction it is a Gaussian. For large scales, the system can be described by anisotropic effective temperatures defined from generalized fluctuation-dissipation relations. In the fast-flow regime the local displacement distributions become Gaussian in both directions and the effective temperatures vanish as ${T}_{\mathtt{eff}}^{\ensuremath{\perp}}\ensuremath{\sim}1/v$ and ${T}_{\mathtt{eff}}^{\ensuremath{\parallel}}\ensuremath{\sim}1/{v}^{3}$ for RB disorder and as ${T}_{\mathtt{eff}}^{\ensuremath{\perp}}\ensuremath{\approx}{T}_{\mathtt{eff}}^{\ensuremath{\parallel}}\ensuremath{\sim}1/v$ for RF disorder.

Non-universality of the dynamic exponent in two-dimensional random media

The diffusion of solutes in two-dimensional random media is important in diverse physical situations including the dynamics of proteins in crowded cell membranes and the adsorption on nano-structured substrates. It has generally been thought that the diffusion constant, D, should display universal behavior near the percolation threshold, i.e., D ~ (ϕ − ϕc)μ, where ϕ is the area fraction of the matrix, ϕc is the value of ϕ at the percolation threshold, and μ is the dynamic exponent. The universality of μ is important because it implies that very different processes, such as protein diffusion in membranes and the electrical conductivity in two-dimensional networks, obey similar underlying physical principles. In this work we demonstrate, using computer simulations on a model system, that the exponent μ is not universal, but depends on the microscopic nature of the dynamics. We consider a hard disc that moves via random walk in a matrix of fixed hard discs and show that μ depends on the maximum possible displacement Δ of the mobile hard disc, ranging from 1.31 at Δ ≤ 0.1 to 2.06 for relatively large values of Δ. We also show that this behavior arises from a power-law singularity in the distribution of transition rates due to a failure of the local equilibrium approximation. The non-universal value of μ obeys the prediction of the renormalization group theory. Our simulations do not, however, exclude the possibility that the non-universal values of μ might be a crossover between two different limiting values at very large and small values of Δ. The results allow one to rationalize experiments on diffusion in two-dimensional systems.

Decay of correlations between cross-polarized electromagnetic waves in a two-dimensional random medium.

The problem of multiple scattering of polarized light in a two-dimensional medium composed of fiberlike inhomogeneities is studied. The attenuation lengths for the density matrix elements are calculated. For a highly absorbing medium it is found that, as the sample thickness increases, the intensity of waves polarized along the fibers decays faster than the other density matrix elements. With further increase in the sample thickness, the off-diagonal elements which are responsible for correlations between the cross-polarized waves disappear. In the asymptotic limit of very thick samples the scattered light proves to be polarized perpendicular to the fibers. The difference in the attenuation lengths between the density matrix elements results in a nonmonotonic depth dependence of the degree of polarization. In the opposite case of a weakly absorbing medium, the off-diagonal element of the density matrix and, correspondingly, the correlations between the cross-polarized fields are shown to decay faster than the intensity of waves polarized along and perpendicular to the fibers.

Propagation of Circularly Polarized Light Through a Two-Dimensional Random Medium

The problem of small-angle multiple-scattering of circularly polarized light in a two-dimensional medium with large fiberlike inhomogeneities is studied. The attenuation lengths for elements the density matrix are calculated. It is found that with increasing the sample thickness the intensity of waves polarized along the fibers decays faster than the other density matrix elements. With further increase in the thickness, the off-diagonal element which is responsible for correlation between the cross-polarized waves dissapears. In the case of very thick samples the scattered field proves to be polarized perpendicular to the fibers. It is shown that the difference in the attenuation lengths of the density matrix elements results in a non-monotonic depth dependence of the degree of polarization.

Features of the energy structure of acoustic fields in the ocean with two-dimensional random inhomogeneities

The paper is devoted to the analytic study and numerical simulation of mid-frequency acoustic signal propagation in a two-dimensional inhomogeneous random shallow-water medium. The study was carried out by the cross section method (local modes). We present original theoretical estimates for the behavior of the average acoustic field intensity and show that at different distances, the features of propagation loss behavior are determined by the intensity of fluctuations and their horizontal scale and depend on the initial regular parameters, such as the emission frequency and size of sound losses in the bottom. We establish analytically that for the considered waveguide and sound frequency parameters, mode coupling effect has a local character and weakly influences the statistics. We establish that the specific form of the spatial spectrum of sound velocity inhomogeneities for the statistical patterns of the field intensity is insignificant during observations in the range of shallow-water distances of practical interest.

Plasmonic nanopillar coupled two-dimensional random medium for broadband light trapping and harvesting

Random textures have proven to be a better option for light localization and energy harvesting in solar cells. On the other hand, plasmonic structures are significant in localizing the fields into submicron domains. We propose a layered structure design that contains the random dielectric medium with a plasmonic nanopillars array as a back reflector, followed by demon- strating its efficient light trapping ability through simulation means. This structure has shown significant enhancement in the broadband absorption of the light spectrum in the wavelength range UV-IR and a higher extinction in the near-infrared wavelengths. The structure also shows the dependence of reflection on the nanopillar height as well as localization in the nano- pillar region. The broadened and red shifted plasmonic nanopillar resonances (transverse and longitudinal) in a high-index medium are shown as the reasons for enhanced broadband absorption. © 2015 Society of Photo-Optical Instrumentation Engineers (SPIE) (DOI: 10.1117/1. JNP.9.093061)

Mode competition of bichromatic laser emission in two-dimensional strong scattering random medium

The mode competition of the bichromatic laser emission in two-dimensional (2D) random medium was studied. Based on the time-dependent theory, a model for dual-wavelength random laser was established. The Maxwell equations and rate equations were combined and solved by using the finite different time domain (FDTD) method. Results show that the emission intensity of both wavelength ranges increases simultaneously with the increasing of the surface-filling fraction. The mode dominance of the bichromatic emission can be switched by changing the scatterer radius. The emission intensity of the longer wavelength increases when enlarging the excitation area. The controllability of these lasing modes may provide a potential application of optical switches.

Coherent transmission of an ultrasonic shock wave through a multiple scattering medium

We report measurements of the transmitted coherent (ensemble-averaged) wave resulting from the interaction of an ultrasonic shock wave with a two-dimensional random medium. Despite multiple scattering, the coherent waveform clearly shows the steepening that is typical of nonlinear harmonic generation. This is taken advantage of to measure the elastic mean free path and group velocity over a broad frequency range (2-15 MHz) in only one experiment. Experimental results are found to be in good agreement with a linear theoretical model taking into account spatial correlations between scatterers. These results show that nonlinearity and multiple scattering are both present, yet uncoupled.

二维随机介质中双波长辐射及模式竞争特性

二维随机介质中双波长辐射及模式竞争特性

Theoretical research on the random lasing from two-dimensional anisotropic media consisted of liquid crystal and mixed dye

The random lasing action in two-dimensional random media is investigated by simultaneously solving Maxwell’s equations and rate equations of electronic population. The random media are composed of scattering liquid crystal (LC) particles and mixed dye materials. The anisotropic scattering LC particles are arranged to be disordered in the spatial orientation of their optical axes. A parameter K = n o /n e ≤ 1 which denotes the ratio of the refractive indexes at two principal axes is defined to characterize the degree of the orientational disorder. The number of the lasing modes increases quickly with the decreasing of ratio K. In addition, the simulation of the external modulation of dielectric constant is studied. Results indicate that the spectrum intensity would be enhanced; whilst the frequencies of the lasing modes do not change significantly.

A study on the effect of filling factor for laser action in dielectric random media

In a random system composed of dielectric materials, laser action is expected to occur from the light localization caused by multiple scattering and interference effect. The wavelengths at which the laser oscillation occurs in random media depend on the mean free path of continuous scattering. Since the mean free path of continuous scattering is dependent on the filling factor, it is important to investigate systematically the effect of the filling factor for the laser action. In the present study, we calculate the Poynting vectors of the light emitted from two-dimensional random media consisting of dielectric rods with population inversion modeled by the negative imaginary part of relative permittivity. The spectra of the radiated Poynting vectors from the two-dimensional random media are shown for several different filling factors and for various values of population inversion. We try to find laser generation which occurs at low population inversion and discuss about the threshold of laser action occurring in dielectric structures with different filling factors. We also study the spacial distribution of the electric field amplitude in several frequency regions where light strongly amplifies.

局域抽运条件下二维无序介质内偏振模式的特性研究

局域抽运条件下二维无序介质内偏振模式的特性研究

Role of quenching on superdiffusive transport in two-dimensional random media

Transport in random media is known to be affected by quenched disorder. From the point of view of random walks, quenching induces correlations between steps that may alter the dynamical properties of the medium. This paper is intended to provide more insight into the role of quenched disorder on superdiffusive transport in two-dimensional random media. The systems under consideration are disordered materials called Lévy glasses that exhibit large spatial fluctuations in the density of scattering elements. We show that in an ideal Lévy glass the influence of quenching can be neglected, in the sense that transport follows to very good approximation that of a standard Lévy walk. We also show that, by changing sample parameters, quenching effects can be increased intentionally, thereby making it possible to investigate systematically diverse regimes of transport. In particular, we find that strong quenching induces local trapping effects which slow down superdiffusion and lead to a transient subdiffusivelike transport regime close to the truncation time of the system.

Stochastic functional analysis of propagation and localisation of cylindrical waves in a two-dimensional random medium

Propagation and localisation of cylindrical waves in a two-dimensional (2D) isotropic and homogeneous random medium is studied using the stochastic functional approach. By expanding the random permittivity fluctuation in the form of a Wiener integral equation, and representing the wave fields by a linear combination of outgoing and incoming waves, the scalar Helmholtz equation is solved in the cylindrical coordinates system. An analytical expression of the cylindrical wave is derived and demonstrates the localisation phenomenon, as well as the wavenumber fluctuation in the random medium. Comparing with the waves in non-random medium, the wave transfer equation between plane wave and cylindrical wave in random medium shows an additional exponential factor to indicate the modulation effect owing to the medium randomness in both the amplitude and phase. Numerical simulations are presented to illustrate the functional dependence of the localisation phenomena.

Stochastic functional analysis of propagation and localization of cylindrical wave in a two-dimensional random medium

Propagation and localization of cylindrical wave in a two-dimensional isotropic and homogeneous random medium is studied. By expanding the random permittivity fluctuation in the form of a Wiener integral equation in the frequency domain, and representing the wave fields by a linear combination of outgoing and incoming waves, the scalar Helmholtz equation is solved by means of stochastic functional approach to obtain the analytical expression of cylindrical wave. The spatial wave energy distribution is derived to demonstrate the localization phenomenon, and the localization length is also calculated. Compared with the waves in non-random medium, the wave transfer equation between plane wave and cylindrical wave in random medium shows an additional exponential factor to indicate the modulation effects due to the medium randomness in both the amplitude and the phase. Numerical simulations are presented to illustrate the functional dependence of the localization phenomenon.

Relaxation dynamics of an elastic string in random media

We investigate numerically the relaxation dynamics of an elastic string in two-dimensional random media by thermal fluctuations starting from a flat configuration. Measuring spatial fluctuations of its mean position, we find that the correlation length grows in time asymptotically as xi approximately (ln t)1/chi . This implies that the relaxation dynamics is driven by thermal activations over random energy barriers which scale as EB(l) approximately l;chi with a length scale l . Numerical data strongly suggest that the energy barrier exponent chi is identical to the energy fluctuation exponent chi=1/3 . We also find that there exists a long transient regime, where the correlation length follows a power-law dynamics as xi approximately t1/z with a nonuniversal dynamic exponent z . The origin of the transient scaling behavior is discussed in the context of the relaxation dynamics on finite ramified clusters of disorder.

Polarization-dependent difference of the power spectra from two-dimensional random media with different shapes

Polarization-dependent difference of the power spectra from a set of two-dimensional (2D) passive random media is investigated by simultaneously solving Maxwell’s equations for both transverse magnetic (TM) and transverse electric (TE) fields. The random media have the same random constitution but different shapes. Results show that both two polarized states are morphology dependent, and the variety of the shapes has more influence on the selection of TM polarized modes than that of TE polarized modes. Such polarization-dependent difference of morphology property presents a new mode-selecting technique for random lasers.

Localization of radiation in two-dimensional random media of finite extent

The localization of electromagnetic waves in a two-dimensional random medium composed of strong scatterers is studied theoretically. It is shown that an allowance for the spatial radiation intensity distribution inside the medium, along with an analysis of the distance dependence of the transmission coefficient, is needed to reveal the localization states in media of finite extent.

Theoretical investigation on temporal properties of random lasers pumped by femtosecond-lasing pulses

Pulsing random lasing property has been investigated in both one- and two-dimensional random medium by numerically solving Maxwell’s equations and rate equations in which the pumping rate is described by a time function with duration of 10s or 100s of femtoseconds. The peak intensity, width and delay time of a random lasing pulse are traced with the variation of the peak intensity, duration, shape and numbers of a pumping pulse. Results show that the behavior of random lasing depends strongly on the pumping process, some of which are in agreement with previously reported experiments pumped by femtosecond-lasing pulses. The present work enriches the knowledge about random lasers, especially in temporal regime, and could offer more guidance for relevant experiments.

Spectral time evolution of polarized modes under local pumping in a two-dimensional random medium

The spectral time evolution of polarized modes under local pumping in two-dimensional (2D) random media is investigated by simultaneously solving Maxwell's equations and rate equations. Also the values of quality factor (Q factor) are obtained for the marked polarized modes by calculating the decay rates of them. The results demonstrate that there exists a critical value of local pumping area for TM modes. If the area is less than this value, the TM modes would have a quicker rise of the peak intensity and smaller Q factor than that of TE modes. Or else the conclusions would be contrary.