Spatial confinement of laser light in active random media

We have observed spatial confinement of laser light in micrometer-sized random media. The optical confinement is attributed to the disorder-induced scattering and interference. Our experimental data suggest that coherent amplification of the scattered light enhances the interference effect and helps the spatial confinement. Using the finite-difference time-domain method, we simulate lasing with coherent feedback in the active random medium.     

Anomalous polarization effects during light scattering in random media

The dependence of the intensity of light backscattered from a layer of a randomly inhomogeneous medium on the polarization of incident light and the size of scatterers has been investigated. The results of numerical simulation have demonstrated that the direction of rotation of the plane of polarization is different in systems with small- and large-scale inhomogeneities. It is shown for the first time that the dependence of the sign of the residual circular polarization on the size of scatterers can be observed in systems described by the Henyey-Greenstein phase function used in simulating biological tissues. A similar anomalous polarization effect, which consists in changing the direction of rotation of the plane of polarization of backscattered light with an increase in the scattering angle, is revealed in studying the coherent backscattering component. These polarization effects are observed in light backscattering from optically active media.     

Generation of light in media with a random distribution of nonlinear domains

We show that the second order nonlinear generation of light, a process that it is assumed to require highly ordered materials, is also possible in structures of randomly oriented nonlinear domains. We explain theoretically why in such disordered structures the efficiency of the nonlinear generation of light grows linearly with the number of domains. Moreover, a higher degree of disorder, obtained when the dispersion is made very large, has no negative effect for the nonlinear light generation. In such conditions, light generation is shown to be equally efficient for any average size of the domains and also to grow linearly with respect to the number of domains.     

Parallel wavefront optimization method for focusing light through random scattering media

A parallel wavefront optimization method is demonstrated experimentally to focus light through random scattering media. The simultaneous modulation of multiple phase elements, each at a unique frequency, enables a parallel determination of the optimal wavefront. Compared to a pixel-by-pixel measurement, the reported parallel method uses the target signal in a highly efficient way. With 441 phase elements, a high-quality focus was formed through a glass diffuser with a peak-to-background ratio of ～270. The accuracy and repeatability of the system were tested through experiments.     

Correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media

The correlation between intensity fluctuations of light scattered from a quasi-homogeneous random media was analytically derived. We showed the correlation depends on spatial Fourier transforms of both the intensity and degree of spatial correlation of scattering potentials of the media, while the normalized correlation equals the squared modulus of the degree of spatial coherence of the scattered fields.     

Coherent recovery of the degree of polarization of light propagating in random anisotropy media

We report on the study of light polarization behavior in random anisotropy scattering media. It is shown that, in the case of low scattering events, the degree of polarization (DOP) demonstrates oscillatory behavior due to the coherent character of light scattering. A strong increase in the DOP is demonstrated by using electro-optic fine tuning of the refractive index modulation depth of the scattering media.     

Lasing in random media

A random laser is a non-conventional laser whose feedback mechanism is based on disorder-induced light scattering. Depending on whether the feedback supplied by scattering is intensity feedback or amplitude feedback, random lasers are classified into two categories: random lasers with incoherent feedback and random lasers with coherent feedback. A brief survey of random lasers with incoherent feedback is presented. It is followed by a review of our recent experimental work on random lasers with coherent feedback, including measurement of the lasing threshold, lasing spectra, emission pattern, dynamical response, photon statistics, speckle pattern and the investigation of relevant length scales. Large disorder leads to spatial confinement of the lasing modes, that is the foundation for the micro random laser. Some theoretical models of random lasers with coherent feedback are briefly introduced. The study of random lasers improves our understanding of the interplay between light localization and coherent amplification.     

Dependence of the circular polarization of backscattered light in random media on anisotropy of scatterers

The scattering of linearly or circularly polarized light from a semi-infinite randomly inhomogeneous medium is considered. Using the Monte Carlo method, it is shown that, in the case of a wide front of incident and scattered optical radiation and irrespective of the degree of scattering anisotropy, the copolarized component of backscattered light dominates the cross-polarized component for the linear polarization and the cross-polarized component dominates the copolarized component for the circular polarization. If the beams of incident and scattered radiation are spatially separated and the size of scatterers exceeds the wavelength, the circular copolarized component dominates the cross-polarized one. A similar effect of the change in direction of the rotation of the plane of polarization in relation to the size of scatterers is revealed for pulsed radiation.     

Violation of light beam reversibility principle in optical media with a random quasi-zero refractive index

The relic abundance of light millicharged particles (MCPs) with the electric charge e′ = 5 × 10^–5 e and with the mass slightly below or above the electron mass is calculated. The abundance depends on the mass ratio η = m _X /m _e and for η < 1 can be high enough to allow MCPs to be the cosmological dark matter or to make a noticeable contribution to it. On the other hand, for η ? 1 the cosmological energy density of MCPs can be quite low, Ω _X h ₀ ² ≈ 0.02 for scalar MCPs, and Ω _X h ₀ ² ≈ 0.001 for spin 1/2 fermions. But even the lowest value of Ω _X h ₀ ² is in tension with several existing limits on the MCP abundances and parameters. However, these limits have been derived under some natural or reasonable assumptions on the properties of MCPs. If these assumptions are relaxed, a patch in the mass–charge plot of MCPs may appear, permitting them to be dark matter particles.     

Coherent backscattering of light by complex random media of spherical scatterers: numerical solution

Novel Monte Carlo techniques are described for the computation of reflection coefficient matrices for multiple scattering of light in plane-parallel random media of spherical scatterers. The present multiple scattering theory is composed of coherent backscattering and radiative transfer. In the radiative transfer part, the Stokes parameters of light escaping from the medium are updated at each scattering process in predefined angles of emergence. The scattering directions at each process are randomized using probability densities for the polar and azimuthal scattering angles: the former angle is generated using the single-scattering phase function, whereafter the latter follows from Kepler's equation. For spherical scatterers in the Rayleigh regime, randomization proceeds semi-analytically whereas, beyond that regime, cubic spline presentation of the scattering matrix is used for numerical computations. In the coherent backscattering part, the reciprocity of electromagnetic waves in the backscattering direction allows the renormalization of the reversely propagating waves, whereafter the scattering characteristics are computed in other directions. High orders of scattering (~10 000) can be treated because of the peculiar polarization characteristics of the reverse wave: after a number of scatterings, the polarization state of the reverse wave becomes independent of that of the incident wave, that is, it becomes fully dictated by the scatterings at the end of the reverse path. The coherent backscattering part depends on the single-scattering albedo in a non-monotonous way, the most pronounced signatures showing up for absorbing scatterers. The numerical results compare favourably to the literature results for nonabsorbing spherical scatterers both in and beyond the Rayleigh regime.     

Fractional precursors in random media

When a broadband pulse penetrates into a dissipative and dispersive medium, phase dispersion and frequency-dependent attenuation alter the pulse in a way that results in the appearance of a precursor field with an algebraic decay. We derive here the existence of precursors in non-dispersive, non-dissipative, but randomly heterogeneous and multiscale media. The shape of the precursor and its fractional power law decay with propagation distance depend on the random medium class. Three principal scattering precursor classes can be identified: (i) in exponentially decorrelating random media, and more generally in mixing random media, the precursor has a Gaussian shape and a peak amplitude that decays as the square root of the inverse of the propagation distance. (ii) In short-range correlation media, with rough multiscale medium fluctuations, the precursor has a skewed shape with a tail that exhibits an anomalous power law decay in time and a peak amplitude that exhibits an anomalous power law decay with propagation distance, both of which depend on the Hurst exponent that characterizes the roughness of the medium. (iii) In long-range correlation media with long-range memory, the situation mimics that of class (ii), but with modified power laws.     

Distance statistics in random media

Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to kth nearest neighbor in a d-dimensional media. Next, we focus our attention in high dimensionality and high neighborhood order limits. High dimensionality makes distance distribution behavior as a delta sequence, with mean value equal to Cerf’s conjecture. Distance statistics in high neighborhood order converges to a Gaussian distribution. The general distance statistics can be applied to detect departures from Poissonian point distribution hypotheses as proposed by Thompson and generalized here.     

Dielectric polarization in random media

The theory of dielectric polarization in random media is systematically formulated in terms of response kernels. The primary response kernel K(12) governs the mean dielectric response at the pointr ₁ to the external electric field at the pointr ₂ in an infinite system. The inverse of K(12) is denoted by L(12); it is simpler and more fundamental than K(12) itself. Rigorous expressions are obtained for the effective dielectric constant ^* in terms of L(12) and K(12). The latter expression involves the Onsager-Kirkwood function ( ^*– ₀)(2 ^*+ ₀) /₀^* (where ₀ is an arbitrary reference value), and appears to be new to the random medium context. A wide variety of series representations for ^* are generated by means of general perturbation expansions for K(12) and L(12). A discussion is given of certain pitfalls in the theory, most of which are related to the fact that the response kernels are long ranged. It is shown how the dielectric behavior of nonpolar molecular fluids may be treated as a special case of the general theory. The present results for ^* apply equally well to other effective phenomenological coefficients of the same generic type, such as thermal and electrical conductivity, magnetic susceptibility, and diffusion coefficients.Work performed under the auspices of the United States Department of Energy. A preliminary report on this work was given at the Eighth West Coast Statistical Mechanics Conference, University of California, Berkeley, 22 June 1982.     

Waves in resonant random media

Electromagnetic properties of resonant inhomogeneous media are investigated. A new type of transverse electromagnetic wave arising due to the effective spatial dispersion is studied. It is shown that scattering on the fluctuations of the resonant frequency of the medium shifts the Cherenkov threshold and reduces the intensity of the Cherenkov radiation.     

Multiple scattering in random media

The paper is an application of a general microscopic approach to the theory of the average scattering matrix for a particle interacting with random scatterers. We present a detailed treatment for the case of uncorrelated positions of the scatterers. First, the general two-body additive approximation is used to truncate the hierarchy of correlation functions for fluctuations. It is shown that the self-energy is accurate through the fourth power of the individual scattering amplitude. Second, the hierarchy is terminated at the next stage. The self-energy is correct to the sixth power of the scattering amplitude.Work supported in part by the National Science Foundation under Contract No. NSF DMR 79-23213.     

Self-trapping in random nonhomogeneous media

The theory of the self-trapping of excitons and current carriers and solitons in random nonhomogeneous media is developed. We obtain laws of velocity of self-trapping for particles in a random potential. At some high temperature we obtain the new inverse Arrhenius law for the self-trapping velocity. The total picture for static soliton behaviour is considered.     

Waves in resonant random media

Abstract

Electromagnetic properties of resonant inhomogeneous media are investigated. A new type of transverse electromagnetic wave arising due to the effective spatial dispersion is studied. It is shown that scattering on the fluctuations of the resonant frequency of the medium shifts the Cherenkov threshold and reduces the intensity of the Cherenkov radiation.     

Population growth in random media

In this second part of a two-part presentation, we continue with the model introduced in Part I. In this part, the initial configuration has one particle at each site to the left of 0 and no particle elsewhere. The expected number of particles observed at a site moving at speed has an exponential growth rate (speed- growth rate) that is computed explicitly. The result reveals two characteristic wavefront speeds: ₁, the speed of the front of zero growth (rightmost particle), and ₂, the speed of the front of maximal growth. The latter speed exhibits a phase transition, changing from zero to positive as the drift in the migration crosses a threshold. The qualitative shape of the growth rate as a function of changes as well. In particular, below the threshold there appears a linear piece, which corresponds to the system exhibiting an intermittency effect.