Enhanced twinkling in left-handed media.

A slab of left-handed material (LHM) with refractive index -1 forms a perfect lens that retains subwavelength information about a source or object. Such lenses are highly susceptible to perturbations affecting their performance. It is shown that illuminating a roughened interface between air and an LHM produces a regime for enhanced focusing of light close to the boundary. This generates caustics that are brighter, fluctuate more, and cause Gaussian speckle at distances closer to the interface than in right-handed matter. These effects present fresh challenges for perfecting the perfect lens.

Perfect lens with not so perfect boundaries.

In manufacturing left-handed media the interfaces will never be perfect; defects and other disturbances to interfaces and material parameters are unavoidable. We report an analytical calculation of electromagnetic wave propagation through a perfect lens with diffuse boundaries. Field localizations are generated in the boundary layers, and the lens' ability to recover evanescent modes in the presence of these boundaries is analyzed and quantified. It is shown that such a diffuse layer produces an effect that is qualitatively similar to a lens with increased losses.

Fluctuations in the zeros of differentiable Gaussian processes.

The stochastic point processes formed by the zero crossings or extremal points of differentiable, stationary Gaussian processes are studied as a function of their autocorrelation function. The properties of these point processes are mapped to the space formed by the parameters appearing in the autocorrelation function, their adopted form being sensitive to the structure of the autocorrelation function principally in the vicinity of the origin. The distribution for the number of zeros occurring in an asymptotically large interval are approximately negative-binomial or binomial depending upon whether the relative variance or Fano factor is greater or less than unity. The correlation properties of the zeros are such that they are repelled from each other or are "antibunched" if the autocorrelation function of the Gaussian process is characterized by a single scale size, but occur in clusters if more than one characteristic scale size is present. The intervals between zeros can be interpreted in terms of the autocorrelation function of the zeros themselves. When bunching occurs the interval density becomes bimodal, indicating the interval sizes within and between the clusters. The interevent periods are statistically dependent on one another with densities whose asymptotic behavior is governed by that of the autocorrelation function of the Gaussian process at large delay times. Poisson distributed fluctuations of the zeros occur only exceptionally but never form a Poisson process.

Continuous and discrete stable processes.

The one-sided Lévy-stable probability densities and the discrete-stable distributions form a doubly stochastic Poisson transform pair. This relationship facilitates the formulation of a class of continuous-stable stochastic processes.

Power-law-distributed level crossings define fractal behavior.

A relationship is established between the autocorrelation function of continuous Gaussian and non-Gaussian stochastic processes and the discrete process that describes their zero or level crossings. Random fractals occur when the distribution for the number of crossings is described by a class of Markov processes whose singlefold statistics are the discrete analog of the Lévy-stable continuous probability densities.

Intensity-weighted phase-derivative statistics.

It is shown that amplitude weighting can improve the accuracy of measurements of the frequency offset of a signal contaminated by multiplicative Gaussian noise. The more general non-Gaussian case is investigated through study of the statistics of a simple phase-screen scattering model. Formulas are derived for the low-order moments of the intensity-weighted phase derivative. Numerical simulation is tested against these results and is used to generate full probability densities that are analytically intractable and to determine the optimum weighting for the non-Gaussian regime of the model. The results are relevant to a variety of remote-sensing and signal-processing problems.

Fractional non-Brownian motion and trapping-time distributions of grains in rice piles.

Non-Gaussian height fluctuations occurring on the fueling time scale of a slowly driven rice pile match those observed in some turbulent/critical phenomena, forming an anticorrelated random fractal process with Hurst exponent H=0.2. Inspired by this observation, the concept of fractional Brownian motion (FBM) is extended to treat stochastic processes with skewed increments. Simulations of this process for antipersistent motion have first return time distribution deviating from the t(-2+H) law for FBM. The first return time distribution of this fractional non-Brownian motion describes and quantitatively determines the trapping-time distribution of grains in rice piles upon incorporating a continuous representation of the additional height fluctuations that occur on the time scale between fueling events.

Characterization of structural reorganization in rice piles.

Diagnostics applied to a rice-pile cellular automaton reveal different mechanisms producing power-law behaviors of statistical attributes of grains which are germane to self organised critical phenomena. The probability distributions for these quantities can be derived from two distinct random walk models that account for correlated clustered behavior through incorporating fluctuations in the number of steps in the walk. The first model describes the distribution for a spatial quantity, the resultant flight length of grains. This has a power-law tail caused by grains moving through a discrete, power-law distributed number of random steps of finite length. Developing this model into a random walk obtains distributions for the resultant flight length with characteristics similar to Lévy distributions. The second random walk model is devised to explain a temporal quantity, the distribution of "trapping" or "residence" times of grains at single locations in the pile. Diagnostics reveal that the trapping time can be constructed as a sum of "subtrapping times," which are described by a Lévy distribution where the number of terms in the sum is a discrete random variable accurately described by a negative binomial distribution. The infinitely divisible, two-parameter, limit distribution for the resultant of such a random walk is discussed, and describes a dual-scale power-law behavior if the number fluctuations are strongly clustered. The form for the distribution of transit times of grains results as a corollary.

Lévy random walks with fluctuating step number and multiscale behavior.

Random walks with step number fluctuations are examined in n dimensions for when step lengths comprising the walk are governed by stable distributions, or by random variables having power-law tails. When the number of steps taken in the walk is large and uncorrelated, the conditions of the Lévy-Gnedenko generalization of the central limit theorem obtain. When the number of steps is correlated, infinitely divisible limiting distributions result that can have Lévy-like behavior in their tails but can exhibit a different power law at small scales. For the special case of individual steps in the walk being Gaussian distributed, the infinitely divisible class of K distributions result. The convergence to limiting distributions is investigated and shown to be ultraslow. Random walks formed from a finite number of steps modify the behavior and naturally produce an inner scale. The single class of distributions derived have as special cases, K distributions, stable distributions, distributions with power-law tails, and those characteristic of high and low frequency cascades. The results are compared with cellular automata simulations that are claimed to be paradigmatic of self-organized critical systems.

Backscatter linear and circular polarization analysis of roughened aluminum.

A study of cross-polarized and copolarized intensities backscattered from roughened aluminum surfaces is presented for both linear and circular incident polarization states. The angular variation of measured Mueller matrices is shown to contain only diagonal elements, as predicted by the reciprocity theorem. The ratio of cross-depolarized to copolarized scattered intensities is significantly larger for circular than for linear input polarization states. In the linear case the ratio saturates beyond 50 degrees , whereas in the circular case the ratio continues to increase monotonically with angle. A phenomenological model for copolarization and cross-polarization intensities is shown to predict the observed behavior of both linear and circular input polarization states up to incident angles of 70 degrees .

Heterodyne detection of enhanced backscatter.

Heterodyne detection has been used to measure the enhanced backscattering from a standard target consisting of a plane mirror positioned behind a moving ground-glass disk (assumed to act as a phase screen). A tilt of the plane mirror in combination with spectral filtering of the detector output allows isolation of the double-scattered component of the light signal. When the illuminating laser and the local oscillator beams are correctly mode matched, the intensity of this signal displays the factor-of-2 increase that denotes full coherent enhancement. This full enhancement is preserved for a wide range of mirror to phase-screen spacing, in contrast with earlier observations in which direct-detection techniques were used.

Emission polarization of roughened glass and aluminum surfaces.

Ellipsometer measurements of the effective complex refractive index at a wavelength of 10.6 µm are made on a series of glass and aluminum surfaces of increasing surface roughness. The measured values are then used to calculate the degree of emission polarization and are shown to be in agreement with the experimentally determined values when depolarization is small. Comparisons are also made with calculations based on the Kirchhoff scattering theory. Both the theory and the experimental results indicate that it is the local surface slope and not the roughness magnitude that is the prime factor in determining the degree of emission polarization from the samples studied.

Optical properties of a planar turbulent jet.

A planar heated air jet was constructed. Its flow properties were characterized and shown to be both reproducible and in good agreement with the results of turbulence theory. The optical properties of the jet were studied with the help of a 632.8-nm He-Ne laser beam. The random phase modulations imposed on the wave front of the beam traversing the jet were measured by interferometric means, and their spectra and variance were determined. The one-dimensional phase fluctuation spectrum obeyed a -8/3 power law as predicted by theory, whereas the phase variance (?(2)) depended on the jet temperature and was studied for values to as high as 0.4 (rad)(2)).