Pulse propagation in time dependent randomly layered media

We study cumulative scattering effects on wave front propagation in time dependent randomly layered media. It is well known that the wave front has a deterministic characterization in time independent media, aside from a small random shift in the travel time. That is, the pulse shape is predictable, but faded and smeared as described mathematically by a convolution kernel determined by the autocorrelation of the random fluctuations of the wave speed. The main result of this paper is the extension of the pulse stabilization results to time dependent randomly layered media. When the media change slowly, on time scales that are longer than the pulse width and the time it takes the waves to traverse a correlation length, the pulse is not affected by the time fluctuations. In rapidly changing media, where these time scales are similar, both the pulse shape and the random component of the arrival time are affected by the statistics of the time fluctuations of the wave speed. We obtain an integral equation for the wave front, that is more complicated than in time independent media, and cannot be solved analytically, in general. We also give examples of media where the equation simplifies, and the wave front can be analyzed explicitly. We illustrate with these examples how the time fluctuations feed energy into the pulse

Correspondence between sound propagation in discrete and continuous random media with application to forest acoustics

Although sound propagation in a forest is important in several applications, there are currently no rigorous yet computationally tractable prediction methods. Due to the complexity of sound scattering in a forest, it is natural to formulate the problem stochastically. In this paper, it is demonstrated that the equations for the statistical moments of the sound field propagating in a forest have the same form as those for sound propagation in a turbulent atmosphere if the scattering properties of the two media are expressed in terms of the differential scattering and total cross sections. Using the existing theories for sound propagation in a turbulent atmosphere, this analogy enables the derivation of several results for predicting forest acoustics. In particular, the second-moment parabolic equation is formulated for the spatial correlation function of the sound field propagating above an impedance ground in a forest with micrometeorology. Effective numerical techniques for solving this equation have been developed in atmospheric acoustics. In another example, formulas are obtained that describe the effect of a forest on the interference between the direct and ground-reflected waves. The formulated correspondence between wave propagation in discrete and continuous random media can also be used in other fields of physics

Multiple scattering of classical waves: from microscopy to mesoscopy and diffusion

A tutorial discussion of the propagation of waves in random media is presented. In first approximation the transport of the multiple scattered waves is given by diffusion theory, but important corrections are present. These corrections are calculated with the radiative transfer or Schwarzschild-Milne equation, which describes intensity transport at the ``mesoscopic'' level and is derived from the ``microscopic'' wave equation. A precise treatment of the diffuse intensity is derived which automatically includes the effects of boundary layers. Effects such as the enhanced backscatter cone and imaging of objects in opaque media are also discussed within this framework. In the second part the approach is extended to mesoscopic correlations between multiple scattered intensities which arise when scattering is strong. These correlations arise from the underlying wave character. The derivation of correlation functions and intensity distribution functions is given and experimental data are discussed. Although the focus is on light scattering, the theory is also applicable to micro waves, sound waves and non-interacting electrons.Comment: Review. 86 pages Latex, 32 eps-figures included. To appear in Rev. Mod. Phy

Circular Bessel field statistics and the pursuit of far-subwavelength resolution

The statistical description of wave propagation in random media is important for many applications. While polarized light in systems with weakly interacting scatterers and sufficient overall scatter has zero-mean circular Gaussian statistics, the underlying assumptions break down in the Anderson localization and weakly scattering regimes. Although probability density functions for wave intensity and amplitude exist beyond Gaussian statistics, suitable statistical descriptions for the field with strong and weak random scatter were unknown. The first analytical probability density function for the field that is effective in both the Anderson localization regime and the weakly scattering regime is derived by modeling the field as a random phasor sum with a random number of contributing terms. This provides a framework for modeling wave propagation in random media, facilitating random media characterization, imaging in and through scatter, and for random laser design. ^ The resolution of far-field imaging systems is diffraction limited. Super resolution techniques that break the diffraction limit are important in the physical, chemical, and biological sciences, and in technology. An imaging method based on object motion with structured illumination and far-field measurement data that results in far-subwavelength image information is proposed. Simulations show that this approach, with generous detector noise, will lead to the ability to distinguish image features on the nanometer scale with visible light. Along different lines, a perfect negative refractive index can act as a superlens, but realistic materials render this approach ineffective. A method to tune the lens material properties is shown to provide enhanced resolution

Simulation of wave propagation in three-dimensional random media

Quantitative error analysis for simulation of wave propagation in three dimensional random media assuming narrow angular scattering are presented for the plane wave and spherical wave geometry. This includes the errors resulting from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive index of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared to the spatial spectra of intensity. The numerical requirements for a simulation of given accuracy are determined for realizations of the field. The numerical requirements for accurate estimation of higher moments of the field are less stringent