Intensity fluctuations in a moving random medium

We consider the intensity fluctuations arising when a point source of radiation moves in a randomly inhomogeneous scattering medium. The medium itself can also move with a velocity whose component normal to the direction of propagation can have an arbitrary distribution. We derive an expression for the space-time autocorrelation function of the intensity fluctuations transverse to the direction of propagation. The result is analysed for some particular cases and it is shown how the resulting information can be useful in examining the behaviour of random media in situations of practical interest.     

Statistical theory of the propagation of optical radiation in turbulent media

The problem of the propagation of a plane light wave in a turbulent medium is studied on the basis of the ideas of statistical topography. A cluster (caustic) structure of the intensity of the wave field in a plane perpendicular to the direction of propagation of the wave is analyzed both in the region of weak intensity fluctuations and in the region of saturated fluctuations. The specific (per unit area) values of the total area of the regions where the intensity is greater than a fixed level, the fraction of the power confined in these regions, and the total perimeter and average number of such regions are estimated. It is shown that estimates of this kind can be made on the basis of a knowledge of the joint one-point probability distribution of the intensity and transverse gradient of the wave field. Zh. éksp. Teor. Fiz. 111, 2044–2058 (June 1997)     

Long-range intensity correlations for the multiple scattering of waves in unordered media

The long-range correlations in the reflected and transmitted fluxes in the case of the coherent transport of waves in an unordered medium with discrete inhomogeneities are considered. The correlator and spectrum of the intensity fluctuations are expressed in a general form in terms of the one-center scattering amplitude and the propagators of the mean radiated intensity. The random interference of the waves and the fluctuations of the number of scattering centers in a microvolume of the medium are taken into account simultaneously. Detailed calculations are performed for two limiting radiation propagation regimes, viz., spatial diffusion and small-angle multiple scattering. It is shown that the conservation of the total flux upon elastic scattering leads to the formation of a dip in the spectrum and, accordingly, a negative correlation between the intensities at large distances. In the case of spatial diffusion this feature is displayed upon reflection, and in the case of small-angle multiple scattering it is displayed upon transmission through a slab. The relative roles of the various sources of intensity fluctuations, as well as the sensitivity of the correlations to factors that influence the wave propagation regime, viz., the finite size of the scattering sample, absorption in the medium, and the presence of a frequency shift in the incident waves, are analyzed. We find that fluctuations in the distribution of the scatterers show up most strongly in a medium with strong, i.e., “non-Born,” centers, especially if they exhibit absorption. Zh. éksp. Teor. Fiz. 111, 1674–1716 (May 1997)     

Qualitative theory of amplitude and phase fluctuations in a medium with anisotropic turbulent irregularities

Abstract

Wave propagation in an anisotropic turbulent medium is studied assuming that the anisotropy coefficient η is constant for all scales of inhomogeneities. A qualitative method of studying the amplitude and phase fluctuations is developed. Formulae have been obtained for the phase structure functions and scintillation index for the medium with spectrum power index 3<μ<5 and anisotropy coefficient η≥1. Two particular cases have been studied in detail—propagation along and across the axis of the stretching of irregularities. During propagation along a short axis of inhomogeneities the fluctuations are decreasing and the phase structure function and scintillation index turn out to be η^μ?2 times smaller as compared with isotropic case. At the same time, during propagation along the long axis of inhomogeneities the phase structure function in vertical plane and the scintillation index are η times greater than in the isotropic medium.     

Singularities in forward scattering through random media

Abstract

We consider a random medium in which scattering is exclusively in the forward direction. Waves are emitted by an object in the medium and Fourier components of the intensity are shown to propagate independently. At small wavevectors the intensity propagates very simply through increasing thickness, z, of medium, as λ ^z , and Fourier components of the object can easily be reconstructed. For wavevectors greater than a critical value, q _c , the intensity changes with z in a more complex fashion making it very difficult to reconstruct the object. They develop a simple model for the singularity and apply it to the reconstruction of an object degraded by passage through a random medium.     

Joint moments of the wave beam amplitude and inverse power in an absorbing random medium with lens properties

Abstract

This paper presents a derivation of a system of closed equations for joint moments of the amplitude and inverse power of a wave beam propagating in a regularly inhomogeneous dissipative random medium. The radiation transfer in the medium is characterized by non-conservation of the total radiation energy flux and by the existence of power fluctuations. The statistics of the wave beam power fluctuations have been studied. Information on the power statistical characteristics is applied to close the system of equations for joint moments. For task parameters which are not very strict (an effective radius of the wave beam should be considerably less than the outer scale of the turbulence) a system of independent equations for arbitrary joint moments has been obtained. The equations for the first two lower joint moments of the beam intensity and inverse power have been solved analytically. With the solutions obtained the effective wave beam parameters were calculated, i.e. the beam mean displacement, effective broadening and tremble variance (the beam wandering variance) for the propagation of radiation in the refractive channel of an absorbing turbulent medium. Radically new characteristics of the behaviour of the effective parameters in random absorbing and transparent media have been revealed.     

Light transmission in inhomogeneous birefringent medium as a function of propagation and observation angles

We use the Mueller matrix for inhomogeneous linear birefringent media derived in Savenkov et al. [Mueller-matrix model of an inhomogeneous linear birefringent medium: single scattering case. JQSRT 2007;106:475–86] to generate new results on the forward scattering of light using Cloude's coherence matrix method. We show that the intensity of scattered light (m₁₁) as a function of observation angle depends on the difference between refractive indices along the eigen polarizations resulting in intensity lost when unpolarized light propagates parallel to the optical axes compared to propagation orthogonal to the optical axis. For a given inhomogeneity (roughness), depolarization strongly depends on the direction of light propagation in the medium. The depolarization at 90° propagation angle is minimal for any value of inhomogeneity. Sample calculations are based on calcite.     

Backscattering of stationary radiation in time-dependent random media: average intensity and intensity fluctuations

We consider backscattering of stationary radiation in a random medium whose wavespeed fluctuations depend on time and on space. We modify a previous derivation of the equations that govern the range-evolution of the spectra of the ensemble-averaged forward-and back-propagating components of the field and their second-order statistics, and extend the approach to treat the fourth-order statistics. The latter are governed by integro-difference equations that account for the broadening of the signal spectra due to the time-dependence of the random fluctuations. In the quasi-monochromatic regime, where spectra owing to a monochromatic excitation remain confined to a narrow band over extensive ranges, the integro-difference equations transform into ordinary differential equations that govern the time-dependence of the quantities of interest. We use this simplification to track the power fluxes and their fluctuations (scintillation) in a one-dimensionally stratified slab, where the wave-speed fluctuations depend on the range-coordinate normal to the planes of stratification, and also to treat modal propagation in a duct, where the wave-speed fluctuations depend on all three spatial dimensions. The results suggest that a Gaussian equilibrium is approached at large ranges, on a suitably defined backscattering scale that depends on the medium parameters and the geometry.     

Fluctuations of acoustic field in a granular medium

Results of an experimental study of sound propagation in a granular medium are presented. It is found that, in the case of excitation of a harmonic signal with a constant amplitude, the acoustic response of a single grain strongly varies in time. The dependence of the harmonic component amplitudes in the response spectrum on the level of signal excitation proves to be nonmonotonic and also strongly varies in time. The most intense fluctuations are observed in the subharmonic component of the propagating signal. The intensity fluctuation spectra of the harmonic components of the response are obtained for the frequency range of 10⁻⁴−10⁻¹ Hz. A possible mechanism that may be responsible for the slow fluctuations of an acoustic field in a granular medium is discussed.

     

Correlation characteristics of waves in lossy media with smooth fluctuations of the refractive index with oblique incidence on boundary

Abstract

The features of coherence function (and angular spectrum) and also the fluctuation of amplitude and phase of wavefield in a random strongly absorptive medium are investigated in the case of arbitrary angle of incidence at the surface.

In this paper it is elucidated that with oblique incidence a dissipation in the random medium can accelerate the accumulation of wave fluctuations and its incoherence. This effect strongly depends on the rate of decrease of the ‘wings’ of the scattering indicatrix. An analytical theory (Rytov's approximation and modified method of parabolic equation) has been modelled by Monte Carlo simulation of wave propagation, and also by numerical solution of the model transfer equation. It is revealed that the width of an angle spectrum can nonmonotonically change with the immersion to the absorptive medium.     

Multiple light scattering from a moving layer of Brownian particles: comparison with a rigid phase screen

Abstract

The temporal fluctuations in the intensity of light scattered by a moving layer of emulsions and suspensions containing Brownian particles are investigated experimentally, and a comparison is made with light scattered by a translating phase screen. The intensity fluctuations of the scattered light are detected through an imaging system, which collects the light emanating only from a limited volume in the medium. The effect of translational motion of the particle layer on the decay rate of the autocorrelation function of intensity fluctuations depends on the illuminating form of a laser beam and on the point spread function of the imaging system. The Brownian motion of the particles causes the scattered light to fluctuate more rapidly than that arising from the translating phase screen. In the multiple-scattering regime, the influence of this diffusional motion increases with an increase of the particle concentration in the layer.     

Squeezed states of light pulses in the presence of a self-effect in an inertial nonlinear medium

A systematic theory of the formation of squeezed states during the propagation of coherent light pulses in a medium with an inertial Kerr nonlinearity is developed. It is established that the region of the spectrum where the quadrature fluctuations are weaker than the shot noise depends on both the relaxation time of the nonlinearity and the magnitude of the nonlinear phase shift. It is also shown that the frequency at which suppression of the fluctuations is greatest can be controlled by adjusting the phase of the pulse. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 7, 481–485 (10 April 1999)     

The random analogue of Epstein's transition layer

Abstract

For a quasi-homogeneous, random medium with variance, varying along the same direction as tanh, the mean Green function is obtained as an exact solution of Dyson's equation in a bilocal approximation. The coherent part of the field of a plane wave, falling on a bounded, randomly fluctuating medium with a non-sharp boundary, is studied in detail. In the case of small-scale fluctuations, a medium of this kind is shown to be a random analogue of a transient Epstein layer.     

Laser-induced spatial structures in a chemically active gas-phase medium illuminated by annular diffracting beams

The laws governing the propagation of diffracting beams in a two-component gaseous mixture are investigated on the basis of a computer simulation. It is discovered that several regions with high concentrations of the reaction product form. It is also found that the beam focus can move both in the direction of beam propagation and in the counter direction, and the change in its position can occur abruptly. It is shown that as time goes on, a high concentration of the reaction product is achieved in the central unilluminated region of the medium near the entrance cross section on account of diffusion (i.e., a diffusional concentration growth occurs). This leads to the formation of a dynamic concentration maximum in this region of the medium. Zh. Tekh. Fiz. 68, 8–14 (March 1998)     

Elastic wave propagation in a randomly stratified solid medium

Abstract

The mean-field method is used to analyse longitudinal and transverse (both SV- and SH-type) wave propagation in an unbounded randomly stratified solid medium. It is assumed that elastic moduli of the medium are constant while a density is a random function of the cartesian coordinate z. For a case of small density fluctuations, expressions are obtained for z-components of effective propagation vectors of P-, SV- and SH-waves for arbitrary relations between wavelengths and a correlation length of the random inhomogeneities. It is shown, that when the correlation length is small in comparison with the wavelengths, the mean-field attenuation coefficients are proportional to the frequency squared. In this case P- and SV-waves convert into each other. When the correlation length is large in comparison with the wavelengths, the mean-field attenuation coefficients are also proportional to the frequency squared, but in this case P- and SV-waves propagate independently.     

Quantum backaction of optical observations on Bose-Einstein condensates

Impressive pictures of moving Bose-Einstein condensates have been taken using phase-contrast imaging [M.R. Andrews et al., Science 273, 84 (1996)]. We calculate the quantum backaction of this measurement technique, assuming the absence of residual absorption. We find that the condensate gets gradually depleted at a universal rate that is proportional to the light intensity and to the inverse cube of the optical wave length. The fewer atoms are condensed the higher is the required intensity to see a picture, and, consequently, the higher is the induced backaction. To describe the quantum physics of phase-contrast imaging we put forward a new approach to quantum-optical propagation. We develop an effective field theory of paraxial optics in a fully quantized atomic medium. Received 25 February 1999     

Transformation of quantum size levels into virtual levels at the boundary between p-GaAs and an AlAs/GaAs superlattice

It is shown that the intensity fluctuations in the speckle pattern arising when light is reflected from a disordered sample are negatively correlated. The relative amplitude of the correlations is two times larger in the exactly backward direction than far from this direction. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 2, 104–109 (25 January 1999)     

Pulse propagation of acoustic waves scattered in a three-dimensional channel

Abstract

In a previous paper (Whitman et al 1999 Waves Random Media 9 1–11) we discussed the scattering of acoustic waves by random sound-speed fluctuations in a two-dimensional channel and presented an asymptotic form for an acoustic pulse propagating in the channel. Here we include the three-dimensional effect of transverse scattering. We find an asymptotic solution in which initially the two-dimensional mode-transfer effect is more important than the transverse scattering effect. However, for large enough propagation distances the transverse scattering effect dominates the pulse spread. In this paper we shall show the form of the pulse shape in both propagation ranges as well as in the transition regime. We shall begin with a discussion of the physics of the problem and then present a mathematical discussion.     

Modification of the Turbulence in the Plasma Boundary of the Wendelstein 7-AS Stellarator Using Electric Probes

The fluctuations in the edge plasmas of magnetic fusion experiments are thought to play an important role in terms of anomalous energy and particle transport. Experiments on Wendelstein 7-AS were conducted with the primary goal to investigate the performance of influencing and modifying the turbulence in the plasma boundary using electrical probes. Two movable poloidal probe arrays were used for the experiments, one located on the inboard side of the vessel and the other on the outboard side. A subset of probe tips was used for actively driving the plasma by different control signals, the remaining probes collected fluctuation data in the plasma boundary. Poloidally, we find a significant cross-correlation between active and passive probes. From analysis of the coherency and phases of the passive probe tips, it can clearly be seen that the background E×B-rotation of the plasma plays a crucial role for the applied signals. In the case of externally driven waves by several phase-locked active probes, the direction of the wave propagation with respect to the plasma rotation (co- or counter-rotating) is essential for a proper coupling to the turbulence. In toroidal direction we find that the propagation of the signals along the magnetic field lines depends on co- or counter-rotation with respect to the background plasma rotation.