Statistics of the fractal structure and phase singularity of a plane light wave propagation in atmospheric turbulence

Numerical experiments are carried out for a plane wave propagating in the atmospheric turbulence for a weak to strong fluctuation condition, i.e., the Rytov index being in a large range of 2x10(-3) to 20. Mainly two categories of propagation events are explored for the same range of Rytov index. In one category the propagation distance and also the Fresnel length are kept fixed with the turbulence strength changing. In the other the turbulence strength is kept fixed with the distance changing. The statistical characteristics of the scintillation index, the maximum and minimum of the intensity, the fractal dimension of the intensity image, and the number density of the phase singularity are analyzed. The behaviors of the fractal dimension and the density of the phase singularity present obvious differences for the two categories of propagation. The fractal dimension depends both on the Rytov index and the Fresnel length. In both weak and strong fluctuation conditions the dimension generally increases with the Rytov index, but is at minimum at the onset region. The phase singularity density is coincident with the theoretical results under a weak fluctuation condition, and has a slowly increasing manner with the Rytov index in the strong fluctuation condition. The dependence on the Fresnel size is confident and there is no saturation for the phase singularity.     

Laser beam propagation in atmospheric turbulence

The optical effects of atmospheric turbulence on the propagation of low power laser beams are reviewed in this paper. The optical effects are produced by the temperature fluctuations which result in fluctuations of the refractive index of air. The commonly-used models of index-of-refraction fluctuations are presented. Laser beams experience fluctuations of beam size, beam position, and intensity distribution within the beam due to refractive turbulence. Some of the observed effects are qualitatively explained by treating the turbulent atmosphere as a collection of moving gaseous lenses of various sizes. Analytical results and experimental verifications of the variance, covariance and probability distribution of intensity fluctuations in weak turbulence are presented. For stronger turbulence, a saturation of the optical scintillations is observed. The saturation of scintillations involves a progressive break-up of the beam into multiple patches; the beam loses some of its lateral coherence. Heterodyne systems operating in a turbulent atmosphere experience a loss of heterodyne signal due to the destruction of coherence.     

Speckle-field propagation in 'frozen' turbulence: brightness function approach

Speckle-field long- and short-exposure spatial correlation characteristics for target-in-the-loop (TIL) laser beam propagation and scattering in atmospheric turbulence are analyzed through the use of two different approaches: the conventional Monte Carlo (MC) technique and the recently developed brightness function (BF) method. Both the MC and the BF methods are applied to analysis of speckle-field characteristics averaged over target surface roughness realizations under conditions of 'frozen' turbulence. This corresponds to TIL applications where speckle-field fluctuations associated with target surface roughness realization updates occur within a time scale that can be significantly shorter than the characteristic atmospheric turbulence time. Computational efficiency and accuracy of both methods are compared on the basis of a known analytical solution for the long-exposure mutual correlation function. It is shown that in the TIL propagation scenarios considered the BF method provides improved accuracy and requires significantly less computational time than the conventional MC technique. For TIL geometry with a Gaussian outgoing beam and Lambertian target surface, both analytical and numerical estimations for the speckle-field long-exposure correlation length are obtained. Short-exposure speckle-field correlation characteristics corresponding to propagation in 'frozen' turbulence are estimated using the BF method. It is shown that atmospheric turbulence-induced static refractive index inhomogeneities do not significantly affect the characteristic correlation length of the speckle field, whereas long-exposure spatial correlation characteristics are strongly dependent on turbulence strength.     

Low-dimensional chaos and wave turbulence in plasmas

We investigated drift-wave turbulence in the plasma edge of a small tokamak by considering solutions of the Hasegawa-Mima equation involving three interacting modes in Fourier space. The resulting low-dimensional dynamics presented periodic as well as chaotic evolution of the Fourier-mode amplitudes, and we performed the control of chaotic behaviour through the application of a fourth resonant wave of small amplitude.     

Cyclotron wave propagation in silver

Azbel'-Kaner cyclotron resonance in metals is accompanied by electromagnetic waves propagating in a direction perpendicular to the magnetic field. Taking into account the anisotropy of the silver Fermi surface, the dispersion relation for these waves is calculated in the limit where the wavelength is much smaller than the orbit diameter of the electrons. Thus it is shown that a number of previously observed oscillations in the surface impedance of a semiinfinite silver specimen arise from points of zero-group velocity on the dispersion relation. Physically, the oscillations reflect a matching of the electron-orbit diameter with an integer number of wavelengths. They may, therefore, be looked upon as geometric resonances in the surface impedance, complementary to the temporal cyclotron resonances. The surface impedance is calculated under the assumption of specular surface scattering. Satisfactory agreement with experiments is obtained by using an independent-particle model for the electron gas and band parameters based on APW calculations. The influence of the Fermi-surface geometry is demonstrated by comparing with calculations for a cylindrical and a spherical Fermi surface. The electric field in the metal is calculated for selected magnetic fields, and the expected result of a transmission experiment is presented. Finally, the absence of Fermi liquid effects in the experiments is briefly discussed.     

Non-symmetrical wave propagation in arteries

Summary For a better understanding of the effects of initial stress on flow in elastic tubes, the propagation of a harmonic and non-symmetrical wave in an initially stressed thick cylindrical shell filled with an inviscid fluid is studied. Although the blood is known to be a non-Newtonian fluid, for simplicity, it is assumed to be a non-viscous, while the elastic tube is considered to be isotropic and incompressible. Utilizing the theory of small deformations superimposed on large initial static deformation, for a non-symmetrical perturbed motion the governing differential equations are obtained in cylindrical polar coordinates. Due to variability of the coefficients of the resulting differential equations of the solid body, the field equations are solved by truncated power series method. Applying the boundary conditions, the dispersion relation is obtained as a function of inner pressure, axial stretch and the thickness ratio. It is observed that the wave speed of the non-symmetrical wave is large as compared to the axially symmetrical case. Various special cases are also discussed in the paper.     

Optical pulse propagation in a Fabry-Perot etalon: analytical discussion

The phase modulation and dispersion property of a Fabry-Perot etalon are investigated analytically. It is demonstrated that within the resonant dispersion region in the etalon transmission spectrum, effective time delay of light pulse propagation can be achieved, and the maximum delay period can be simply related to the mirror reflectivity and optical length of the etalon. With a much simplified model, the influences of etalon parameters on the transmitted Gaussian pulse are evaluated, and simple relations regarding pulse distortion and energy loss are obtained to illustrate the temporal properties of the etalon.     

Ultrasonic wave propagation in two-phase media: Spherical inclusions

The scattering theory, recently developed via the extended method of equivalent inclusion, is used to study the propagation of time-harmonic waves in two-phase media of elastic matrix with randomly distributed elastic spherical inclusion materials. The elastic moduli and mass density of the composite medium are determined as functions of frequencies when given properties and concentration of the spheres and the matrix. Velocities and attenuation of ultrasonic waves in two-component media are determined. An averaging theorem that requires the equivalence of the strain energy and the kinetic energy between the effective medium and the original matrix with inhomogeneities is employed to derive the effective moduli and mass density. The functional dependency of these quantities upon frequencies and concentration provides a method of data analysis in ultrasonic evaluation of material properties. Numerical results for effective moduli, velocity and/or attenuation as functions of concentration of spherical inclusion material, or porosity, are graphically displayed.     

Mode coupling approach to beam propagation in atmospheric turbulence

A mode coupling approach based on the modal theory of coherence is suggested for the study of partially coherent beams in atmospheric turbulence. An approximate expression is derived for the mode power coupling coefficients, and some specific cases are studied using numerical methods. Several general results derived from the properties of the coupling coefficients are also presented.     

Acoustic wave propagation in Laves-phase compounds

We have studied the acoustic wave propagation in the hexagonal structured materials TiCr₂, ZrCr₂ and HfCr₂. In this paper, we have calculated the orientation dependence of three types of acoustic wave velocity and Debye average velocity using second order elastic constants. The six second order elastic constants are calculated for these materials at 300 K using Lenard-Jones Potential. An anomalous behaviour in orientation dependent acoustic wave velocity is obtained which is due to the combined effect of elastic constants and density. These velocity data are important for their structural information and to differentiate them from third group nitrides.     

Aberration in nonlinear acoustic wave propagation

Theory and simulations are presented indicating that imaging at the second-harmonic frequency does not solve the problem of ultrasonic wave aberration. The nonlinearity of acoustic wave propagation in biological tissue is routinely exploited in medical imaging because the improved contrast resolution leads to better image quality in many applications. The major sources of acoustic noise in ultrasound images are aberration and multiple reflections between the transducer and tissue structures (reverberations), both of which are the result of spatial variations in the acoustic properties of the tissue. These variations mainly occur close to the body surface, i.e., the body wall. As a result, the nonlinearly generated, second harmonic is believed to alleviate both reverberation and aberration because it is assumed that the second harmonic is mainly generated after the body wall. However, in the case of aberration, the second harmonic is generated by an aberrated source. Thus the second harmonic experiences considerable aberration at all depths, originating from this source. The results in this paper show that the second harmonic experiences similar aberration as its generating source, the first harmonic.     

Computer-aided instruction in wave propagation phenomena

A `virtual laboratory' which uses computer simulation and visualisation techniques is proposed for the training of high school and college students in the study of wave propagation phenomena. Physical laboratory experiments are replaced by numerical experiments based on a mathematical model and its numerical simulation on a computer. Simple experiments that can be performed in a water tank with simple tools are simulated in the `virtual laboratory' using the wave equation as a mathematical model. As an example the interference between the waves generated by two time harmonic point sources is studied and Bragg's law observed. In the `virtual laboratory' students can design their own experiments and observe the results of the numerical simulations via animation techniques     

Ultrasonic wave propagation in temperature gradients

Ultrasonic methods are being developed for sensing and control of high temperature material processes such as welding and solidification. One of the problems in these methods is the distortion of the sound field caused by the change in material properties due to temperature gradients. This paper describes a ray-tracing method for calculating the effects of temperature on ultrasonic propagation in such systems. In the ray-tracing method, the material is conceptually divided into a number of plane layers. The refraction at each layer boundary is calculated from Snell's law using the sound speeds determined from the temperatures of the adjacent layers. The time required for an ultrasonic pulse to traverse each layer is also calculated, allowing the determination of the total time along a particular path. The method is applied to calculating the time of arrival of echoes from various interfaces around a molten weld pool.     

Pulse propagation and windowed wave functions

Abstract

We apply quasi-distribution methods developed for quantum mechanics to the propagation of pulses in dispersive media with attenuation. We show that a Schrödinger type equation follows for propagation of the pulse for each mode. One then transforms the equation to obtain an equation of evolution in the phase space of position and wavenumber. In this paper we emphasize windowed wave functions and their corresponding phase space quasi-distributions. We obtain the time evolution equation, discuss possible approximations, and compare to the Wigner distribution approximation previously derived by Loughlin and Cohen by different methods.     

Effect of polymer additives on propagation of turbulence front

A study is made of the propagation of a turbulent region formed by vibrations of plates with holes in solutions of polyoxyethylene and guar resin. Polymer additives are found to appreciably affect the motion of a turbulence front.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 43, No. 2, pp. 220–224, August, 1982.     

Elastic wave and energy propagation in angled beams

This investigation comprises an experimental and numerical study of elastic wave propagation in angled beams. Axial impact by two strikers of different lengths was applied to three steel beams, each bent to incorporate a “V” section of different angle in the middle. Finite element simulation using ABAQUS was employed to examine details of the elastic waves generated in the impact tests. The numerical results correlated well with experimental data, and computational simulation was utilized to analyse the propagation of energy associated with the elastic waves. This demonstrated that after several reflections from and transmission across the bends energy is progressively smeared throughout the entire beam and does not concentrate at any particular segment; the bulk of the energy is conveyed via flexural waves. Numerical simulation of wave propagation in a beam with a single angle was also undertaken to study the energy associated with waves reflected from and transmitted across the bend, and how these are affected by the bend angle. The effects of input pulse duration, beam thickness and beam material properties on energy reflection and transmission at a bend are also discussed; this leads to the conclusion that when a longitudinal pulse of a particular frequency impinges on a bend, the ratio between its wavelength and the beam thickness governs the energy reflected from and transmitted across the bend. Moreover, the bend junction geometry (curvature) is found to have a significant influence on the energy reflected and transmitted, especially for obtuse bend angles.     

Characterizing the propagation path in moderate to strong optical turbulence

In February 2005 a joint atmospheric propagation experiment was conducted between the Australian Defence Science and Technology Organisation and the University of Central Florida. A Gaussian beam was propagated along a horizontal 1500 m path near the ground. Scintillation was measured simultaneously at three receivers of diameters 1, 5, and 13 mm. Scintillation theory combined with a numerical scheme was used to infer the structure constant C2n, the inner scale l0, and the outer scale L0 from the optical measurements. At the same time, C2n measurements were taken by a commercial scintillometer, set up parallel to the optical path. The C2n values from the inferred scheme and the commercial scintillometer predict the same behavior, but the inferred scheme consistently gives slightly smaller C2n values.     

Vortex beam propagation through atmospheric turbulence and topological charge conservation

The propagation of vortex beams through weak-to-strong atmospheric turbulence is simulated and analyzed. It is demonstrated that the topological charge of such a beam is a robust quantity that could be used as an information carrier in optical communications. The advantages and limitations of such an approach are discussed.     

Ultrasonic wave propagation in carbon fibre-reinforced plastics

The attenuation and velocity of the longitudinal and shear waves in unidirectional carbon/epoxy composites have been measured as a function of the fibre volume fraction over the frequency range, 1.84 to 11.9 MHz, using the pulse-echo technique. The decrease of attenuation with fibre volume fraction suggested that the high attenuation in the composites was caused by viscoelastic losses in the epoxy matrix rather than scattering losses by the fibre. The attenuation increased with frequency, while the velocity was found to be independent of frequency.