Simulation of point-source scintillation through three-dimensional random media
01 May 1990-Journal of The Optical Society of America A-optics Image Science and Vision (Optical Society of America)-Vol. 7, Iss: 5, pp 838-847
TL;DR: In this paper, the intensity spectra and variances for waves emanating from a point source and propagating through extended three-dimensional random media by simulation were calculated and the results agree reasonably closely with the results of laser propagation experiments over kilometer-length paths in the atmosphere.
Abstract: We have calculated intensity spectra and variances for waves emanating from a point source and propagating through extended three-dimensional random media by simulation. Spectra of the medium fluctuations considered were power-law, power-law with inner scale, and Gaussian spectra. The simulations covered the regimes of weak fluctuations and strong focusing, including the peak of the intensity variance and beyond. The intensity variances are substantially larger than both the corresponding results for plane-wave incidence and the theoretical calculations for point sources by other authors. Our simulation results agree reasonably closely with the results of laserpropagation experiments over kilometer-length paths in the atmosphere.
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01 Jan 2008
TL;DR: LaRonde as mentioned in this paper analyzes the conflict in Xinjiang and concludes that the Chinese continue to defeat the separatist movement through a strategy that counters Mao's seven fundamentals of revolutionary warfare, concluding that Mao, as well as the communist leaders who followed him, was also successful at waging protracted counterinsurgency.
Abstract: PROTRACED COUNTERINSURGENCY: CHINESE COIN STRATEGY IN XINJIANG by MAJ J. Scott LaRonde, USA, 95 pages. In 1949, following the conclusion of its revolutionary war against the Chinese Nationalist forces, the People’s Liberation Army (PLA) peacefully occupied China’s western most province of Xinjiang. For nearly sixty years, the PLA has conducted a counterinsurgency against several, mostly Uyghur-led, separatist movements. Despite periods of significant violence, particularly in the early 1950s and again in the 1990s, the separatist forces have not gained momentum and remained at a level one insurgency. Mao ZeDeng is revered as a master insurgent and the father of Fourth Generation Warfare. Strategists in armies worldwide study his writings on revolutionary and guerilla warfare. This monograph concludes that Mao, as well as the communist leaders who followed him, was also successful at waging protracted counterinsurgency. For nearly sixty years, separatist movements in Xinjiang, Tibet, and Taiwan have all failed. This monograph analyzes the conflict in Xinjiang and concludes that the Chinese continue to defeat the separatist movement in Xinjiang through a strategy that counters Mao’s seven fundamentals of revolutionary warfare.
773 citations
TL;DR: In this article, a heuristic model of irradiance fluctuations for a propagating optical wave in a weakly inhomogeneous medium is developed under the assumption that small-scale irradiance fluctuation fluctuations are modulated by large-scale fluctuations of the wave.
Abstract: A heuristic model of irradiance fluctuations for a propagating optical wave in a weakly inhomogeneous medium is developed under the assumption that small-scale irradiance fluctuations are modulated by large-scale irradiance fluctuations of the wave. The upper bound for small turbulent cells is defined by the smallest cell size between the Fresnel zone and the transverse spatial coherence radius of the optical wave. A lower bound for large turbulent cells is defined by the largest cell size between the Fresnel zone and the scattering disk. In moderate-to-strong irradiance fluctuations, cell sizes between those defined by the spatial coherence radius and the scattering disk are eliminated through spatial-frequency filtering as a consequence of the propagation process. The resulting scintillation index from this theory has the form σI2=σx2+σy2+σx2σy2, where σx2 denotes large-scale scintillation and σy2 denotes small-scale scintillation. By means of a modification of the Rytov method that incorporates an amplitude spatial-frequency filter function under strong-fluctuation conditions, tractable expressions are developed for the scintillation index of a plane wave and a spherical wave that are valid under moderate-to-strong irradiance fluctuations. In many cases the models also compare well with conventional results in weak-fluctuation regimes. Inner-scale effects are taken into account by use of a modified atmospheric spectrum that exhibits a bump at large spatial frequencies. Quantitative values predicted by these models agree well with experimental and simulation data previously published. In addition to the scintillation index, expressions are also developed for the irradiance covariance function of a plane wave and a spherical wave, both of which have the form BI(ρ)=Bx(ρ)+By(ρ)+Bx(ρ)By(ρ), where Bx(ρ) is the covariance function associated with large-scale fluctuations and By(ρ) is the covariance function associated with small-scale fluctuations. In strong turbulence the derived covariance shows the characteristic two-scale behavior, in which the correlation length is determined by the spatial coherence radius of the field and the width of the long residual correlation tail is determined by the scattering disk.
331 citations
TL;DR: The existence of the vectorial vortex can be identified with longer propagation distance than the scalar vortex even with vanishing characteristic vortex structure in the irradiance images, indicating the potential advantages of using a vector vortex beam to mitigate atmospheric effects and enable a more robust free space communication channel with longer link distance.
Abstract: We numerically study the propagation properties of vector vortex beams through a turbulent atmosphere. The irradiance pattern, degree of polarization, and scintillation index of radially polarized beam are computed for different propagation distances in an atmosphere with weak and strong turbulences. Corresponding properties of a fundamental Gaussian beam and a scalar vortex beam with topological charge of + 1 propagating through the same atmospheric turbulence conditions are calculated for comparison. With the same initial intensity profile, the vector vortex beam shows substantially lower scintillation than the scalar vortex. The existence of the vectorial vortex can be identified with longer propagation distance than the scalar vortex even with vanishing characteristic vortex structure in the irradiance images. This indicates the potential advantages of using a vector vortex beam to mitigate atmospheric effects and enable a more robust free space communication channel with longer link distance.
222 citations
TL;DR: The split-step Fourier-transform algorithm for numerical simulation of wave propagation in a turbulent atmosphere is refined to correctly include the effects of large-scale phase fluctuations that are important for imaging problems and many beam-wave problems such as focused laser beams and beam spreading.
Abstract: The split-step Fourier-transform algorithm for numerical simulation of wave propagation in a turbulent atmosphere is refined to correctly include the effects of large-scale phase fluctuations that are important for imaging problems and many beam-wave problems such as focused laser beams and beam spreading. The results of the improved algorithm are similar to the results of the traditional algorithm for the performance of coherent Doppler lidar and for plane-wave intensity statistics because the effects of large-scale turbulence are less important. The series solution for coherent Doppler lidar performance converges slowly to the results from simulation.
176 citations
TL;DR: The capability of the split-step solution to simulate the propagation phenomena is shown, and the limitations and numerical requirements for a simulation of given accuracy are established.
Abstract: To analyze the effects of atmospheric refractive turbulence on coherent lidar performance in a realistic way it is necessary to consider the use of simulations of beam propagation in three-dimensional random media. The capability of the split-step solution to simulate the propagation phenomena is shown, and the limitations and numerical requirements for a simulation of given accuracy are established. Several analytical theories that describe laser beam spreading, beam wander, coherence diameters, and variance and autocorrelation of the beam intensity are compared with results from simulations. Although the analysis stems from a study of coherent lidar performance, the conclusions of the method are applicable to other areas related to beam propagation in the atmosphere.
121 citations
References
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TL;DR: In this article, a time-dependent three-space-dimensional laser beam propagation is described, where the authors use a discrete Fourier transform (DFT) method for diffraction problems.
Abstract: The computation of time-dependent three-space-dimensional laser beam propagation is described. The methods are applicable to the propagation of high energy laser beams through the atmosphere in the presence of a horizontal wind and turbulence for most situations of interest. Possible cases are propagation of cw beams through stagnation zones, multi-pulse propagation, including the self-consistent treatment of pulse self-blooming, and propagation involving transonic slewing. The solution of the Maxwell wave equation in Fresnel approximation is obtained by means of a discrete Fourier transform method, which, surprisingly, gives excellent results for diffraction problems. The latter provide a stringent test for the accuracy of any solution method. Considerable use is also made of discrete Fourier transform methods in solving the hydrodynamic equations. The treatment of turbulence is based on the generation of random phase screens at each calculation step along the propagation path. In a time-dependent calculation the random phase screens can be either made to move with the wind at a given propagation position or generated anew for each successive time.
1,105 citations
01 Jan 1977
TL;DR: This article has dealt with various aspects of parabolic approximation methods in underwater acoustics, mostly for propagation of sinusoidal signals, and extensions to time-dependent problems are also available: pulse propagation, moving sources and receivers, frequency shifting effects due to rapid temporal variations of oceanic conditions, and so forth.
Abstract: This article has dealt with various aspects of parabolic approximation methods in underwater acoustics, mostly for propagation of sinusoidal signals Extensions of these methods to time-dependent problems are also available: pulse propagation, moving sources and receivers, frequency shifting effects due to rapid temporal variations of oceanic conditions, and so forth However, an adequate description of these extensions would require another long section and it was felt that the principles involved in making parabolic approximations have been sufficiently illustrated Parabolic equation methods in underwater acoustics were developed only in the last few years, and as more and more use is made of these methods we may expect that many of the important modelling problems in ocean acoustics may be solved
618 citations
TL;DR: An extended random medium is modeled by a set of 2-D thin Gaussian phase-changing screens with phase power spectral densities appropriate to the natural medium being modeled, showing that under weak scattering the small-scale Fresnel length structure of the medium dominates the intensity scattering pattern.
Abstract: An extended random medium is modeled by a set of 2-D thin Gaussian phase-changing screens with phase power spectral densities appropriate to the natural medium being modeled. Details of the algorithm and limitations on its application to experimental conditions are discussed, concentrating on power-law spectra describing refractive-index fluctuations of the neutral atmosphere. Inner and outer scale effects on intensity scintillation spectra and intensity variance are also included. Images of single realizations of the intensity field at the observing plane are presented, showing that under weak scattering the small-scale Fresnel length structure of the medium dominates the intensity scattering pattern. As the strength of scattering increases, caustics and interference fringes around focal regions begin to form. Finally, in still stronger scatter, the clustering of bright regions begins to reflect the large-scale structure of the medium. For plane waves incident on the medium, physically reasonable inner scales do not produce the large values of intensity variance observed in the focusing region during laser propagation experiments over kilometer paths in the atmosphere. Values as large as experimental observations have been produced in the simulations, but they require inner scales of the order of 10 cm. Inclusion of an outer scale depresses the low-frequency end of the intensity spectrum and reduces the maximum of the intensity variance. Increasing the steepness of the power law also slightly increases the maximum value of intensity variance.
435 citations
TL;DR: In this paper, the problem of wave propagation in a random medium is formulated in terms of Feynman's path integral, which turns out to be a powerful calculational tool.
Abstract: The problem of wave propagation in a random medium is formulated in terms of Feynman’s path integral. It turns out to be a powerful calculational tool. The emphasis is on propagation conditions where the rms (multiple) scattering angle is small but the log‐intensity fluctuations are of order unity—the so‐called saturated regime. It is shown that the intensity distribution is then approximately Rayleigh with calculable corrections. In an isotropic medium, the local or Markov approximation which is commonly used to compute first and second (at arbitrary space–time separation) moments of the wave field is explicitly shown to be valid whenever the rms multiple scattering angle is small. It is then shown that in the saturated regime the third and higher moments can be obtained from the first two by the rules of Gaussian statistics. There are small calculable corrections to the Gaussian law leading to ’’coherence tails.’’ Correlations between waves of different frequencies and the physics of pulse propagation are studied in detail. Finally it is shown that the phenomenon of saturation is physically due to the appearance of many Fermat paths satisfying a perturbed ray equation. For clarity of presentation much of the paper deals with an idealized medium which is statistically homogeneous and isotropic and is characterized by fluctuations of a single typical scale size. However, the extension to inhomogneous, anisotropic, and multiple scale media is given. The main results are summarized at the beginning of the paper.
264 citations
01 Jun 1983
TL;DR: In this article, an analytical/numerical technique is presented that provides a solution to the parabolic wave equation and allows for direct calculation of the received time-domain signal after propagation of a widebandwidth waveform through a turbulent ionized medium.
Abstract: An analytical/numerical technique is presented that provides a solution to the parabolic wave equation and allows for direct calculation of the received time-domain signal after propagation of a wide-bandwidth waveform through a turbulent ionized medium. The results are applicable to the case of satellite communication or to radar observation through a frequency-selective transionospheric propagation channel. A number of examples of the application of multiple phase-screen (MPS) techniques are given that enhance intuitive understanding of wave propagation. Numerical predictions of scattering through a striated barium cloud are compared to experimental observations. Good agreement is also shown between MPS calculations and theoretical results for cases in both weak and strong scattering regimes.
250 citations