Propagation In Turbulent Atmosphere Research Articles

Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence

For propagation in turbulent atmosphere, the radius of curvature variations for annular, dark hollow and flat topped beams are examined under a single formulation. Our results show that for collimated beams, when examined against propagation length, the dark hollow, flat topped and annular Gaussian beams behave nearly the same as the Gaussian beam, but have larger radius of curvature values. Increased partial coherence and turbulence levels tend to lower the radius of curvature. Bigger source sizes on the other hand give rise to larger radius of curvature. Dark hollow and flat topped beams have reduced radius of curvature at longer wavelengths, whereas the annular Gaussian beam seems to be unaffected by wavelength changes; the radius of curvature of the Gaussian beam meanwhile rises with increasing wavelength.

Temporal-frequency spectra for optical wave propagating through non-Kolmogorov turbulence

Nowadays it has been accepted that the Kolmogorov model is not the only possible turbulent one in the atmosphere, which has been confirmed by the increasing experimental evidences and some results of theoretical investigation. This has prompted the scientist community to study optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, using a non-Kolmogorov power spectrum which has a more general power law instead of standard Kolmogorov power law value 11/3 and a more general amplitude factor instead of constant value 0.033, the temporal power spectra of the presentative amplitude and phase effects, irradiance and angle of arrival fluctuations, have been derived for horizontal link in weak turbulence. And then the influence of spectral power-law variations on the temporal power spectrum has been analyzed. It is anticipated that this work is helpful to the investigations of atmospheric turbulence and optical wave propagation in the atmospheric turbulence.

Trajectory of an optical vortex in atmospheric turbulence

Trajectory of an optical vortex has been identified for its propagation in atmospheric turbulence using numerical simulations. An analytical expression has been found, relating the radial departure of the vortex in plane perpendicular to the direction of propagation, to the refractive index structure function parameter and the inner scale of turbulence. The angular orientation of the vortex in the same transverse plane is found to be related to the anisotropy of the medium. The obtained results provide an alternative way to find turbulent parameters with the help of optical vortices.

Spectral changes in electromagnetic stochastic beams propagating through turbulent atmosphere

It is known that the spectrum of light can change on propagation, even in free space. Such changes are due to its coherence properties. We determine how the spectrum of a stochastic electromagnetic beam of any state of coherence changes on propagation in atmospheric turbulence. We illustrate the results by examining changes in the spectrum of an electromagnetic Gaussian Schell-model beam whose spectrum consists of a single spectral line with a Gaussian profile, which propagates through atmospheric turbulence, with Kolmogorov power spectrum. The results are of interest for optical communications through the atmosphere and for laser radar systems.

Nonlinear propagation of spark-generated N-waves in atmosphere: theoretical and experimental assessment of the shock front structure

Extensive outdoor and laboratory-scale experiments on sonic boom propagation in turbulent atmosphere have shown that shock wave amplitude and rise time are important parameters responsible for sonic boom annoyance. However, accurate measurement of the shock front structure with standard microphone remains a challenge due to the broadband spectrum of the N-wave shock front. In this work the experimental setup utilizing a spark source has been designed and built to investigate nonlinear N-wave propagation in homogeneous medium. Short duration (30μs) and high amplitude (1 kPa) spherically divergent N-waves were generated. In addition to acoustic measurements with 1/8" B&K microphones, the shadowgraphy method using short duration flash lamp (20 ns) and CCD camera was employed to assess the shock front structure at different distances from the spark. It is shown that the shock rise time measured by the shadowgraphy method was in a good agreement with the theoretical predictions and it was 10 times shorter than in microphone measurements. The widening of the shock in acoustic measurements was therefore due to the limited bandwidth of the microphone. The combination of modeling, acoustic and optical measurements provided an accurate calibration of the shock wave measuring system. [Work supported by RFBR and INTAS.]

Generation of infinitely long phase screens for modeling of optical wave propagation in atmospheric turbulence

Numerical modeling of optical wave propagation in atmospheric turbulence is traditionally performed by using the so-called ‘split’-operator method, where the influence of the propagation medium's refractive index inhomogeneities is accounted for only within a set of infinitely narrow phase distorting layers (phase screens). These phase screens are generated on a numerical grid of finite size, which corresponds to a rather narrow slice (spatial area) of atmospheric turbulence. In several important applications including laser target tracking, remote sensing, adaptive optics, and atmospheric imaging, optical system performance depends on atmospheric turbulence within an extended area that significantly exceeds the area associated with the numerical grid. In this paper we discuss methods that allow the generation of a family of long (including infinitely long) phase screens representing an extended (in one direction) area of atmospheric turbulence-induced phase distortions. This technique also allows the generation of long phase screens with spatially inhomogeneous statistical characteristics.

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.

Study on the Effect of Laser Beam Propagation on the Slant Path through Atmospheric Turbulence

According to Huygens-Fresnel principle, the spreading radius and angle of beams are obtained with different height of drone on the slant path. The Mellin transform technique is applied to the wander effects of the collimating laser beam propagation in atmospheric turbulence on the slant path with different heights of drone and different outer-scales of turbulence. And apply the ITUR turbulence structure constant model which is altitude dependent to calculate the beam spreading and wander variance. The conclusions indicate that beam spreading and wander on the slant path depend on incident wave length, the height of drone and initial beam radius. And the effect of the atmospheric turbulence to laser beam propagation on the slant path is smaller than which is on the horizontal path. Because the drone is higher; the intensity of the turbulence is weaker.

Propagation of a cosh-Gaussian beam through an optical system in turbulent atmosphere

The propagation of a cosh-Gaussian beam through an arbitrary ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity at any receiver plane are obtained. As an elementary example, the average intensity and its radius at the image plane of a cosh-Gaussian beam through a thin lens are studied. To show the effects of a lens on the average intensity and the intensity radius of the laser beam in turbulent atmosphere, the properties of a collimated cosh-Gaussian beam and a focused cosh-Gaussian beam for direct propagation in turbulent atmosphere are studied and numerically calculated. The average intensity profiles of a cosh-Gaussian beam through a lens can have a shape similar to that of the initial beam for a longer propagation distance than that of a collimated cosh-Gaussian beam for direct propagation. With the increment in the propagation distance, the average intensity radius at the image plane of a cosh-Gaussian beam through a thin lens will be smaller than that at the focal plane of a focused cosh-Gaussian beam for direct propagation. Meanwhile, the intensity distributions at the image plane of a cosh-Gaussian beam through a lens with different w(0) and Omega(0) are also studied.

Simulator for general-type beam propagation in turbulent atmosphere

A simulator is designed in MATLAB code which gives the propagation characteristics of a general-type beam in turbulent atmosphere. When the required source and medium parameters are entered, the simulator yields the average intensity profile along the propagation axis in a video format. In our simulator, the user can choose the option of a "user defined beam" in which the source and medium parameters are selected as requested by the user by entering numerical values in the relevant menu boxes. Alternatively, the user can proceed with the option of "pre-defined beam" in which the average intensity profiles of beams such as annular, cos-Gaussian, sine-Gaussian, cosh-Gaussian, sinh-Gaussian, their higher-order counterparts and flat-topped can be observed as they propagate in a turbulent atmosphere. Some samples of the simulator output are presented.

Convergence of general beams into Gaussian intensity profiles after propagation in turbulent atmosphere

It is shown that a general shaped laser beam will eventually approach a Gaussian average intensity profile after propagation in turbulent atmosphere. In our formulation, source field at the exit plane of the laser is taken as the product of arbitrary functions of source transverse coordinates with Gaussian exponential modulations. Following the expansion of the arbitrary functions in terms of Hermite polynomials, the average receiver intensity expression is derived using the extended Huygens–Fresnel principle and the conditions for the intensity profile to assume a Gaussian shape are stated. The results are illustrated by simulating various source field distributions.

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.

Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere

Hermite-cosine-Gaussian (HcosG) laser beams are studied. The source plane intensity of the HcosG beam is introduced and its dependence on the source parameters is examined. By application of the Fresnel diffraction integral, the average receiver intensity of HcosG beam is formulated for the case of propagation in turbulent atmosphere. The average receiver intensity is seen to reduce appropriately to various special cases. When traveling in turbulence, the HcosG beam initially experiences the merging of neighboring beam lobes, and then a TEM-type cosh-Gaussian beam is formed, temporarily leading to a plain cosh-Gaussian beam. Eventually a pure Gaussian beam results. The numerical evaluation of the normalized beam size along the propagation axis at selected mode indices indicates that relative spreading of higher-order HcosG beam modes is less than that of the lower-order counterparts. Consequently, it is possible at some propagation distances to capture more power by using higher-mode-indexed HcosG beams.

Near Gaussian approximation for light propagation in the intermittent atmospheric turbulence

Intermittency is an essential property of turbulent atmosphere, and is one of the core content in modern turbulence theory. But, when we consider the problem of wave propagation in turbulent atmosphere, we always evade this property and use the assumption of a Gaussian probability distribution of dielectric permittivity fluctuation. In this paper, we discussed the intermittent effects on light propagation in turbulent atmosphere. According to the fact that the variance of dielectric permittivity fluctuation is very small, we explicitly expanded the equations of optical statistical moments to the fourth-order cumulant functions and considered their solutions. As for the second-order moment which is important i n optical applications, we have analyzed it emphatically by the hierarchical str uctures model. Our results indicate that the optical effects of turbulent interm ittency are negligible and the conventional Gaussian assumption is rational.

White noise in atmospheric optics

We consider a stochastic bilinear system model for laser propagation in atmospheric turbulence. The model consists of a random Schrodinger equation in which the white noise input is multiplied by the state. We consider approximate product form solutions of the Trotter-Kato type, and use these product forms to relate the Hilbert space-valued white noise model and the Ito equation model. We also consider white noise as the limit of a sequence Ornstein-Uhlenbeck processes. Finally, we consider approximate solutions using the Feynman-Ito equation, and an approximate calculation of the mean field without using the Markov approximation.

Two-dimensional modelling of optical propagation in turbulent atmosphere

The split step method was used to model plane wave optical propagation in a turbulent atmosphere for inner scales of turbulence of 0 and 5.1 mm. The intensity scintillation index was derived from the random field along the propagation path. The propagation parameters cover weak scattering and strong scattering conditions. >

Intensity properties of partially coherent beam waves

The extended Huygens-Fresnel principle is used to investigate the lateral coherence and the average on-axis intensity of partially coherent beam waves propagating in the turbulent atmosphere. A factor that determines the shift of the focal point toward the source when a beam wave propagates in turbulence is calculated. It is also shown that optimum beam wave propagation in atmospheric turbulence occurs for wavelength in the IR.

Phase approximation of the Huygens–Kirchhoff method in problems of space-limited optical-beam propagation in turbulent atmosphere

This Letter presents a rigorous mathematical proof of the applicability of a phase approximation in the Huygens–Kirchhoff method for the problems of space-limited optical-beam propagation in a turbulent atmosphere.

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.