On the scintillation index of a multiwavelength Gaussian beam in a turbulent free-space optical communications channel

The scintillation statistics of a multiwavelength Gaussian optical beam are characterized when the beam is subjected to a turbulent optical channel. It is assumed that the level of turbulence in the atmosphere ensures a weak-turbulence scenario and that fluctuations in the signal intensity are due to variations in the refractive index of the medium, which in turn are caused by regional temperature variations due to atmospheric turbulence. Furthermore, it is assumed that the propagation path is nearly horizontal and that the heights of the transmitter and receiver justify a near-ground propagation assumption. The Rytov approximation is used to arrive at the desired results. Furthermore, it is assumed that the first- as well as second-order perturbation terms are present in modeling the impact of atmosphere-induced scintillation. Numerical results are presented to shed light on the performance of multiwavelength optical radiation in weak turbulence and to underscore the benefits of the proposed approach as compared with its single-wavelength counterpart in combating the effect of turbulence. Furthermore, it is shown that if the separation of wavelengths used is sufficiently large, wavelength separation affects the scintillation index in a measurable way.     

Scintillation index of optical spherical wave propagating through biological tissue

Effects of the tissue turbulence on the propagation of an optical spherical wave are analysed. For this purpose, scintillation index of an optical spherical wave which is propagating in a soft tissue is formulated and evaluated in weakly turbulent soft tissue. Scintillation index of the optical spherical wave is examined against the changes in the tissue parameters which are the tissue length between the optical spherical wave source and the detector, random variations in the refractive index of the tissue and the outer scale of the tissue turbulence. According to our graphical outputs, it is observed that increase in the random variations of the refractive index of the tissue results in an increase in the scintillation index at a certain realization of the turbulence spectrum. On the other hand, larger outer scales and longer tissue lengths yield larger scintillations. The variation of the scintillation index of the optical spherical wave versus the wavelength is also investigated. It is found that at small tissue lengths, wavelength has almost no effect on the scintillations; however, when the tissue length reaches a certain value, shorter wavelengths give rise to larger intensity fluctuations.     

Threshold detection in the presence of atmospheric turbulence

Recently there has been increased interest in threats to spacecraft from ground-based lasers. It has been suggested that some spacecraft should use laser-threat-warning receivers. We consider the effects of atmospheric turbulence on threshold detection of optical signals by an exoatmospheric receiver. The results are applicable to both cw and pulsed optical illumination that results from ground-based lasers. In particular we obtain accurate analytical expressions, over a wide range of conditions of practical interest, that yield the required signal-to-noise ratio for a given (single-event) probability of detection, false-alarm rate, and turbulence-induced log-intensity variance. The degrading effects of atmospheric turbulence on threshold detection are most important for large zenith angles in the blue-green region of the visible. As an illustrative example, a false-alarm rate of 1 in 3 years is assumed, and specific numerical results are presented for the required signal-to-noise ratio necessary to obtain a detection probability of at least 95% over a range of optical wavelengths and propagation conditions of interest.     

Scintillation of astigmatic dark hollow beams in weak atmospheric turbulence

The scintillation properties of astigmatic dark hollow beams (DHBs) in weak atmospheric turbulence were investigated in detail. An explicit expression for the on-axis scintillation index of an astigmatic DHB propagating in weak atmospheric turbulence was derived. It was found that the scintillation index value of an astigmatic DHB with suitable astigmatism (i.e., ratio of the beam waist size in the x direction to that in the y direction), dark size, beam waist size, and wavelength can be smaller than that of a stigmatic DHB and that of stigmatic and astigmatic flat-topped, annular, and Gaussian beams in weak atmospheric turbulence particularly at long propagation ranges. Our results will be useful in long-distance free-space optical communications.     

Common omissions and misconceptions of wave propagation in turbulence: discussion

This review paper addresses typical mistakes and omissions that involve theoretical research and modeling of optical propagation through atmospheric turbulence. We discuss the disregard of some general properties of narrow-angle propagation in refractive random media, the careless use of simplified models of turbulence, and omissions in the calculations of the second moment of the propagating wave. We also review some misconceptions regarding short-exposure imaging, propagation of polarized waves, and calculations of the scintillation index of the beam waves.     

A transport model for broadening of a linearly polarized,coherent beam due to inhomogeneities in a turbulent atmosphere

Traditional models for beam broadening include both a diffractive term, owing to the source aperture, and a beam ‘wandering’ term that stems from refractive index variations in the atmosphere. Here we derive a novel beam broadening term that depends on the properties of atmospheric turbulence. The derivation rests on a transport formulation of the propagation problem whereby the magnitude of the electric field is viewed as the density of a fluid, moving in a flow that is driven by the refractive index perturbations. Properties of the transport solutions are obtained using Lagrangian coordinates and are demonstrated to be entirely consistent with existing theory on the subject. The new factor predicts appreciable (25% in our example) increases in beam broadening for applications requiring propagation over very long optical paths and heavy turbulence.     

Spiral spectrum of anomalous vortex beams propagating in a weakly turbulent atmosphere

ABSTRACT

We study the spiral spectrum of anomalous vortex beams propagating through a turbulent atmosphere. Based on the Huygens–Fresnel integral and the Rytov approximation, the integral expression and then the analytical expression for the spiral spectrum of anomalous vortex beams in the weakly turbulent atmosphere are derived. The capacity of wireless optical links using the anomalous vortex beam is obtained. It is found that the spiral spectrum of the anomalous vortex beam is less affected by turbulence than that of the Laguerre-Gaussian beam. And thus, the information capacity of wireless optical links using the anomalous vortex beam is larger than that using the Laguerre-Gaussian beam. The influence of beam order, wavelength, topological charge, propagation distance, refractive index structure constant and the radius of receiver aperture on spiral spectrum is investigated. These results contribute to reduce the disturbing effects of atmospheric turbulence on the orbital angular momentum of the vortex beam.     

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.     

Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence

Abstract

Atmospheric turbulence severely limits the performance of ground-based imaging and laser propagation systems. Some observational results, showing atmospheric turbulence which does not obey Kolmogorov's theory, have prompted the study of optical propagation through non-Kolmogorov turbulence. This paper presents a theoretical approach to analyse the spatial and temporal characterizations of phase fluctuations in non-Kolmogorov turbulence. The spatial structure function, the temporal structure function and the temporal power spectrum of phase fluctuations are derived. The generalized coherence length ρ₀, the characteristic frequency f_R and the characteristic time T_R are expressed as functions of the index structure constant along the propagation path and the wind velocity. The long exposure MTF, the short exposure MTF and the imaging Strehl ratio are computed.     

Effects of different beacon wavelengths on atmospheric compensation in strong scintillation

During strong scintillation, the number and location of branch points in a distorted optical field induced by atmospheric turbulence are closely related to the characteristic parameters of the turbulence effect, propagation distance, and wavelength. It is necessary to consider the effect of the beacon's wavelength on the adaptive optics system that is used to compensate for atmospheric turbulence. Our analytical results show that the performance of adaptive optics can be improved by nearly a factor of 2 when the beacon's wavelength is chosen slightly longer than the wavelength of the main laser in the branch points considered.     

Propagation properties of flat-topped beams in a turbulent atmosphere

Based on the extended Huygens–Fresnel principle and the quadratic approximation for phase structure function, the analytical formulas for the average irradiance of the phase-locked and the non-phase-locked radial modified flat-topped array beams in turbulence have been derived. The propagation properties of radial modified flat-topped array beams have been investigated. It is found that the irradiance distributions of the radial flat-topped array beams propagating in turbulence are different from those in free space. The propagation properties depend on the refractive index structure constant, the beam order and the array radius. The power in the bucket (PIB) for the array beams increases with the decrease of the array radius for a given propagation distance. For a certain bucket radius, there exhibits a PIB maximum upon propagation. The optimal propagation distance becomes shorter along with the increasing refractive index structure constant, and the PIB maximum increases with bucket radius.     

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.     

Effect of anisotropy on intensity fluctuations in oceanic turbulence

For an optical spherical wave propagating in an oceanic turbulent medium, the effect of anisotropy on the received intensity fluctuations is investigated. For different anisotropy factors, the variations of the scintillation index vs. the ratio that determines the relative strength of temperature and salinity in the index fluctuations, the rate of dissipation of the mean squared temperature, the rate of dissipation of the turbulent kinetic energy, viscosity, link length and the wavelength are plotted. It is found that, for all the oceanic turbulence and the link parameters of interest, as the medium becomes more anisotropic, the intensity of the optical spherical wave fluctuates less. It is concluded that the performance of an optical wireless communication systems (OWCS) operating in anisotropic oceanic turbulence is better than the performance of OWCS operating in isotropic oceanic turbulence.     

Scintillation index and bit error rate of hollow Gaussian beams in atmospheric turbulence

Based on the Huygens–Fresnel principle and Rytov method, the on-axis scintillation index is derived for hollow Gaussian beams (HGBs) in weak turbulence. The relationship between bit error rate (BER) and scintillation index is found by only considering the effect of atmosphere turbulence based on the probability distribution of intensity fluctuation, and the expression of the BER is obtained. Furthermore, the scintillation and the BER properties of HGBs in turbulence are discussed in detail. The results show that the scintillation index and BER of HGBs depend on the propagation length, the structure constant of the refractive index fluctuations of turbulence, the wavelength, the beam order and the waist width of the fundamental Gaussian beam. The scintillation index, increasing with the propagation length in turbulence, for the HGB with higher beam order increases more slowly. The BER of the HGBs increases rapidly against the propagation length in turbulence. For propagating the same distance, the BER of the fundamental Gaussian beam is the greatest, and that of the HGB with higher order is smaller.     

Polarization changes in a partially coherent radially polarized doughnut beam through turbulent ocean

On the basis of the extended Huygens–Fresnel integral principle and unified theory of coherence and polarization of light, we studied the effects of oceanic turbulence on polarization properties of a partially coherent radially polarized doughnut (PCRPD) beam. The ocean-induced fluctuations in the refractive index are assumed be driven by temperature and salinity fluctuations. Numerical examples of changes in polarization properties, such as the degree of polarization, the degree of ellipticity, and the orientation angle in the oceanic turbulence for the PCRPD beam, are given. Our analysis demonstrates how polarization of the PCRPD beam is affected by statistical properties of the source and by several parameters of oceanic turbulence. We find that the propagation of the PCRPD beam is different from that of stochastic beams in oceanic turbulence. The degree of polarization for the PCRPD beam approaches a certain steady value, and the elliptical polarized state of the fully polarized portion of the beam will become fully linear in the far field.     

湍流下自由空间光通信的光纤耦合效率及补偿

采用光纤部件的自由空间光通信系统需要把接收到的光束耦合进单模光纤中,然而由于大气湍流的影响,使光纤耦合效率下降.本文把基于大气湍流参数的单模光纤耦合效率表达式推广到斜程传输情景,仿真了耦合效率与湍流强度及传输距离和天顶角之间的关系.为了补偿湍流效应,提高光纤耦合效率,本文提出了用一种新颖的无模型盲优化波前校正技术,用随...     

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.     

Scintillation of pseudo-Bessel correlated beams in atmospheric turbulence

The concept of pseudo-Bessel correlated beams is introduced, and their scintillation properties on propagation through turbulence are investigated. By using the Rytov approximation, the scintillation index of pseudo-Bessel correlated beams is formulated in weak turbulence. The study of scintillation is extended into strong turbulence by numeric simulations. It is shown that by choosing an appropriate coherence parameter, pseudo-Bessel correlated beams have lower scintillation than comparable fully coherent beams in both weak and strong turbulence. In addition, the configuration of pseudo-Bessel correlated beams is modified by adding a horizontal beamlet; the scintillation properties of these modified beams are also discussed.     

Scintillations of cos-Gaussian and annular beams

Based on the generalized beam formulation, we derive the scintillation index and selectively evaluate it for cos-Gaussian and annular beams propagating in weak atmospheric turbulence. Dependence of the scintillation index on propagation length, focusing and displacement parameters, wavelength of operation, and source size are individually investigated. From our graphical outputs, it is observed that a cos-Gaussian beam exhibits lower scintillations and thus has a tendency to be advantageous over a pure Gaussian beam particularly at lower propagation lengths. It is also found that at longer propagation lengths, this advantage switches to the side of the annular beam. Furthermore, the scintillation index of a focused annular beam will be below those of both Gaussian and cos-Gaussian beams starting at earlier propagation distances. When analyzed against source sizes, it is seen that cos-Gaussian beams will offer advantages at relatively large source sizes, while the reverse will be applicable for annular beams.