Experimental study and numerical simulation of laser beams propagation through the turbulent aerojet

A detailed experimental study of spatial characteristics for laser beams propagating through the turbulent aerojet has been performed. The obtained results for radiation wavelengths of 0.53, 1.06, and 10.6 microm were used for the development of the numerical mathematical model for beam propagation through an extreme turbulent medium. The combination of parameters and algorithms for the numerical model was determined, which made it possible to obtain computational laser beam spatial characteristics that agreed quite well with the experimental data. Good agreement between the results points to the possibility, in principle, to regard the central jet area as a medium locally homogeneous in the statistical sense and anisotropic on the turbulent outer scales.     

Log-amplitude and phase fluctuations of higher-order annular laser beams in a turbulent medium

Log-amplitude and phase-correlation and structure functions of higher-order annular laser beams in a turbulent atmosphere are derived. A higher-order annular beam source is defined as the superposition of two different higher-order Hermite-Gaussian beams. A special case of such an excitation is the annular Gaussian beam in which two beams operate at fundamental modes of different Gaussian beam sizes, yielding a doughnut-shaped (annular) beam when the second beam is subtracted from the first beam. Our formulation utilizes Rytov approximation, which makes it applicable in the weak-turbulence regime, especially for log-amplitude fluctuations. Limiting cases of our formulations correctly match with known higher-order-mode solutions that in turn reduce to the Gaussian-beam-wave (TEM00-mode) results. Our results can be applied to determine the scintillation index and the phase fluctuations in free-space optics links under higher-order annular laser beam excitation. Except for the numerical evaluation of a specific example covering an annular Gaussian beam, the results in general are left in integral form and need to be numerically evaluated in detail to obtain quantitative results.     

Analysis of algorithms for adaptive control of laser beams in a nonlinear medium

Adaptive correction for thermal blooming by multidither and phase-conjugation algorithms is analyzed with the use of numerical models of beams propagating in a nonlinear medium. Methods to increase the stability of these algorithms are proposed. The influence of an adaptive mirror on the efficiency and the divergence of correction algorithms is considered. The feasibility of amplitude-phase control with a two-mirror adaptive optics system is also analyzed.     

Simulation of laser propagation in a turbulent atmosphere

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.     

Mathematical formulation for the propagation of sound through a turbulent jet

Summary The sound propagation through a nonuniform turbulent jet flow field is studied by means of a system of linearized equations governing the acoustic variables. These equations depend on the fluctuating flow-field variables which can be prescribed by experimental results. It is shown that the correlations of the acoustic variables depend throughout the flow field on the space-time correlation of the turbulent velocities and on the mean flow variables and their gradients.The contributions to this paper by this author are a result of work performed under NASA Grant NGR 47-102-001.     

Propagation of partially coherent flat-topped beams through a turbulent atmosphere

Based on the modified beam model for flat-topped beams and the Schell model for partially coherent light, an expression for partially coherent flat-topped (PCFT) beams has been proposed. The propagation characteristics of PCFT beams with circular symmetry through a turbulent atmosphere have been studied. By using the generalized Huygens-Fresnel integral and Fourier transform method, the expressions for the cross-spectral density function and the average intensity have been given and the analytical expression for the root-mean-square width has been derived. The effects of the beam order, the spatial coherence, and the turbulent parameter on the intensity distributions and beam spreading have been discussed in detail. Our results show that the on-axis intensity of the beams decreases with increasing turbulence and decreasing coherence of the source, whereas the on-axis intensity of the beams in the far field decreases slightly with increasing beam order. The relative spreading of PCFT beams is smaller for beams with a higher order, a lower degree of global coherence of the source, a larger inner scale, and a smaller outer scale of the turbulence.     

Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulent atmosphere

Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beam intensities in a turbulent atmosphere are investigated. The received intensity is formulated by applying the extended Huygens-Fresnel principle to generalized Hermite-hyperbolic-Gaussian and Hermite-sinusoidal-Gaussian beam incidences. From this result, the association to different types of Hermite-hyperbolic-Gaussian and Hermite-sinusoidal-Gaussian beams are defined. The average receiver intensity expressions for Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams are evaluated and plotted against the variations in source parameters and propagation conditions. It is observed that the propagation of Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams in turbulence have many similarities to their counterparts, Hermite-cosine-Gaussian and Hermite-cosh-Gaussian laser beams, that are examined earlier. It is further observed that under certain conditions the main features of the previously established reciprocity concept between cosine-Gaussian and cosh-Gaussian beams are mostly applicable to Hermite-sine-Gaussian and Hermite-sinh-Gaussian laser beams.     

Multifractality of laser beam spatial intensity in a turbulent medium

We present the results of a laser beam passing through a turbulent medium. First we measure the geometric parameters and the spatial coherence of the beam as a function of wind velocities. A multifractal detrended fluctuation analysis algorithm is applied to determine the multifractal scaling behavior of the intensity patterns. The measurements are fitted with models used in the analysis of river runoff records. We show the surprising result that the multifractality decreases when the spatial coherence of the laser is decreased. Universal scaling properties could be applied to the spatial characterization of a laser propagating in a turbulent medium or random medium.     

Measurement of the energy of wide laser beams in a turbulent atmosphere

An analysis of one possible method of determining the energy of a laser pulse that has traversed a test path is given. Based on a model of phase screens and the Monte-Carlo method of statistical tests, the conditions of propagation of laser pulses in air are modeled and geometric parameters of the measurement system which are optimal from the point of view of error minimization are determined. __________ Translated from Izmeritel’naya Tekhnika, No. 9, pp. 21–25, September, 2006.     

Propagation factors of laser array beams in turbulent atmosphere

The propagation factors of phased locked laser array beams of radial and rectangular symmetries in a turbulent atmosphere are investigated based on the extended Huygens–Fresnel integral and the Wigner distribution function. Analytical propagation formulae for the propagation factors are derived and numerical examples are illustrated. We find that unlike their propagation invariant properties in free space, the propagation factors of laser array beams increase when propagating in turbulent atmosphere, and are closely related to the parameters of initial beams and the atmosphere.     

Correlation and structure functions of Hermite-sinusoidal-Gaussian laser beams in a turbulent atmosphere

To study the performance of atmospheric optical links by using Hermite-sinusoidal-Gaussian laset beam sources, we derive the log-amplitude and the phase correlation and structure functions of such beams in a turbulent atmosphere. Our formulations correctly reduce to the known higher-order mode correlation and structure functions, which in turn reduce to the fundamental-mode (TEM00-mode) results. Several special cases of our formulation are presented, among which the case involving Hermite-cosh-Gaussian dependence is especially noted, since this case is of interest to us owing to the nature of cosh dependence exhibiting the concentration of the energy in the outer lobes of the beam.     

Single beam one-way imaging through a thick dynamic turbulent medium

A new method to record an image through a thick dynamic phase distorting medium by using a photorefractive LiNbO3 crystal is demonstrated. The method uses only one beam of light, the object light. By making use of the photorefractive fanning effect, gratings are formed in the LiNbO3 crystal through the interference between the object light and its own fanning light. Because the time scale of the distorting fluctuation is much shorter than the writing time of the LiNbO3 crystal, the fluctuated light does not induce any fanning. Therefore only the static portion of the image is recorded in the crystal, and the intensity distribution of the image can then be reconstructed at any later time.     

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.     

Changes in the spectrum of radial array beams through turbulent atmosphere

According to the extended Huygens–Fresnel principle, the propagation formulas of the spectrum for correlated superposition radial array Gaussian Schell-model (RAGSM) beams in a turbulent atmosphere have been derived. The spectral properties of correlated superposition RAGSM beams in free space and in turbulence have also been compared and analyzed. The results show that there exist two identical spectral maxima for the normalized on-axis spectrum of RAGSM beams at one critical position against propagation distance. When the propagation distance is large enough, the on-axis relative spectral shifts in free space and those in turbulence tend to a steady nonzero and zero value, respectively. The off-axis relative spectral shift in free space exhibits a blue-shift alternating with red-shift against off-axis distance, and it depends on the array radius and the beamlet number; whereas the spectral shift has a rapid transition in turbulence. In addition, the on-axis and off-axis relative spectral shifts also depend on the characteristic parameters of turbulence, the beam parameters, and the array parameters.     

Average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere

The average intensity and spreading of cosh-Gaussian laser beams in the turbulent atmosphere are examined. Our research is based principally on formulating the average-intensity profile at the receiver plane for cosh-Gaussian excitation. The limiting cases of our formulation for the average intensity are found to reduce correctly to the existing Gaussian beam wave result in turbulence and the cosh-Gaussian beam result in free space (in the absence of turbulence). The average intensity and the broadening of the cosh-Gaussian beam wave after it propagates in the turbulent atmosphere are numerically evaluated versus source size, beam displacement, link length, structure constant, and two wavelengths of 0.85 and 1.55 microm, which are most widely used in currently employed free-space-optical links. Results indicate that in turbulence the beam is widened beyond its free-space diffraction values. At the receiver plane, analogous to the case of free space, this diffraction eventually leads to transformation of the cosh-Gaussian beam into an oscillatory average-intensity profile with a Gaussian envelope.     

Scintillation index of flat-topped Gaussian laser beam in strongly turbulent medium

In a strongly turbulent medium, the scintillation index of flat-topped Gaussian beams is derived and evaluated. In the formulation, unified solution of Rytov method is utilized. Our results correctly reduce to the existing strong turbulence scintillation index of the Gaussian beam, and naturally to spherical and plane wave scintillations. Another checkpoint of our result is the scintillation index of flat-topped Gaussian beams in weak turbulence. Regardless of the order of flatness, scintillations of flat-topped Gaussian beams in strong turbulence are found to be determined mainly by the small-scale effects. For large-sized beams in moderate and strongly turbulent medium, flatter beams exhibit smaller scintillations.     

Spectral changes of polychromatic stochastic electromagnetic vortex beams propagating through turbulent atmosphere

The unified theory of coherence and polarization and the propagation law of 2 × 2 cross-spectral density are employed to investigate spectral changes of the polychromatic stochastic electromagnetic vortex beam propagating in turbulent atmosphere. It is shown that the spectral changes of a polychromatic stochastic electromagnetic vortex beam in turbulent atmosphere differ from those of the beam without vortex. Specially, the on-axis relative spectral shifts exhibit not only blue-shift, but also red-shift. It is also shown that the topological charge, the correlation length and the refractive index structure constant influence the spectral changes of polychromatic stochastic electromagnetic vortex beams in a turbulent atmosphere.