Analytical equations for mutual spatial coherence functions of counter-propagating laser beams in integrated transmit/receive optical systems are derived. These equations being fourfold integrals allow estimating the diffraction parameters of transceivers and turbulent propagation conditions, under which a cryptographic key can be generated based on the principle of reciprocity. For particular cases, the degree of coherence of counter-propagating beams and the degree of coherence averaged over the receiver aperture are calculated as functions of generalized parameters describing the turbulence intensity and diffraction at the apertures.
Statistical characteristics of the orbital angular momentum (OAM) of a Laguerre-Gaussian laser beam propagating through a turbulent atmosphere have been studied in the Monte Carlo numerical simulation. We have analyzed variations in the probability density of OAM versus its initial value, turbulent conditions along the propagation path, the diffraction parameter of the beam, and the receiving aperture size. This distribution is shown to be symmetrical near-Gaussian for an infinite receiving aperture and to be well approximated by an Edgeworth series. The probability density function significantly changes for finite-size apertures. The range of sizes of the receiving aperture has been found where fluctuations of the moment of energy flux density and fluctuations of light flux recorded can be considered uncorrelated.
The efficiency of using an Airy axisymmetric beam for energy transfer and concentration to a given point in a randomly inhomogeneous medium is studied. Capabilities of this beam are assessed in comparison with beams of other types. The variance of beam wandering is calculated. For the given parameters of the transmitting system, path length, and degree of turbulent distortions, the intensity at the axis of the considered Airy beam is shown to be much lower than that of other beams, the Airy beam is compared with. In addition, the Airy beam is characterized by smaller wandering.
For a vortex axisymmetric Airy beam, the second-order mutual coherence function for the complex amplitude of the wave field was calculated by two methods. The first method assumed previous calculation of the complex amplitude of wave field of the beam in a turbulent medium based on the Monte Carlo technique, while the second method used the well-known representation of the solution of equation for the second-order spatial coherence function. Coherent properties of the beam at different values of parameters are studied.
In this study, we predict qualitatively the random wander of the Airy vortex beam propagating in a statistically homogeneous turbulent atmosphere based on the earlier revealed regularity [5] that the variances of random wander of vortex laser beams propagating in the turbulent atmosphere and having identical orbital angular momenta and identical transverse size in the source plane are different, if the effective volumes occupied by the beams in the homogeneous medium are different. The larger is the volume occupied by the beam in space, the smaller is the variance of the beam wander.
The dependences of the orbital angular momentum of a Laguerre–Gaussian beam propagating through a turbulent atmosphere on its azimuthal index and atmospheric turbulence strength are analyzed in the numerical simulation. The effect of errors in alignment of the beam and receiver axes on the average value and variance of orbital angular momentum fluctuations is studied. The statistics of the orbital angular momentum distribution at the end of the atmospheric propagation path is analyzed.
In this paper, the role of the vortex phase in the initial structure of wave field of the modified Bessel-Gaussian laser beam propagating in the atmosphere with weak turbulence, as well as in statistical regularities of beam wandering is studied by the semi-analytical method. The variance of the beam wandering depending on the diffraction conditions and the degree of turbulent distortions is determined. It is shown that the higher is the topological charge of the beam and its radial frequency, the smaller is the random wandering of the beam.
Numerical simulation and analytical calculations of the variance of fluctuations of the total orbital angular momentum (OAM) of Laguerre—Gaussian and Gaussian laser beams propagating in the randomly inhomogeneous atmosphere have been carried out. It is shown that as such beams propagate in the weakly turbulent atmosphere, the relative variance of OAM fluctuations remains much smaller than the relative variance of intensity fluctuations.
Statistical characteristics of the vortex laser beams propagating in the turbulent atmosphere are analyzed. The vortex beams are appeared to be less affected by turbulence as compared with the conventional beams: for the vortex beam the variance of random displacements and the variance for fluctuations of the orbital angular momentum, which are induced by atmospheric turbulence less than these characteristics for the vortexless beam, beams having a larger topological charge are founded to be more stable.
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