Yahya Baykal

Analysis of reciprocity of cos-Gaussian and cosh-Gaussian laser beams in a turbulent atmosphere

In a turbulent atmosphere, starting with a cos-Gaussian excitation at the source plane, the average intensity profile at the receiver plane is formulated. This average intensity profile is evaluated against the variations of link lengths, turbulence levels, two frequently used free-space optics wavelengths, and beam displacement parameters. We show that a cos-Gaussian beam, following a natural diffraction, is eventually transformed into a cosh-Gaussian beam. Combining our earlier results with the current findings, we conclude that cos-Gaussian and cosh-Gaussian beams act in a reciprocal manner after propagation in turbulence. The rates (paces) of conversion in the two directions are not the same. Although the conversion of cos-Gaussian beams to cosh-Gaussian beams can happen over a wide range of turbulence levels (low to moderate to high), the conversion of cosh-Gaussian beams to cos-Gaussian beams is pronounced under relatively stronger turbulence conditions. Source and propagation parameters that affect this reciprocity have been analyzed.

Flat topped beams and their characteristics in turbulent media

The source and receiver plane characteristics of flat topped (FT) beam propagating in turbulent atmosphere are investigated. To this end, source size, beam power and M(2) factor of source plane FT beam are derived. For a turbulent propagation medium, via Huygens Fresnel diffraction integral, the receiver plane intensity is found. Power captured within an area on the receiver plane is calculated. Kurtosis parameter and beam size variation along the propagation axis are formulated. Graphical outputs are provided displaying the variations of the derived source and receiver plane parameters against the order of flatness and propagation length. Analogous to free space behaviour, when propagating in turbulence, the FT beam first will form a circular ring in the center. As the propagation length increases, the circumference of this ring will become narrower, giving rise to a downward peak emerging from the center of the beam, eventually turning the intensity profile into a pure Gaussian shape.

Scintillation index of flat-topped Gaussian beams

The scintillation index is formulated for a flat-topped Gaussian beam source in atmospheric turbulence. The variations of the on-axis scintillations at the receiver plane are evaluated versus the link length, the size of the flat-topped Gaussian source, and the wavelength at selected flatness scales. The existing source model that represents the flat-topped Gaussian source as the superposition of Gaussian beams is employed. In the limiting case our solution correctly matches with the known Gaussian beam scintillation index. Our results show that for flat-topped Gaussian beams scintillation is larger than that of the single Gaussian beam scintillation when the source sizes are much smaller than the Fresnel zone. However, this trend is reversed and scintillations become smaller than the Gaussian beam scintillations for flat-topped sources with sizes much larger than the Fresnel zone.

M2-factor of coherent and partially coherent dark hollow beams propagating in turbulent atmosphere.

Analytical formula is derived for the M(2)-factor of coherent and partially coherent dark hollow beams (DHB) in turbulent atmosphere based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function. Our numerical results show that the M(2)- factor of a DHB in turbulent atmosphere increases on propagation, which is much different from its invariant properties in free-space, and is mainly determined by the parameters of the beam and the atmosphere. The relative M(2)-factor of a DHB increases slower than that of Gaussian and flat-topped beams on propagation, which means a DHB is less affected by the atmospheric turbulence than Gaussian and flat-topped beams. Furthermore, the relative M(2)-factor of a DHB with lower coherence, longer wavelength and larger dark size is less affected by the atmospheric turbulence. Our results will be useful in long-distance free-space optical communications.

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 elliptical Gaussian beam in turbulent atmosphere

A tensor method is used to formulate the on-axis scintillation index for an elliptical Gaussian beam (EGB; astigmatic Gaussian beam) propagating in a weak turbulent atmosphere. Variations of the on-axis scintillation of an EGB are studied. It is interesting to find that the scintillation index of an EGB can be smaller than that of a circular Gaussian beam in a weakly turbulent atmosphere under certain conditions and is closely related to the ratio of the beam waist size along the long axis to that along the short axis of the EGB, the wavelength, and the structure constant of the turbulent atmosphere.

Scintillations of partially coherent multiple Gaussian beams in turbulence

For an incidence composed of partially coherent multiple Gaussian beams, Huygens-Fresnel principle-based on-axis scintillation index is formulated in a weakly turbulent homogeneous horizontal atmospheric path. Our general formulation is applied to two examples of partially coherent annular and partially coherent flat-topped Gaussian beams. Compared to partially coherent single Gaussian beam scintillations, annular beam scintillations seem to possess higher values for all partial coherence levels, whereas flat-topped Gaussian beam intensity fluctuations are slightly larger, especially at lower coherence levels and at larger source sizes. At the same source partial coherence, annular beams exhibit smaller scintillations for larger ring sizes. For flat-topped Gaussian beams, except for very small and very large source sizes, as the number of Gaussian beams forming the flatness increases, intensity fluctuations also increase, a trend applicable for different degrees of coherence. A trend valid for both single and multiple Gaussian incidence, except for certain annular beams of large primary beam sizes, is that the scintillations decrease as the source becomes less coherent. Being applicable for all degrees of source coherences, for both beams examined, scintillations increase steadily as the Rytov plane wave scintillation index increases.

Average irradiance and polarization properties of a radially or azimuthally polarized beam in a turbulent atmosphere

Analytical formulas are derived for the average irradiance and the degree of polarization of a radially or azimuthally polarized doughnut beam (PDB) propagating in a turbulent atmosphere by adopting a beam coherence-polarization matrix. It is found that the radial or azimuthal polarization structure of a radially or azimuthally PDB will be destroyed (i.e., a radially or azimuthally PDB is depolarized and becomes a partially polarized beam) and the doughnut beam spot becomes a circularly Gaussian beam spot during propagation in a turbulent atmosphere. The propagation properties are closely related to the parameters of the beam and the structure constant of the atmospheric turbulence.

Formulation of correlations for general-type beams in atmospheric turbulence.

Log-amplitude and phase correlations of general-type beams are formulated in atmospheric turbulence. A general beam is described as the superposition of many sets of multimode contents, each mode being off-axis Hermite-Gaussian. Since the Rytov solution is utilized, the formulas are valid in the weakly turbulent regime. The results are presented in integral forms that should be numerically evaluated for the specific beam type of interest. Our general beam results correctly reduce to the existing solutions for the correlations of limiting-case beams such as higher-order single-mode, multimode, off-axis Hermite-Gaussian, Hermite-sinusoidal-Gaussian, higher-order-annular, flat-topped-Gaussian, and thus naturally fundamental mode, plane, and spherical waves. Scintillation index and phase fluctuations in atmospheric optical links employing such special beams will be examined in future using the results reported here.

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.