Field correlations of multimode optical beams in underwater turbulence.

For multimode optical beams, field correlations at the receiver plane are found in underwater turbulence. Field correlations of single high order beams in underwater turbulence are special cases of our formulation. Variations of field correlations against the underwater turbulence parameters and the diagonal length from various receiver points are examined for different multimode and single high order beams. Stronger underwater turbulence is found to reduce the field correlations of multimode and single high order optical beams. The results will be of help in heterodyne detection analysis and fiber coupling efficiency in an underwater medium experiencing turbulence.

Correlations of multimode optical incidences in a turbulent biological tissue.

In a turbulent biological tissue, field correlations at the observation plane are found when a multimode optical incidence is used. For different multimode structures, variations of the multimode field correlations are evaluated against the biological tissue turbulence parameters, i.e., the strength coefficient of the refractive-index fluctuations, fractal dimension, characteristic length of heterogeneity, and the small length-scale factor. Using a chosen multimode content, for specific biological tissue types of liver parenchyma (mouse), intestinal epithelium (mouse), upper dermis (human), and deep dermis (mouse), field correlations are evaluated versus the strength coefficient of the refractive-index fluctuations and small length-scale factor. Again, with a chosen multimode content, behavior of the field correlations is studied against the strength coefficient of the refractive-index fluctuations for various diagonal lengths and the transverse coordinate at the observation plane. Finally, the field correlation versus the strength coefficient of the refractive-index fluctuations is reported for different single modes, which are special cases of multimode excitation. This topic is being reported in the literature for the first time, to our knowledge, and the presented results can be employed in many important biological tissue applications.

Correlation of multimode fields in atmospheric turbulence.

Multimode field correlations are evaluated in atmospheric turbulence. High order field correlations are special cases of the results that we obtained in this paper. Field correlations are presented for various numbers of multimodes, various multimode contents of the same number of modes, and various high order modes versus the diagonal distance from various receiver points, source size, link length, structure constant, and the wavelength. Our results will be of help especially in the design of heterodyne systems operating in turbulent atmosphere and fiber coupling efficiency in systems employing multimode excitation.

Field correlations of partially coherent optical beams in underwater turbulence.

Field correlations of partially coherent optical beams at the receiver plane are formulated and evaluated in underwater turbulence. Variations of the field correlations are examined against changes in the degree of source coherence, diagonal length from the receiver point, receiver point, propagation distance, source size, ratio of temperature to salinity contributions to the refractive index spectrum, rate of dissipation of mean-squared temperature, and rate of dissipation of kinetic energy per unit mass of fluid. Under any underwater turbulence and link conditions, it is found that field correlations at the receiver plane reduce when the optical source becomes less coherent.

Scintillation and bit error rate in bidirectional laser communications between an aerial vehicle and a satellite using annular optical beams in strong turbulent atmosphere.

Scintillation index is examined for annular optical beams in a strong atmospheric medium of a slant path. On-axis scintillations have small- and large-scale components and are formulated for the uplink/downlink of aerial vehicle-satellite laser communications. For this purpose, the unified Rytov method and the amplitude spatial filtering of the atmospheric spectrum are utilized. Performances given by the average bit error rate (BER) are investigated by employing the corresponding scintillation index, which is found by using intensity having gamma-gamma distribution. Strong atmospheric turbulence effects on the scintillation index and BER of the collimated annular optical beam having various thicknesses are reported for the up/down vertical links, and these are compared with the scintillations of the collimated Gaussian optical beams against propagation length, source size, and the zenith angle with the selected thickness. Utilizing the scintillations found, BER changes against average signal-to-noise ratio (SNR)are plotted for up/down vertical links. The scintillation index and BER in the downlink are found to be different than the scintillation index and BER in the uplink for strong atmospheric turbulence, mainly because the structure constant is a function of the altitude. Considering the location where the aerial vehicle and satellite are deployed as the reference points, annular beams are more advantageous than the Gaussian beams at up/down slant link lengths. The effect of the thickness of the annular beam is apparent for the uplink, where thin annular beams are more advantageous at small link lengths and thick annular beams are more advantageous at large link lengths. In the downlink, thin annular beams are more advantageous at all link lengths.

Minimization of the scintillation index of sinusoidal Gaussian beams in weak turbulence for aerial vehicle-satellite laser communications.

Minimization of the on-axis scintillation index of sinusoidal Gaussian beams is investigated by using the modified Rytov method in weak atmospheric turbulence for uplink/downlink of aerial vehicle-satellite laser communications. Among the focused cosh-Gaussian (cosh-G), cos-Gaussian (cos-G), annular, and Gaussian beams, a suitable displacement parameter for a cosh-G beam is determined that will minimize the scintillation index in uplink and downlink configurations. Then, for both uplink and downlink, the variations of the scintillation index against the propagation distance, source size, and zenith angle are examined and compared among themselves to show the optimum beam that possesses the minimum scintillation index. Sinusoidal Gaussian beams that are focused at the receiver and obtained by employing the appropriate displacement parameter, which we name the optimum beams, are recommended to obtain smaller intensity fluctuations in atmospheric wireless optical communication systems operating in vertical links in weak turbulence.

M-pulse amplitude modulation of a flat-topped beam for aeronautical laser communications.

Using the Rytov method, bit error rate (BER) performances of M-pulse amplitude modulation (M-PAM) are investigated for a flat-topped beam when such a beam is employed in an aeronautical laser communication system operating in vertical paths having weak atmospheric turbulence. By using the on-axis scintillation index and the log-normal distributed intensity, the average BER (⟨BER⟩) is evaluated for M-PAM when M=2,4,8. The scintillation indices of collimated flat-topped beams of various flatness orders N are compared against propagation lengths, source sizes, and zenith angle for laser communication vertical paths, including uplink and downlink. Also, the ⟨BER⟩ versus the average signal to noise ratio (⟨SNR⟩) is examined for various beam flatness orders. It is shown that as the flatness order increases, the scintillation index decreases. Taking one of the best flatness order values, N=15, for reducing the scintillations, ⟨BER⟩ versus propagation lengths, source sizes, zenith angle, and ⟨SNR⟩ are found for various values of M. When M is increased, the ⟨BER⟩ is found to deteriorate.

Bit error rate of focused Gaussian beams in weak oceanic turbulence.

Formulation of the on-axis scintillation index of a focused Gaussian beam in weak oceanic turbulence is derived by using the Rytov method, and using this formulation, the average bit error rate (BER) is evaluated. The scintillation indices of collimated, focused Gaussian, plane, and spherical beams are compared. The scintillation index and BER versus the average signal-to-noise ratio is found by using the log-normal distributed intensity for the collimated and focused Gaussian beams, which are exhibited for various source sizes α(s), focal lengths F(s), rates of dissipation of the mean squared temperature χ(T), and rates of dissipation of the turbulent kinetic energy per unit mass of fluid ε. Focused beams are found to have important advantages over collimated beams. For the focused beam, as the source size increases, the scintillation index and BER decrease. When the focal length is equal to the propagation length, the BER is found to possess the smallest value. The BER is proportional to χ(T), but inversely proportional to ε.

Intensity fluctuations of flat-topped beam in non-Kolmogorov weak turbulence.

Results obtained on the intensity fluctuations of flat-topped Gaussian beams in weakly turbulent non-Kolmogorov horizontal atmospheric optics links are represented. Effects on the scintillation index of the power law α that describes the non-Kolmogorov spectrum are examined. Our results correctly reduce to the existing intensity fluctuations of flat-topped beams in Kolmogorov turbulence. Variation of the scintillation index against non-Kolmogorov power law α exhibits a peak at the worst power law α(w), which happens to be smaller than the Kolmogorov power law of 11/3. If the power law is smaller (larger) than α(w), increase in α will increase (decrease) the intensity fluctuations. Evaluation of the scintillation index at the worst power law results in smaller fluctuations for a Gaussian beam at short propagation distances; however, at long propagation distances flatter beams happen to possess smaller fluctuations. The scintillation change versus the source size follows a similar trend regardless whether the flat-topped beam propagates in a Kolmogorov or non-Kolmogorov medium.

Equivalence of structure constants in non-Kolmogorov and Kolmogorov spectra.

We find the equivalence of the structure constants in non-Kolmogorov and Kolmogorov spectra in a turbulent atmosphere. As the reference point, the spherical wave scintillation index in a non-Kolmogorov medium is used. Relations of the structure constants are found to be functions of the power law of the turbulence spectrum and the Fresnel zone. It will be useful to employ the equivalence of the structure constants in making performance comparisons found with non-Kolmogorov and Kolmogorov spectra.

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.

Annular beam scintillations in strong turbulence.

A scintillation index formulation for annular beams in strong turbulence is developed that is also valid in moderate and weak turbulence. In our derivation, a modified Rytov solution is employed to obtain the small-scale and large-scale scintillation indices of annular beams by utilizing the amplitude spatial filtering of the atmospheric spectrum. Our solution yields only the on-axis scintillation index for the annular beam and correctly reduces to the existing strong turbulence results for the Gaussian beam--thus plane and spherical wave scintillation indices--and also correctly yields the existing weak turbulence annular beam scintillations. Compared to collimated Gaussian beam, plane, and spherical wave scintillations, collimated annular beams seem to be advantageous in the weak regime but lose this advantage in strongly turbulent atmosphere. It is observed that the contribution of annular beam scintillations comes mainly from the small-scale effects. At a fixed primary beam size, the scintillations of thinner collimated annular beams compared to thicker collimated annular beams are smaller in moderate turbulence but larger in strong turbulence; however, thinner annular beams of finite focal length have a smaller scintillation index than the thicker annular beams in strong turbulence. Decrease in the focal length decreases the annular beam scintillations in strong turbulence. Examining constant area annular beams, smaller primary sized annular structures have larger scintillations in moderate but smaller scintillations in strong turbulence.