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 a partially coherent optical Gaussian wave in tissue turbulence.

For a partially coherent Gaussian optical wave, field correlations in turbulent tissues are examined. Changes in the field correlations are evaluated when the degree of source coherence, diagonal length from the receiver point, transverse receiver coordinate, tissue type, tissue length, source size, characteristic length of heterogeneity, strength coefficient of the refractive-index fluctuations, fractal dimension, and the small length-scale factor of the turbulent tissue vary. Investigated turbulent tissue types are liver parenchyma (mouse), upper dermis (human), intestinal epithelium (mouse), and deep dermis (mouse). For all the examined tissue types, field correlations are found to increase as the degree of source coherence, fractal dimension, and small length-scale factor increase and as the diagonal length from the receiver point, transverse receiver coordinate, tissue length, characteristic length of heterogeneity, and strength coefficient of the refractive-index fluctuations decrease. For the coherent source, an increase in the source size will increase the field correlations; however, for the partially coherent source, this trend is reversed.

Structure functions for optical waves in a complex medium of turbulent biological tissues.

Although optical wave propagation is investigated based on the absorption and scattering in biological tissues, the turbulence effect can also not be overlooked. Here, the closed-form expressions of the wave structure function (WSF) and phase structure function (PSF) of plane and spherical waves propagating in biological tissue are obtained to help with future research on imaging, intensity, and coherency in turbulent biological tissues. This paper presents the effect of turbulent biological tissue on optical wave propagation to give a perception of the performance of biomedical systems that use optical technologies. The behavior of optical waves in different types of turbulent biological tissues such as a liver parenchyma (mouse), an intestinal epithelium (mouse), a deep dermis (mouse), and an upper dermis (human) are investigated and compared. It is observed that turbulence becomes more effective with an increase in the characteristic length of heterogeneity, propagation distance, and the strength of the refractive index fluctuations. However, an increase in the fractal dimension, wavelength, and small length scale factor has a smaller turbulence effect on the propagating optical wave. We envision that our results may be used to interpret the performance of optical medical systems operating in turbulent biological tissues.

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.

Scintillation and BER analysis of cosine and cosine-hyperbolic-Gaussian beams in turbulent ocean.

Effects of source beam, link, and oceanic turbulence parameters on the scintillation index and bit error rate (BER) performance of cosine (cos) and cosine-hyperbolic (cosh) Gaussian light beams have been investigated in order to improve wireless optical communication link performance in oceanic turbulence. The Nikishov and Nikishov power spectrum of oceanic water and extended Huygens Fresnel principle were used in our evaluations; the results were obtained via MATLAB. The scintillation index and BER were examined versus oceanic turbulence parameters, which are the rate of dissipation of mean-square temperature, the ratio of temperature and salinity contributions to the refractive index spectrum, and the dissipation rate of kinetic energy per unit fluid mass of fluid. Further, the scintillation index and BER are investigated against the source size, propagation distance, and complex displacement parameters of cos- and cosh-Gaussian beams. This study aimed to select the suitable sinusoidal beam to be employed in order to increase the performance of underwater wireless optical communication systems operating in oceanic turbulence.

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.

Performance of M-ary pulse position modulated optical wireless communications systems in the marine atmosphere.

The marine atmosphere exhibits different turbulence spectrum characteristics when compared to the turbulence spectra of the land atmosphere and underwater medium. The performance of M-ary pulse position modulated (PPM) optical wireless communications (OWC) systems operating in the marine atmosphere, as measured by the bit error rate (BER), is studied here. In our investigation, the scintillation index and the average intensity in marine atmospheric turbulence are used. The variations of BER performance are reported against the marine atmospheric turbulence parameters for various values of the average current gain of the avalanche photodetector (APD), data bit rate of the OWC link, and M value of the M-ary PPM.

Adaptive optics corrections of scintillations of Hermite-Gaussian modes in an oceanic medium.

Adaptive optics correction of the scintillation index is found when Hermite-Gaussian laser beams are used in oceanic turbulence. Adaptive optics filter functions are used to find how the tilt, focus, astigmatism, coma, and total correction will behave under high order mode excitation. Reduction of the oceanic scintillation under various oceanic turbulence and system parameters is examined under different high order modes. Also, the effects of the source size, wavelength, and link length on the total adaptive optics correction of Hermite-Gaussian modes in an oceanic medium are investigated for different modes.

SNR advantage of anisotropy in oceanic optical wireless communications links.

Signal-to-noise ratio (SNR) of an optical wireless communication (OWC) link that operates in anisotropic oceanic turbulence is evaluated. To find the SNR advantage of the anisotropy in the oceanic turbulent medium, SNR in anisotropic oceanic turbulence is normalized by the SNR in isotropic oceanic turbulence. The dB values of this normalized SNR are examined versus the oceanic turbulence parameters of the ratio of temperature to salinity contributions to the refractive index spectrum, the rate of dissipation of mean-squared temperature, the rate of dissipation of kinetic energy per unit mass of fluid at various oceanic anisotropic factors, the avalanche multiplication factors, the radii of receiver aperture, link lengths, and detector responsivity values. It is found that as the oceanic turbulence becomes more anisotropic, at any link parameter, the SNR of the OWC link becomes advantageous over the isotropic counterpart.

Performance of M-ary pulse position modulation for aeronautical uplink communications in an atmospheric turbulent medium.

This paper discusses the bit-error-rate (BER) performance of an aeronautical uplink optical wireless communication system (OWCS) when a Gaussian beam is employed and the M-ary pulse position modulation technique is used in an atmospheric turbulent medium. Weak turbulence conditions and log-normal distribution are utilized. The Gaussian beam is assumed to propagate on a slant path, the transmitter being ground-based, and the airborne receiver is on-axis positioned. Variations of BER are obtained against the variations in the link length, Gaussian beam source size, zenith angle, wind speed, wavelength, modulation order, data bit rate, equivalent load resistor, avalanche photodetector gain, and detector quantum efficiency. It is observed that the performance of the aeronautical uplink OWCS is affected from atmospheric turbulence significantly.

Off-axis average transmittance and beam spread of a partially coherent flat-topped beam in a turbulent underwater medium.

The effects of oceanic turbulence on the off-axis optical transmittance and beam spread are examined when a partially coherent flat-topped beam wave propagates in an underwater medium. To observe the oceanic turbulence effect, the power spectrum of homogeneous and isotropic oceanic water combining the effects of salinity and temperature is used. Employing the extended Huygens-Fresnel integral and Carter's definition for the general beam formulation that is applied to a partially coherent flat-topped beam, the effects of the parameters of power spectrum, the link on the off-axis average transmittance, and beam spread are analyzed. The results obtained with the help of the MATLAB program indicate that if the flatness of the optical beam increases, the average transmittance increases, and the beam spread decreases. Partial coherence is found to be inversely proportional to the average transmittance and directly proportional to beam spread. Increase in the source size is found to increase the average transmittance and to reduce the beam spread. Loss of the kinetic energy of fluid causes less turbulence. The rate of dissipation of kinetic energy per unit mass of fluid is directly proportional to the average transmittance, while it is inversely proportional to the beam spread. The rate of dissipation of the mean square temperature is inversely proportional to the average transmittance and directly proportional to the beam spread. When the temperature-induced optical turbulence is dominant, the average transmittance almost never decreases. However, the salinity-induced optical turbulence sharply reduces the average transmittance and increases the beam spread of the partially coherent flat-topped beam in underwater turbulence. When the off-axis parameter becomes larger, average transmittance decreases.

Effect of strong atmospheric non-Kolmogorov turbulence on the M-ary PSK subcarrier intensity modulated free space optical communications system performance.

Atmospheric turbulence is one of the significant phenomena that degrades the free space optical (FSO) communications system performance, and thus designers need to define the requirements related to turbulence and optimize the system design to ensure optimum performance. The subcarrier intensity modulation (SIM) shows superiority in terms of bandwidth usage over the other modulation techniques. Performance of FSO communication systems exercising M-ary phase-shift-keying (PSK) SIM with the PIN photodiode receiver is evaluated in non-Kolmogorov strong atmospheric turbulence when a Gaussian beam is used as the excitation. Bit-error-rate (BER) of PSK SIM FSO communication systems is examined, and the results are presented versus the non-Kolmogorov atmospheric turbulence and positive-intrinsic-negative (PIN) photodetector parameters such as PIN photodetector responsivity, equivalent load resistor, modulation order, noise factor, bandwidth, propagation distance, and beam source size.

Structure parameter of anisotropic atmospheric turbulence expressed in terms of anisotropic factors and oceanic turbulence parameters.

The structure parameter of the anisotropic atmospheric turbulence is expressed in terms of atmospheric, oceanic anisotropic factors in x and y directions, and the oceanic turbulence parameters, which are the wavelength, the link length, the ratio of temperature to salinity contributions to the refractive index spectrum, the rate of dissipation of mean-squared temperature, and the rate of dissipation of kinetic energy per unit mass of fluid. For the purpose of expressing the structure parameter of the anisotropic atmospheric turbulence in terms of atmospheric, oceanic anisotropic factors and the oceanic turbulence parameters, the spherical wave scintillation indices that are found in weak anisotropic atmospheric turbulence and in weak oceanic turbulence are equated to each other. We aim to utilize the structure parameter expressed in this paper in the evaluations of various physical entities such as the average intensity, scintillation index, and beam spread in anisotropic oceanic turbulence by exploiting the existing solutions for the same physical entities in anisotropic atmospheric turbulence. Use of this structure parameter will help us to obtain the anisotropic oceanic turbulence results easily because such results will be found by just inserting the structure parameter expressed in this paper to the already reported corresponding results of anisotropic atmospheric turbulence.

Bit error rate of pulse position modulated optical wireless communication links in oceanic turbulence.

The upper bound of the average bit error rate (BER) of a pulse position modulated (PPM) optical wireless communication (OWC) link operating in oceanic turbulence is formulated. BER variations against the changes in the ratio of temperature to salinity contributions to the refractive index spectrum, the rate of dissipation of mean-squared temperature, and the rate of dissipation of kinetic energy per unit mass of fluid are found at various data bit rates, average current gains of the avalanche photodiode (APD), and M values of the M-ary PPM. It is found that under any oceanic turbulence parameters, BER performance of the PPM OWC system becomes favorable at smaller data bit rates, M values, and at larger average current gains of APD.

M-ary pulse position modulation performance in non-Kolmogorov turbulent atmosphere.

The performance of atmospheric optical wireless communication systems in terms of the bit error rate (BER) is investigated when a Gaussian laser beam propagating in non-Kolmogorov turbulence is M-ary pulse-position-modulated (PPM). BER variations against the changes in different parameters such as the non-Kolmogorov power law exponent, symbol number, data bit rate, avalanche photodetector gain, equivalent load resistor, detector quantum efficiency, wavelength, turbulence structure constant, and the Gaussian beam source size are analyzed. Making the design of the PPM optical wireless communication system able to operate in a non-Kolmogorov atmosphere will give better BER performance if the parameters are taken into account in line with the trends presented in our results.

Effect of anisotropy on bit error rate for an asymmetrical Gaussian beam in a turbulent ocean.

Effect of anisotropy on the average bit error rate (BER) is investigated when an asymmetrical Gaussian beam is propagated in an anisotropic turbulent ocean. BER is found to decrease in response to an increase in anisotropy levels in the x and y directions. Higher average signal-to-noise ratio, wavelength, and microscale length yield smaller BER values. BER starts to rise with an increase in the asymmetrical beam source size in the x and y directions, source size ratio in the x and y directions, salinity and temperature contribution factor, the dissipation of the mean squared temperature, and the propagation distance. At the fixed source size ratio in the x and y directions of the asymmetrical beam source size, larger source sizes increase BER. An anisotropic turbulent ocean seems to exhibit better BER values as compared with an isotropic turbulent ocean.

M-ary pulse position modulation performance in strong atmospheric turbulence.

The performance of an M-ary pulse position modulated (PPM) optical wireless communication system operating in strong atmospheric turbulence is investigated. Bit error rate (BER) is employed as the measure for the performance. In our overall performance formulation, average received power as measured by a finite-sized avalanche photodiode (APD) detector is used by the help of the extended Huygens-Fresnel principle. For the aperture averaged scintillation evaluations, the asymptotic Rytov theory with the gamma-gamma intensity statistics is utilized. Gamma-gamma statistics together with the large-scale and the small-scale log-intensity variances yield the scintillation index valid both in weak and strong atmospheric turbulence regimes. BER variations versus the plane wave scintillation index are examined at different values of receiver aperture diameters, data bit rates, M values of M-ary PPM, quantum efficiency, and average APD gain.