Rytov Method Research Articles

Scintillation index and outage probability of vortex Gaussian beams for horizontal links in weak atmospheric turbulence

Abstract By using Rytov method, for the Gaussian vortex beam, off-axis scintillation index of is examined in horizontal laser communication links operating in weakly turbulent atmosphere. Performances of laser communication systems, defined by the outage probability in this study, is evaluated by the use of lognormal distributed intensity in finding the scintillation index. Off-axis scintillation index of vortex Gaussian beams is analytically derived and evaluated in horizontal atmospheric link. The scintillation index obtained from the figures drawn versus the source size and propagation length is used to calculate the outage probability. It is found that turbulence affects vortex Gaussian beam less when compared with Gaussian beams that are non-vortex. Our important finding is that the scintillation index reduces when the topological charge increases.

Bit error rate of M-pulse position modulated laser beams for vertical links operating in weak oceanic turbulence

Abstract The on-axis scintillation index of laser beams is investigated by employing the Rytov method in weakly turbulent oceanic medium for up/downlink coupling of laser communication between any underwater vehicles or divers. For vertical link, the formulation of the on-axis scintillation index of laser beams is derived analytically and evaluated for plane, collimated Gaussian and spherical beams in specific medium, including the Atlantic Ocean at mid and low latitudes associating temperature and salinity changes at low latitude, at mid latitude-summer and at mid latitude-winter. Using the scintillation index, bit error rate (BER) performances of M-pulse position modulation (M-PPM) are investigated for these types of laser beam. The variations of the scintillation index against the uplink/downlink propagation distances, source size and zenith angle are examined, and BER variations versus the Kolmogorov microscale and the symbol orders, and results are compared. It is noted that the behavior of the scintillation index that depends on the relative strength of temperature and salinity fluctuations which changes in depth, is different for uplink/downlink, and for each latitude due to its distinct characteristics. Source size that minimizes the scintillation index values is in the range of about 0.1 cm-0.2 cm for all latitudes.

Average capacity and bit error rate of vortex gamma beams propagating in non-Kolmogorov atmospheric turbulence.

In recent years, free-space optical communication based on various vortex beams has gained significant attention due to its high channel capacity and low bit error rate (BER). To investigate a novel type of vortex beam (termed as gamma beam) and its application in free-space optical communication (FSO), a comprehensive analysis of its transmission performance in weak-to-strong non-Kolmogorov turbulence has been conducted for the first time. Based on the extended Rytov method, the propagation behaviors of the gamma beam via weak-to-strong non-Kolmogorov turbulent atmosphere is explored, revealing that gamma beams may outperform LG beams and HyGG beams in certain short links. Numerical calculations are performed to analyze the effects of transmission distance, rms beam radius, receiver aperture, and other parameters on the average capacity and BER. Our results are potentially significant for free-space optical communication based on orbital angular momentum.

Average capacity and ABER for perfect optical vortex system in weakly to strongly turbulent oceans

Based on the modified Rytov method, the reception probability spectrum, average bit error rate (ABER), and average channel capacity of the perfect optical vortex (POV) optical system using quadrantal amplitude modulation (QAM) are derived by introducing the mutual coherence function of POV in weak to strong turbulent seawater. The relationship between eddy topological charge, seawater turbulence characteristic parameters, optical system performance parameters, reception probability spectrum the bit error rate, and the average capacity of the POV optical system is numerically analyzed. The following important results are obtained: in long-distance turbulent seawater, the conclusion that the radius of bright ring POV remains almost constant in short-distance standing water and running water is still valid. 4-QAM is more suitable for signal modulation of the POV system in moderate to strong turbulent seawater. The increase of the vortex ring will lead to the increase of the crosstalk degree between vortex modes and the bit error rate of the POV system. Medium to strong turbulence changes the properties that the transmission ability of POV vortex signal mode in non-turbulent media is independent of the topological charge of the vortex. The transmission performance of vortex signals of the POV optical system can be improved by choosing a smaller half-beamwidth of signal, a higher ring radius to the half-beamwidth ratio of the signal, a lower topological charge of vortex mode, a longer signal wavelength, and higher SNR of the optical system.

Scintillation of the orbital angular momentum of a Bessel Gaussian beam and its application on multi-parameter multiplexing.

The scintillation of the orbital angular momentum (OAM) of a Bessel Gaussian beam was derived based on the Rytov method to characterize the performance of the OAM communication. Moreover, a multi-parameter demultiplexing method was also proposed which could decode the OAM state, the amplitude and two additional beam width information dimensions. The advantages of the OAM states as the communication carrier over the beam intensity were that the minimum scintillation of the fundamental mode was smaller, and its corresponding radius also diverged slower. The coefficient of variation of the decoding amplitude was approximated to the square root of the radial minimum scintillation, and it provided an estimated decoding precision for the input sample selection. This study not only provided theoretical basis for communication link design, but also had a promising application on the large capacity beam multiplexing in free-space laser communication.

Performance of bit error rate of laser beams for LIDAR used in marine atmospheric weak turbulence

The performance of laser beams is investigated for light detection and ranging (LIDAR) systems in marine weak atmospheric turbulence by using the Rytov method. Formulation, on-axis, of the scintillation indices of LIDAR systems, which is obtained for plane, collimated Gaussian, and spherical beams, is appraised for average bit error rate (BER) by utilizing the log-normal distributed intensity. Values, obtained for these beams, are checked against source sizes, target sizes, normalized target size parameters, propagation lengths, and the average signal-to-noise ratio (SNR) for specified parameters. It is observed that the target size that minimizes the scintillation index is independent of the source size. The target size minimizing scintillation index is approximately 10 − 3 c m . Variations in source size and target size values, independently of each other, affect the scintillation index and the performance of marine LIDAR system links. The contribution of the outer scale turbulence to the deterioration is more evident than the inner scale turbulence.

Laser beam scintillations of LIDAR operating in weak oceanic turbulence

The formulation of light detection and ranging (LIDAR) systems is derived and examined for the scintillation index, evaluated on-axis, of laser beams in horizontal links in the ocean with weak turbulence by utilizing the Rytov method. These scintillation indices, obtained for the Gaussian beam which is collimated, the limits of plane and spherical waves, are depicted versus the source size, target size, and parameter of the normalized reflector size. It is found that the source size, target size, and normalized reflector size parameter, lessening the scintillation index evaluated on-axis, are approximately 0.44 cm, 56 × 10 − 4 c m , and 2.2, respectively. Additionally, by using these values that minimize the scintillation index, the variation of the scintillations is shown against the propagation distance, radius of reflector, temperature and salinity fluctuation effects, mean squared temperature, and turbulent kinetic energy dissipation rate per unit mass of fluid at various selected source size and radius of reflector values.

General statistical model of irradiance fluctuations in free space optics.

A model for the received irradiance statistical distribution for turbulence induced fading channels is derived. The derivation is based on expanding the extended Rytov method by associating a doubly stochastic process to model large scale scintillation. In particular, the large scale induced fluctuations are modeled as the product of arbitrary numbers of gamma and inverse gamma random variables, while the small scale induced irradiance fluctuations are modeled as a single gamma random variable. Closed form expressions for the probability density function (pdf), cumulative distributions, and moment generating function are given. Also, a procedure is proposed for associating the pdf parameters with the large and small scale induced variances. The proposed model is seen to contain many previously published models, such as gamma-gamma (GG) and Fischer-Snedicor F, as special cases. Moreover, two new fading distributions are introduced and analyzed, and plots for the proposed pdfs are generated and compared with often used models and measurements, thus showing the accuracies of the derived models.

Scintillation of Laser Beams in Weak Atmospheric Turbulence for Aerial Vehicle in the Use of LIDAR

Formulation of on-axis scintillation of laser beams is found in weak atmospheric turbulence for aerial vehicle in the use of light detection and ranging (LIDAR) systems by employing the Rytov method. The formulation derived for collimated Gaussian, plane and spherical beams is evaluated in vertical link involving up/down link. In this medium, the behavior of these beams in terms of deterioration is examined. In this context, the on-axis scintillation index values are plotted versus normalized target size parameter, target size, source size, propagation distance and zenith angle, and the results are obtained for LIDAR systems operating for aerial vehicle in vertical atmospheric link by using ground/space transceiver. The degradation is greater in operating with ground transceiver than in operating with space transceiver. Additionally, while the on-axis scintillation index is minimized in the smaller target size in use of ground transceiver than in use of space transceiver, that is, it can also be minimized in the larger target size in use of space transceiver. The values of source size and the normalized target size parameter minimizing the obtained scintillation index, are 1.2 cm, 10, and 6 cm and 5 for ground transceiver and space transceiver, respectively.

Irradiance probability density function for turbulence induced fading in free space optics.

A model for the irradiance probability density function for turbulence induced fading in free space optical communications is derived. The derivations are based on expanding on the extended Rytov method by associating a doubly stochastic process to model large scale scintillation. In particular, the small scale induced irradiance fluctuations are modeled by a single gamma distribution, while the large scale induced fluctuations are modeled as a doubly stochastic process of gamma and inverted gamma distributions, thus better approximating the lognormal distribution. The resultant distribution's probability density and cumulative density functions are both given in closed forms. Moreover, the resultant model parameters are given based on strong scintillation theory. Through comparison with previously published results and experimental data, including lognormal and gamma-gamma distributions, it is concluded that the proposed model agrees well with measurements for weak and strong scintillation conditions in cases of both aperture averaging and a point like receiver. Therefore, the proposed model can be used for the performance analysis of optical wireless systems.

Effects of turbulent atmosphere on the propagation properties of vortex Hermite-cosine-hyperbolic-Gaussian beams

The propagation properties of a vortex Hermite-cosh-Gaussian beam (vHChGB) in atmospheric turbulence are investigated based on the extended Huygens–Fresnel diffraction integral and Rytov method. The analytical formula for the average intensity of a vHChGB propagating in turbulent atmosphere is derived in detail. The influence of the turbulence strength on the intensity distribution under the change of beam parameters conditions is illustrated numerically and discussed. Results show that the profile of the initial vHChGB remains unchanged within small propagation distance range, and at certain propagation distance a central peak intensity appears, and finally the beam evolves into Gaussian profile–like in far-field. The rising speed of the central peak intensity is faster when the turbulence strength is larger or the beam parameters such as the beam order, the vortex charge and the Gaussian waist width are smaller. With a small decentered parameter b, the beam profile changes faster as the wavelength is larger, whereas the reverse behavior occurs when b is large. The obtained results may be useful for the practical applications of vHChGB in optical communications and remote sensing.

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.

Propagation of vortex cosine-hyperbolic-Gaussian beams in atmospheric turbulence

In this paper, the propagation properties of a vortex cosh-Gaussian beam (vChGB) in turbulent atmosphere are investigated. Based on the extended Huygens–Fresnel diffraction integral and the Rytov method, the analytical expression for the average intensity of the vChGB propagating in the atmospheric turbulence is derived. The effects of the turbulent strength and the beam parameters on the intensity distribution and the beam spreading are illustrated numerically and analyzed in detail. It is shown that upon propagating, the incident vChGB keeps its initial hollow dark profile within a certain propagation distance, then the field loses gradually its central hole-intensity and transformed into a Gaussian-like beam for large propagation distance. The rising speed of the central peak is demonstrated to be faster when the constant strength turbulence or the wavelength are larger and the Gaussian width is smaller. The obtained results can be beneficial for applications in optical communications and remote sensing.

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.

Focused and collimated Gaussian laser beam scintillation in weakly turbulent marine atmospheric medium

The scintillation index on the axis for Gaussian beams focused and collimated in weak marine turbulence is formulated via the usage of Rytov method. The average bit error rate <BER> is evaluated using this formulation. The scintillation index and <BER> versus propagation distance and source size are determined by using the log-normal distributed. Intensity for the collimated and focused. Gaussian beams, which are exhibited for wavelength, source size, focal length, and <SNR>. The focused beams are revealing more advantageous than collimated beams in an atmospheric marine environment. The findings of this study are significant for optical communication system performance in this layer.

Multimode laser beam scintillations in weak atmospheric turbulence for vertical link laser communications

Scintillation index of multimode laser beams used for communication systems in vertical paths of weak atmospheric turbulent medium are examined by employing the Rytov method. On-axis scintillation index is examined versus the source size, propagation distance and zenith angle for vertical link including uplink and downlink. At the selected values of source sizes and propagation distances, scintillation responses of multimode laser beams are evaluated. In general, it is found for both uplink and downlink that the laser beam with multimode content has larger scintillation noise as compared to a Gaussian laser beam. However, for the downlink at L=700 km, at the chosen parameters, the multimode beam possessing larger mode content, is found to attain slightly smaller scintillations.

Polymer composites based on polyvinyl chloride nanofibers and polypropylene films for terahertz photonics

The optical properties of the polymer composites consisting of polyvinyl chloride nanofibers and polypropylene films in the frequency range of 0.2–1.0 THz were studied, and the mechanical properties of polyvinyl chloride nanofibers and the structure porosity were investigated. An iterative mathematical model based on effective medium theory was used to describe the effective refractive index and absorption coefficient of the polymer composites. The permittivity tensors of the composites were calculated using the Rytov method. We found that the refractive indices of the composites increased with the increase of polypropylene contents, while absorption coefficients remained the same. The polarization-dependencies of THz optical properties of the composites were relatively low. The proposed composites have the potential to be used as materials for terahertz optical components.

Intensity characteristics of double-half inverse Gaussian hollow beams through turbulent atmosphere

The propagation characteristics of a double-half inverse Gaussian hollow beam (DHIGHB) through atmospheric turbulence are investigated theoretically. The on-axis average intensity of the beam passing through a turbulent atmosphere is derived in closed-form under the framework of the Huygens–Fresnel diffraction integral and the Rytov method. Numerical examples have been performed to illustrate the dependence of the on-axis intensity on the index structure constant of the atmospheric turbulence and the parameters of the incident DHIGHB. It is shown that upon propagating the DHIGHB will have a bright central spot, and the on-axis intensity will reach a threshold value at certain propagation distance zm, and after that the beam will retrieve its original dark hollow characteristics. This conversion is quicker for large constant strength turbulence, large wavelength and small initial beam waist size.

Influence of eddy diffusivity ratio on Gaussian beam under weak to strong oceanic turbulence

ABSTRACTThe oceanic turbulence refraction power spectrum model with a function of the eddy diffusivity ratio is adopted. By using the Rytov method, the scintillation index (SI) is derived using the aperture averaging technique for Gaussian beam under weak to strong oceanic turbulence. Variations of the SI in weak to strong oceanic turbulence are evaluated versus link length and the oceanic turbulence parameters such as the ratio of temperature to salinity contributions to the refractive index spectrum, the rate dissipation of the mean squared temperature, and the rate of dissipation of kinetic energy per unit mass of fluid. Considering the eddy diffusivity ratio of salinity to temperature, the effects of the ratio of temperature to salinity contributions to the refractive index spectrum on the performance of underwater wireless optical communication (UWOC) systems in weak to strong turbulence are analysed.

Hermite Gaussian beam scintillations in weak atmospheric turbulence for aerial vehicle laser communications

Scintillation index of Hermite Gaussian beams used for air vehicle communication systems in vertical paths of weak atmospheric turbulent medium are investigated by employing the modified Rytov method. By evaluating the on-axis scintillation index, variations of the scintillation indices of these beams are examined against the changes in the Gaussian beam size of the Hermite Gaussian beam mode, propagation distances and the zenith angles at the realistic propagation distances involved in uplink and downlink configurations. In the atmospheric environment, for uplink, the Hermite Gaussian beam modes have no advantage over the Gaussian beams at short propagation distances like L=20km,as well as at long propagation distances like L=700km. However, for downlink, although Hermite Gaussian beam modes are disadvantageous over the Gaussian beams at short propagation distances like L=20km, they are found advantageous over the Gaussian beams at long propagation distances like L=700km. The results of this study may encourage to use Hermite Gaussian beams, especially in the air vehicle laser communication links, and can be used in the design of an optical wireless communication link utilizing the vertical atmospheric medium.