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.

Propagation through and characterization of atmospheric and oceanic phenomena: introduction to the joint feature issue in Applied Optics and Journal of the Optical Society of America A.

This joint feature issue in Applied Optics and JOSA A collects articles focused on the topic of propagation through and characterization of atmospheric oceanic phenomena. The papers cover a broad range of topics, many of which were addressed at the 2023 Propagation Through and Characterization of Atmospheric Oceanic Phenomena (pcAOP) Topical Meeting at the Optica Imaging Congress in Boston, Massachusetts, 14-17 August 2023. These papers are supplemented by numerous examples of the current state of research in the field. This is the first pcAOP feature issue, with the intention to produce an issue on this topic every two years.

Propagation through and characterization of atmospheric and oceanic phenomena: introduction to the joint feature issue in Applied Optics and Journal of the Optical Society of America A.

This joint feature issue in Applied Optics and JOSA A collects articles focused on the topic of propagation through and characterization of atmospheric oceanic phenomena. The papers cover a broad range of topics, many of which were addressed at the 2023 Propagation Through and Characterization of Atmospheric Oceanic Phenomena (pcAOP) Topical Meeting at the Optica Imaging Congress in Boston, Massachusetts, 14-17 August 2023. These papers are supplemented by numerous examples of the current state of research in the field. This is the first pcAOP feature issue, with the intention to produce an issue on this topic every two years.

Monte-Carlo based vertical underwater optical communication performance analysis with chlorophyll depth profiles.

Although underwater wireless optical communication (UWOC) has the advantages of high speed, low latency, and high confidentiality, the transmission of light in water will be affected by the absorption and scattering of particles, which will lead to the aggravation of channel path loss as well as channel pulse spreading, finally causing false codes. Therefore, how to analyze the channel impulse response (CIR) effectively is a key task in channel modeling. In this paper, we consider a two-way underwater vertical line-of-sight (LOS) communication system model, based on the inherent optical property (IOP) model of chlorophyll, using the Kopelevich phase function containing water depth information, the CIR curves under different water types and transceiver configurations are plotted using the Monte-Carlo Simulation (MCS). The obtained simulation results are fitted with the double gamma function (DGF) model and the Gaussian model, respectively. The Gaussian model exhibits better properties than the DGF model in each water condition. Based on the closed-form expression of the CIR obtained from the Gaussian model, we solve for the bit error rate (BER) and 3-dB bandwidth of the system under different settings. The conclusions obtained can be used for the design and optimization of underwater vertical channels.

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.

Aperture-averaged scintillation for a weak underwater turbulence-affected Gaussian beam using the OTOPS model.

The calculation of optical system performance for laser beam propagation in optical turbulence, such as bit error rate (BER), signal-to-noise ratio, and probability of fade, requires the knowledge of scintillation. In this paper, we show the analytical expressions of the aperture-averaged scintillation using a new recently introduced power spectrum of the refractive index fluctuations for underwater turbulence, the oceanic turbulence optical power spectrum (OTOPS). In addition, we use this main result to investigate the impact of weak oceanic turbulence on free-space optical system performance for a propagating Gaussian beam wave. Similar to the atmospheric turbulence case, results show that aperture averaging can reduce the mean BER and the probability of fade several orders of magnitude if the receiver aperture is chosen with a diameter larger than the Fresnel zone, L/k. Being valid for weak turbulence regime in any natural waters, results present the variations of irradiance fluctuations and the performance of underwater optical wireless communication systems depending on the practical values of average temperature and average salinity concentration that can be encountered in any world's waters.

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.

Absorption, scattering, and optical turbulence in natural waters.

The Beer-Lambert-Bouguer law characterizes attenuation of an optical plane wave resolved in terms of absorption and scattering of a medium it passes through. However, the optical turbulence present in a medium may also cause severe local attenuation in beam-like light fields. This study aims to incorporate the effects of absorption and scattering with that of optical turbulence in Earth's natural waters. To do so, expression for the turbulence induced local attenuation coefficient is developed first for the on-axis position of the lowest-order Gaussian beam, being dependent on the source's wavelength, width, and propagation distance. We present a comparison among turbulence, absorption, and scattering effects for different Jerlov water types. Our results show that underwater turbulence can cause attenuation quantitatively comparable to that of absorption. This study enables a direct comparison of absorption, scattering, and turbulence effects and will benefit the diagnostics of imaging, sensing, and communication systems operating underwater.

Temporal statistics of irradiance fluctuations in an underwater turbulent medium.

Expressions for the temporal covariance function and temporal frequency spectrum for a plane wave propagation in an underwater turbulent medium are developed analytically. Temporal correlation in moving natural water is presented, which is shown to be dependent upon the moving velocity, the delay between two instants of time, propagation distance, average temperature, and average salinity concentration. Coherence time and zero crossing time also are calculated. The results show that the velocity of the moving natural water has a significant impact on the temporal correlation of irradiance fluctuations. Additionally, the propagation distance, average temperature, average salinity concentration, and temperature-salinity gradient ratio also impact the temporal correlation up to a certain level.

Structure function, coherence length, and angle-of-arrival variance for Gaussian beam propagation in turbulent waters.

Wave structure function, coherence length, and angle-of-arrival variance are derived analytically for a Gaussian beam propagating in an underwater turbulent medium. The recently introduced oceanic turbulence optical power spectrum model [J. Opt. Soc. Am. A37, 1614 (2020)JOAOD60740-323210.1364/JOSAA.399150] is used, and results are obtained for the case of large separations. The effect of temperature, salinity, rates of dissipation of mean-squared temperature and energy, temperature-salinity gradient ratio, wavelength, and aperture diameter, is presented. Further, a Gaussian beam is compared with the plane and spherical waves in terms of their effect on wave structure function, coherence length, and angle-of-arrival fluctuations. The presented results can be beneficial to set the parameters of imaging and communication systems using a Gaussian beam in an underwater turbulent medium and can be used for the optimization of the design of these systems.

Electromagnetic phase coherence gratings for atmospheric applications.

We propose using electromagnetic phase coherence gratings (EMPCGs) for fine spatial segregation in polarimetric components of stationary beams on their propagation in atmospheric turbulence. Unlike for other beams, e.g., non-uniformly correlated EM beams, the off-axis shifts occurring in polarimetric components of EMPCGs are shown to be invariant with respect to the local turbulence strength. This effect may lead to implementation of novel techniques for direct energy, imaging, and wireless optical communication systems operating in the presence of turbulent air.

Underwater imaging in optical turbulence: average temperature and salinity effects.

Classic imaging systems may experience deleterious effects of optical turbulence, leading to their quality degradation induced by image jitter and blur. Using a recently introduced model for the refractive index power spectrum of natural water turbulence accounting for average temperature in the range of 0°-30°C and average salinity concentration in NaCl in the range of 0-40 ppt, we derive expressions for turbulence-induced modulation transfer functions. Our analysis indicates that the imaging systems are very sensitive not only to the variance of fluctuations in these parameters but also to their average values. Our results are essential for underwater optical engineering, providing regional and seasonal variations in optical turbulence.

Adaptive optics correction in natural turbulent waters.

The recently introduced power spectrum of the refractive index fluctuations of the natural oceanic water turbulence is applied to an underwater communication system in the presence of adaptive optics corrections. The effects of the average temperature (0-30°C), the average salinity (0-40 ppt), the temperature-salinity gradient ratio (0-400°C/ppt), and the wavelength of the source (400-700 nm) on such a system are considered for the first time, to the best of our knowledge. It is revealed that even in the presence of adaptive optics the communication system's operation is severely affected by the regional and seasonal averages and fluctuations in the water's refractive index.

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.

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.

On channel capacity of FSO communication systems in anisotropic non-Kolmogorov strong turbulent atmosphere.

Average channel capacity of free space optical (FSO) communication systems using a Gaussian beam with the intensity modulation and direct detection technique is investigated in anisotropic non-Kolmogorov strong turbulent atmosphere. The channel model is selected as gamma-gamma distribution, which is valid for strong turbulence. Obtained results show that anisotropy in both the horizontal and vertical affects the average channel capacity of an FSO communication system positively. Average channel capacity increases with the increase of photodetector quantum efficiency, wavelength, Gaussian beam source size, inner scale length, and non-Kolmogorov power law exponent. An increase of link length, turbulence structure constant, and noise variance causes a decrease in average channel capacity. The average channel capacity falls very little with the increase of outer scale length.

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.

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.