Applications of Lasers for Sensing and Free Space Communications: introduction to the feature issue.

This feature issue highlights the latest developments in laser-based sensing and free space communications. In total, 15 papers were published in Applied Optics, including an invited review paper that celebrates the legacy of David L. Fried.

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.

Equivalent refractive-index structure constant of non-Kolmogorov turbulence: comment.

The paper by Y. Li, W. Zhu, X. Wu, and R. Rao entitled "Equivalent refractive-index structure constant of non-Kolmogorov turbulence," Opt. Express23(18), 23004 (2015).10.1364/OE.23.023004 relates the non-Kolmogorov turbulence structure constant to the classical structure constant for Kolmogorov turbulence by imposing equality of their respective structure functions at large separation distances, higher than the outer scale. As opposed to previous attempts to relate the two structure constants, the approach of Li et al. is anchored on a measurable meteorological parameter, the outer scale. The error lies in the fact that the authors have used a default Kolmogorov structure function with an infinite outer scale. A subsequent assumption of a finite outer scale is not compatible with the initial assumption. In this paper we show the correct procedure to obtain the relationship between the non-Kolmogorov and Kolmogorov structure constants which is based on an explicitly finite outer scale used throughout all calculations.

Influence of bandwidth error on the performance of adaptive optics systems for uncooperative beacons.

We discuss the capability of adaptive optics to increase the performance of laser systems operating in atmospheric turbulence. Our approach is based on the Zernike filter functions, Taylor's frozen-flow hypothesis, and bandwidth limitations of a realistic servo control system. System performance is analyzed in terms of the Strehl ratio on target. Our results for plane-wave geometry indicate that adaptive optics can be effective even when engaging fast moving targets and that moderate closed-loop bandwidths of ∼100Hz would suffice for most analyzed scenarios. Applications of interest are beam delivery systems and free-space optical communications.

Improving system performance by using adaptive optics and aperture averaging for laser communications in oceanic turbulence.

We theoretically investigate the effectiveness of adaptive optics correction for Gaussian beams affected by oceanic turbulence. Action of an idealized adaptive optics system is modeled as a perfect removal of a certain number of Zernike modes from the aberrated wavefront. We focused on direct detection systems and we used the aperture-averaged scintillation as the main metric to evaluate optical system performances. We found that, similar to laser beam propagation in atmospheric turbulence, adaptive optics is very effective in improving the performance of laser communication links if an optimum aperture size is used. For the specific cases we analyzed in this study, scintillation was reduced by a factor of ∼7 when 15 modes were removed and when the aperture size of the transceiver was large enough to capture 4-5 speckles of the oceanic turbulence-affected beam.

Calculating structure function constant from measured Cn 2 in non-Kolmogorov and anisotropic turbulence including inner scale effects.

Optical scintillometers used to characterize turbulence are based on assumptions of isotropic, Kolmogorov turbulence following a κ-11/3 spectral power law. However, experimental data suggest that the turbulence may at times be anisotropic and non-Kolmogorov. In this work, consideration is given to converting from the structure function constant, Cn2, based on isotropic, Kolmogorov statistics to its generalized anisotropic, non-Kolmogorov form, C˜n2, for point receiver and large-aperture receiver scintillometers. It is found that C˜n2 is dependent not only on power law and anisotropy parameters but that it is also a function of inner scale. The large-aperture scintillometer is found to be less sensitive to power law and inner scale than the point-aperture receiver. The optical parameters of two-fielded scintillometers are modeled as practical examples of these behaviors.

Measuring anisotropy ellipse of atmospheric turbulence by intensity correlations of laser light.

An experimental study has been performed of a laser beam propagating horizontally through the near-ground atmosphere above a grassy field at the University of Miami (UM) Coral Gables campus. The average intensity, scintillation index, and intensity correlation function are measured in the receiver plane for three channels with different turbulent conditions and at three different heights above the ground. Our results reveal that along short links (210 m) only the intensity correlation function captures the anisotropic information of turbulence, corresponding to the refractive index anisotropy ellipse of atmospheric fluctuations. In addition, we report an interesting phenomenon relating to turbulence eddy orientation near the ground. We confirmed that the experimental results are in agreement with the numerical simulations based on the multiple phase-screen method. Our findings provide an efficient method of determining the anisotropic parameters of atmospheric turbulence.

Gaussian beam propagation in anisotropic turbulence along horizontal links: theory, simulation, and laboratory implementation.

Experimental and theoretical work has shown that atmospheric turbulence can exhibit "non-Kolmogorov" behavior including anisotropy and modifications of the classically accepted spatial power spectral slope, -11/3. In typical horizontal scenarios, atmospheric anisotropy implies that the variations in the refractive index are more spatially correlated in both horizontal directions than in the vertical. In this work, we extend Gaussian beam theory for propagation through Kolmogorov turbulence to the case of anisotropic turbulence along the horizontal direction. We also study the effects of different spatial power spectral slopes on the beam propagation. A description is developed for the average beam intensity profile, and the results for a range of scenarios are demonstrated for the first time with a wave optics simulation and a spatial light modulator-based laboratory benchtop counterpart. The theoretical, simulation, and benchtop intensity profiles show good agreement and illustrate that an elliptically shaped beam profile can develop upon propagation. For stronger turbulent fluctuation regimes and larger anisotropies, the theory predicts a slightly more elliptical form of the beam than is generated by the simulation or benchtop setup. The theory also predicts that without an outer scale limit, the beam width becomes unbounded as the power spectral slope index α approaches a maximum value of 4. This behavior is not seen in the simulation or benchtop results because the numerical phase screens used for these studies do not model the unbounded wavefront tilt component implied in the analytic theory.

Two spatial light modulator system for laboratory simulation of random beam propagation in random media.

An optical system consisting of a laser source and two independent consecutive phase-only spatial light modulators (SLMs) is shown to accurately simulate a generated random beam (first SLM) after interaction with a stationary random medium (second SLM). To illustrate the range of possibilities, a recently introduced class of random optical frames is examined on propagation in free space and several weak turbulent channels with Kolmogorov and non-Kolmogorov statistics.

General scale-dependent anisotropic turbulence and its impact on free space optical communication system performance.

We generalize a recently introduced model for nonclassic turbulent spatial power spectrum involving anisotropy along two mutually orthogonal axes transverse to the direction of beam propagation by including two scale-dependent weighting factors for these directions. Such a turbulent model may be pertinent to atmospheric fluctuations in the refractive index in stratified regions well above the boundary layer and employed for air-air communication channels. When restricting ourselves to an unpolarized, coherent Gaussian beam and a weak turbulence regime, we examine the effects of such a turbulence type on the OOK FSO link performance by including the results on scintillation flux, probability of fade, SNR, and BERs.

SLM-based laboratory simulations of Kolmogorov and non-Kolmogorov anisotropic turbulence.

In this paper, we present a laboratory setup to simulate anisotropic, non-Kolmogorov turbulence. A sequence of numerical phase screens that incorporate the turbulence characteristics were applied to a spatial light modulator placed in the path of a laser beam with a Gaussian intensity profile and the resulting far-field intensity patterns were recorded by a CCD camera. The values of scintillation at the position of the maximum intensity were extracted from the images and compared with theoretical values. Our experimental results show a trend that is in agreement with known theoretical expressions; however, the turbulence rescaling due to anisotropy shows some discrepancy with theory and requires more investigation.

Introducing the concept of anisotropy at different scales for modeling optical turbulence.

In this paper, the concept of anisotropy at different atmospheric turbulence scales is introduced. A power spectrum and its associated structure function with inner and outer scale effects and anisotropy are also shown. The power spectrum includes an effective anisotropic parameter ζ(eff) to describe anisotropy, which is useful for modeling optical turbulence when a non-Kolmogorov power law and anisotropy along the direction of propagation are present.

Propagation of electromagnetic stochastic beams in anisotropic turbulence.

The effects of anisotropic, non-Kolmogorov turbulence on propagating stochastic electromagnetic beam-like fields are discussed for the first time. The atmosphere of interest can be found above the boundary layer, at high (more than 2 km above the ground) altitudes where the energy distribution among the turbulent eddies might not satisfy the classic assumption represented by the famous 11/3 Kolmogorov's power law, and the anisotropy in the direction orthogonal to the Earth surface is possibly present. Our analysis focuses on the classic electromagnetic Gaussian Schell-model beams but can either be readily reduced to scalar and/or coherent beams or generalized to other beam classes. In particular, we explore the effects of the anisotropic parameter on the spectral density, the spectral degree of coherence and on the spectral degree of polarization of the beam.

Light propagation through anisotropic turbulence.

A wealth of experimental data has shown that atmospheric turbulence can be anisotropic; in this case, a Kolmogorov spectrum does not describe well the atmospheric turbulence statistics. In this paper, we show a quantitative analysis of anisotropic turbulence by using a non-Kolmogorov power spectrum with an anisotropic coefficient. The spectrum we use does not include the inner and outer scales, it is valid only inside the inertial subrange, and it has a power-law slope that can be different from a Kolmogorov one. Using this power spectrum, in the weak turbulence condition, we analyze the impact of the power-law variations α on the long-term beam spread and scintillation index for several anisotropic coefficient values ς. We consider only horizontal propagation across the turbulence cells, assuming circular symmetry is maintained on the orthogonal plane to the propagation direction. We conclude that the anisotropic coefficient influences both the long-term beam spread and the scintillation index by the factor ς(2-α).