Beam Wander Research Articles

Light field camera study of near-ground turbulence anisotropy and observation of small outer-scales.

Understanding turbulence effects on laser beam propagation is critical to the emerging design, study, and test of many long-range free space optical (FSO) communication and directed energy systems. Conventional studies make the prevalent assumption of isotropic turbulence, while more recent results suggest anisotropic turbulence for atmospheric channels within a few meters elevation above the ground. As countless FSO systems have been and continue to be deployed in such channels, analysis of anisotropic modelings has become one of the fastest growing areas in FSO research. This in turn motivates new tools that can distinguish anisotropic characteristics to improve both modeling accuracy and physical interpretations. Wavefront sensors such as Shack-Hartmann sensors, interferometers, and plenoptic sensors have been devised and used in experiments; however, they all require rigid alignments that lack resilience against temperature gradient buildup and beam wander. We find that by using a light field camera (LFC) that extracts perturbation of individual light rays, the wave structure function of turbulence can be retrieved with high reliability. Furthermore, we find through experiments that the outer scales of near-ground turbulence tend to be a magnitude smaller than conventional theoretical assumptions, agreeing with new findings by others but being absent in current theoretical modelings. As a result, we believe that the LFC is an ideal candidate in the frontier of turbulence research; it is both commercially available and easy to adapt to turbulence experiments.

Beam wander in wireless optical communications between misaligned transceivers in oceanic turbulence.

In this paper, we investigate the beam wander in oceanic turbulence taking into account the misaligned displacements caused by slight changes in the position and attitude of the underwater platform. First, we derive the longitudinal distance and radial distance or the misaligned displacements according to the relationship between the misaligned transceivers. Then, we formulate the beam wander variance of a Gaussian beam propagating through oceanic turbulence. Finally, we obtain the beam wander variance in underwater wireless optical communications between the misaligned transceivers according to longitudinal distance. In addition, we express the mean pointing error displacements.

Continuous-Variable Quantum Key Distribution Over Air Quantum Channel With Phase Shift

Continuous-variable quantum key distribution (CV-QKD) over air quantum channel enables to provide unconditional information security, which is the one of most promising techniques for information wireless transfer. Since the air channel is of fluctuation in nature due to the presence of air turbulence, the random variations have to be taken into account when the security of CV-QKD is analyzed. We study the secret key rate of CV-QKD over the air quantum channel in this paper. The fluctuation of air channel is characterized by beam wandering and phase distortion under weak air turbulence conditions. The impact of fluctuation on the CV quantum signals is reflected by transmittance perturbation and phase shift. Our numerical results show that the secret key rate may keep relatively high level as the air quantum link increases at the outset. However, when the air link distance further increases beyond certain range, the secret key rate decreases strikingly since the both transmittance perturbation and the phase shift simultaneously deteriorate the performance of CV-QKD. Nevertheless, operating the CV-QKD under weak air turbulence conditions is available.

Effect of Airy Gaussian vortex beam array on reducing intermode crosstalk induced by atmospheric turbulence.

Vortex beam carrying angular momentum (OAM) will be disturbed by the random fluctuation of the refraction index of turbulent atmosphere, resulting in intermodal crosstalk among the different OAM modes. Recent advances have demonstrated that the employment of the abruptly autofocusing vortex beams can potentially mitigate the crosstalk effect. In this paper, a new type of abruptly autofocusing vortex beams, called Airy Gaussian vortex beam array (AGVBA) is proposed. By means of multi-plane wave optics simulation, the degradation of signal mode for AGVBA propagating through isotropic atmospheric turbulence is studied. In a comparison with the conventional abruptly autofocusing vortex beams, such as the ring Airy vortex beam (RAVB) and the Airy vortex beam array (AVBA), it is shown that AGVBA achieves more centralized intensity as well as a larger spot at the focal plane, thus can effectively balance the beam spreading and beam wander effect, resulting in mitigation of intermodal crosstalk.

Research on the system performance of Gaussian minimum-shift keying with M-distribution in satellite-to-ground laser communication

In this paper, a Gaussian minimum shift keying (GMSK) modulation based on M-distribution is proposed for uplink satellite-to-ground laser communication systems. Considering the noise caused jointly by intensity scintillation, beam wander and angle of arrival (AOA) fluctuations in the satellite-to-ground laser uplink communication, the closed-form expression of bit error rate (BER) of GMSK modulation system is derived. The system performance under weak, medium and strong turbulence is studied. The relationship between signal-to-noise ratio and BER is analyzed using simulations, and compared with the differential phase shift keying modulation currently used in the satellite-to-ground laser communication systems. Furthermore, the effects of zenith angle, receiver aperture, transmitter beam radius and divergence angle on the system performance are studied. This research work provides guidance for system performance analysis of uplink satellite-to-ground laser communication.

Propagation properties of partially coherent crescent-like beams under maritime environment.

Based on the extended Huygens-Fresnel principle, the analytical expressions for the intensity distribution, effective radius of curvature, beam wander, Strehl ratio, and the power in the bucket of a partially coherent crescent-like (PCCL) beam under the maritime environment are derived. The propagation properties of the PCCL beams through the maritime environment are investigated in detail. Numerical results indicate that, for the maritime environment, the propagation properties and beam quality of a PCCL beam are closely related to its initial beam parameters and the turbulence parameters. Comparative analyses are performed for the new models under the marine turbulence and the terrestrial turbulence. It turns out that the marine turbulence influences the beam width and the beam wander more than the terrestrial turbulence does. Also, the beam quality of the PCCL beams in marine turbulence can be improved by choosing a large beam width, high coherence length, or short wavelength. The PCCL beams have a range-dependent tilt, which can be useful for some practical applications, such as traveling around an obstacle. The results are of significance for over-the-sea communication systems.

Experimental study of reducing beam wander by modulating the coherence structure of structured light beams.

We study the beam wander of a class of structured light beams, Hermite-Gaussian correlated Schell-model (HGCSM) beams, in theory and in experiment. It is found that modulating the coherence structure of a structured light beam can reduce the turbulence-induced beam wander, i.e., a HGCSM beam with larger mode orders or lower coherence experiences smaller beam wander. Our experimental results are consistent with theoretical predictions, and the insights here suggest that HGCSM beams could be useful in free-space optical communications.

Approximations wander model for the Lommel Gaussian-Schell beam through unstable stratification and weak ocean-turbulence

By analyzing the construction features of a Lommel Gaussian-Schell beam and the beam wander for Gaussian beams, we derive the closed-from approximations expression for the wander of Lommel Gaussian-Schell beam through unstable stratification and weak ocean-turbulence. Turbulence conditions with a smaller outer- and inner-scale of turbulence usually cause smaller beam wander. There is a extremum value βex of the beam paraxial coefficient corresponding to the maximum beam wander for given parameters of turbulence and beam. We can utilize larger beam waist, longer wavelength, higher quantum number of orbital angular momentum and larger asymmetry factor, meanwhile, avoid extremum value βex to reduce the beam wander. The influence of salinity fluctuations of turbulent ocean on beam wander is greater than temperature fluctuations. Under the assumption of unit diffusivity ratio, the beam wander is either underestimated or overestimated.

Performance improvement of free-space continuous-variable quantum key distribution with an adaptive optics unit

We propose a method to enhance the performance of the free-space continuous-variable quantum key distribution (FSCVQKD) by utilizing an adaptive optics (AO) unit at the receiver’s side to suppress wavefront distortions caused by high-order wavefront aberrations for fault-tolerant detection. Benefiting from the AO unit, the high-order wavefront aberrations can be corrected and thus effectively improve the mixing efficiency of homodyne detection, which enhances the performance of FSCVQKD. Considering the fact that the closed-loop control bandwidth of AO unit and the atmospheric coherence length have an important effect in performance improvement for FSCVQKD, in this paper, we analyze the performance of our protocol with AO unit under different closed-loop control bandwidths and atmospheric coherence lengths, respectively. The analysis is performed by considering the three specific scenarios of turbulence which are frequent challenges in FSCVQKD protocol, namely beam wandering, randomly blocked and log-normal distribution. In addition, we also study the impact of AO-added noise on our protocol. Simulation results show that all in the beam wandering case, the randomly blocked case and the log-normal distribution, the use of AO unit can enhance the performance of FSCVQKD protocol by adjusting the closed-loop control bandwidth of AO unit and the atmospheric coherence length in appropriate ranges with the case of fixed Greenwood frequency in the presence of AO-added noise.

Eavesdropper's ability to attack a free-space quantum-key-distribution receiver in atmospheric turbulence

The ability of an eavesdropper (Eve) to perform an intercept-resend attack on a free-space quantum key distribution (QKD) receiver by precisely controlling the incidence angle of an attack laser has been previously demonstrated. However, such an attack could be ineffective in the presence of atmospheric turbulence due to beam wander and spatial mode aberrations induced by the air's varying index of refraction. We experimentally investigate the impact turbulence has on Eve's attack on a free-space polarization-encoding QKD receiver by emulating atmospheric turbulence with a spatial light modulator. Our results identify how well Eve would need to compensate for turbulence to perform a successful attack by either reducing her distance to the receiver, or using beam wavefront correction via adaptive optics. Furthermore, we use an entanglement-breaking scheme to find a theoretical limit on the turbulence strength that hinders Eve's attack.

Identifying orbital angular momentum modes in turbulence with high accuracy via machine learning

The orbital angular momentum (OAM) of a Laguerre–Gaussian beam (LGB) is classified using the support vector machine (SVM) model. The scintillation index, beam width, and beam wander of the Gaussian beam and the LGB at the receiving site are taken as feature vectors, and the OAM number of a LGB is taken as the label in the training and test samples. The influences on the detection accuracy of the number of training samples, the transmission distance, and the different ways of grouping OAM values are analyzed, where the detection accuracy is defined as the percentage of correctly detected OAM. The results show that only a few training samples are needed up to a range of 4000 m to achieve saturation accuracy. When the transmission distance is within 2500 m, the detection accuracy of a single SVM model in four turbulent environments ( 10−14, 10−15, ) is close to 100%. When the distance increases, detection accuracy decreases gradually, and in the range of 4000 m the detection accuracy is more than 91%. Compared with the traditional spiral spectrum expansion method, the SVM model has obvious advantages. In addition, when the range of OAM to be detected is large, the OAM values may be grouped thereby improving the accuracy when using the multi-SVM models for joint detection.

Transmission and detection of informationally loaded beams of wavelength 1530 nm in a random fluctuating medium

The propagation of variously structured vortex beams of wavelength 1530 nm through a random distorting medium was experimentally investigated. An effect of the aerosol barrier on the scintillation index of the beam was analyzed. The possibility of the correlation detection of the presence of a vortex phase under the beam wandering caused by a flow of warm air was experimentally investigated.

Approximate expression of beam wander of Gaussian array beams through oceanic turbulence

The general analytical formula of beam wander through oceanic turbulence is derived. An accurate approximate expression of this general formula is given based on the oceanic turbulence parameter characteristics. This approximation clearly indicates the relationship between beam wander and propagation distance, oceanic turbulence parameters (the rate of dissipation of kinetic energy per unit mass of fluid, the rate of dissipation of mean-squared temperature, the ratio of temperature and salinity contributions to the refractive index spectrum) as well as the beam spreading. Furthermore, the Gaussian array beams are considered as an example and another approximation is expressed considering that the laser beam underwater propagation distance is usually short. This approximation has quite simple and clear form which is convenient for engineering estimation. Numerical results verified the accuracy of the two approximation expressions and illustrate the beam wander characteristics under different oceanic turbulence conditions. Our results will be beneficial to evaluate the beam wander characteristics and select beam parameters in optical underwater communication systems.

Propagation of partially coherent vortex beams in atmospheric turbulence by a spatial light modulator

We study the spectral density of partially coherent vortex beams propagating in atmospheric turbulence by numerical simulation and experiments with a spatial light modulator. On the basis of the new simulation method proposed in our previous work, we extend the research objective from coherent beams to partially coherent beams. The spectral density of partially coherent vortex beams propagating in Kolmogorov and non-Kolmogorov turbulence is studied by further optimization of the simulation method with beam wander. Consistent results between numerical simulation and experiments are obtained to prove our standpoint. The study of the spectral density of partially coherent beams propagating in a turbulent environment with the improved simulation method proposed by us is helpful for improving the accuracy of simulating partially coherent beams in optical study. It is of great significance for the comprehensive research of beam propagation in turbulence.

Beam-wander analysis in turbulent ocean with the effect of the eddy diffusivity ratio and the outer scale.

In this paper, we theoretically analyze the beam wander variance for the Gaussian beam propagation through weak oceanic turbulence. Particularly, we consider the effect of the eddy diffusivity ratio of salinity to temperature as well as the outer scale on the beam wander. To get to the tractable theoretical results, we first develop an approximate oceanic refractive-index spectrum with the outer scale and variable eddy diffusivity ratio. Based on this spectrum in weak turbulence, we then derive the closed-form expression for the beam wander variance. We present numerical results to show that the beam wander is either overestimated or underestimated as compared to the previous analyses which set the eddy diffusivity ratio to one. In addition, the finite outer scale of turbulence can significantly reduce the beam wander for Gaussian beams.

Reduction of speckle noise and mitigation of beam wander in tunable external cavity quantum cascade lasers using rotating diamond/KBr pellet coupled with multimode fiber.

We experimentally demonstrate speckle noise reduction and beam wander mitigation by using a rotating diamond/KBr pellet and a multimode fiber (MMF). As the diamond/KBr diffuser is rotated, the reflected speckle images that are captured by an infrared camera are temporally averaged. We demonstrate 78% speckle noise reduction by averaging 25 frames, which is within 80% of the theoretical contrast reduction. Large beam position fluctuations are also significantly suppressed by adding the MMF. This combination of beam wander mitigation and speckle reduction offers significant benefits for emerging optical technologies that use quantum cascade lasers as illumination sources.

Enhanced vortex beams resistance to turbulence with polarization modulation

Adopting a vortex beam with poor coherence can reduce turbulence-induced beam spreading and wander effects in the atmosphere, but it intensifies the degradation rate of its beam profile from a doughnut shape into a Gaussian shape. Transmission quality of Orbital–angular–momentum (OAM) mode carried by a vortex beam is closely related to its evolution of intensity distribution. After appropriate polarization modulation, a radially polarized vortex beam has a better performance on the reduction of beam spreading and wander effects than its scalar counterpart. A radially polarized vortex beam can also lower the degradation rate of its beam profile and keep “OAM information” a longer distance. Therefore, appropriate polarization modulation can be an effective approach to mitigate the adverse turbulent effects on OAM-based systems operated in the atmosphere.

Long-range propagation through inhomogeneous turbulent atmosphere: analysis beyond phase screens

Many applications rely on the propagation of electromagnetic waves through extended regions of the atmosphere over which the refractive index can vary in a complex manner. Gradients and curvature of the mean refractive index profile result in ray bending and the associated phenomena of mirages, atmospheric lensing, and wave trapping in parabolic cavities. Stochastic refractive index fluctuations due to turbulence cause a random displacement of the trajectory and give rise to the wander, or spot dancing, of a propagating optical beam. In this paper we model these features of the refractive index profile locally and describe propagation through the corresponding regions. We derive formulas for the mean ray path that capture the effects of both atmospheric turbulence and variations in the mean refractive index profile, including the non-paraxial effects associated with the bending of the guiding ray path. We also give formulas for the mean-squared transverse displacement of a ray from the mean trajectory, which can provide for example an estimate of the magnitude of the beam wander due to turbulence.

Turbulence-induced power drops as extreme events

Free-space optical communication links through the atmosphere are degraded mainly by the action of scintillation and beam wander. Both phenomena are responsible for fiber coupling misalignments at the receiver. Henceforth, the signal is corrupted by random power drops, which can be identified as extreme events, with particular statistical properties. In this work, we performed experiments and simulations to gain insight into understanding these extremes events and their relation with scintillation and wander at a receiver. Particularly, this sequence also inherits the same long term correlations of the original data.

Characterizing vortex beams from a spatial light modulator with collinear phase-shifting holography.

We demonstrate collinear phase-shifting holography for measuring complex optical modes of twisted light beams with orbital angular momentum (OAM) generated by passing a laser through a spatial light modulator (SLM). This technique measures the mode along the direction of propagation from the SLM and requires no additional optics, so it can be used to aid alignment of the SLM, to efficiently check for the effects of beam wander, and to fully characterize generated beams before use in other experiments. Optimized error analysis and careful SLM alignment allow us to generate and measure OAM with purity as high as 99.9%.