Beams In Turbulent Atmosphere Research Articles

Second-order coherence and polarization characteristics of partially coherent radially polarized cosh-Gaussian vortex beams in a turbulent atmosphere

The second-order coherence and polarization characteristics of partially coherent radially polarized cosh-Gaussian vortex (PCRPChGV) beams in atmospheric turbulence are investigated based on the extended Huygens–Fresnel principle. The analytical propagation formulas of cross-spectral density matrix, average intensity and degree of polarization (DOP) for PCRPChGV beams in turbulence are derived. The influences of initial correlation length, cosh factor and turbulence intensity on average intensity, on-axis intensity and DOP of PCRPChGV beams are examined numerically. Results show that with increasing propagation distance, the PCRPChGV beam evolves from the initially separated double-lobe spot into overlapping double-lobe spot, and Gaussian spot. The corresponding intensities of the two Cartesian components of light field rotate markedly around the beam axis in a unique manner. Initial correlation length and cosh factor have an obvious influence on the position and size of normalized on-axis intensity peak, respectively. In addition, PCRPChGV beams in moderate turbulence have strong anti-turbulence ability.

Twisted splitting and propagation factor of superimposed twisted Hermite-Gaussian Schell-model beams in turbulent atmosphere

We believe this to be a new superposition twisted Hermite-Gaussian Schell-model (STHGSM) beam hat is proposed. Analytic formulas for the intensity distribution and propagation factor of the STHGSM beam in non-Kolmogorov turbulence are derived by utilizing the generalized Huygens-Fresnel principle (HFP) and the Wigner function. The evolution characteristics of STHGSM beams propagating are numerically calculated and analyzed. Our findings indicate that the light intensity of the STHGSM beam gradually undergoes splitting and rotation around the axis during propagation through non-Kolmogorov turbulence, eventually evolving into a diagonal lobe shape at a certain distance of transmission. The anti-turbulence capability of the beam strengthens with higher beam order or twist factor values.

Propagation of the autofocusing Lommel–Gaussian vortex beam with I-Bessel beam in turbulent atmosphere

Propagation of the autofocusing Lommel–Gaussian vortex beam with I-Bessel beam in turbulent atmosphere

Time-varying propagation model and dynamic-feedback-phase correction for multiplexed orbital angular momentum beams in atmospheric turbulence.

Freespace optical (FSO) communication in an outdoor setting is complicated by atmospheric turbulence (AT). A time-varying (TV) multiplexed orbital angular momentum (OAM) propagation model to consider AT under transverse-wind conditions is formulated for the first time, and optimized dynamic correction periods for various TV AT situations are found to improve the transmission efficiency. The TV nature of AT has until now been neglected from modeling of OAM propagation models, but it is shown to be important. First, according to the Taylor frozen-turbulence hypothesis, a series of AT phase screens influenced by transverse wind are introduced into the conventional angular-spectrum propagation analysis method to model both the temporal and spatial propagation characteristics of multiplexed OAM beams. Our model shows that while in weak TV AT, the power standard deviation of lower-order modes is usually smaller than that of higher-order modes, the phenomena in strong TV AT are qualitatively different. Moreover, after analyzing the effective time of each OAM phase correction, optimized dynamic correction periods for a dynamic feedback communication link are obtained. An optimized result shows that, under the moderate TV AT, both a system BER within the forward-error-correction limit and a low iterative computation volume with 6% of the real-time correction could be achieved with a correction period of 0.18 s. The research emphasizes the significance of establishing a TV propagation model for exploring the effect of TV AT on multiplexed OAM beams and proposing an optimized phase-correction mechanism to mitigate performance degradation caused by TV AT, ultimately enhancing overall transmission efficiency.

Robust autofocusing propagation in turbulence

Abstract Turbulence in complex environments such as atmosphere and biological media has always been a great challenge to the beam propagation application in optical communication, optical trapping and manipulation. To overcome this challenge, this study comprehensively investigate the robust propagation of traditional Gaussian beam and autofocusing beam in turbulent environments. In order to select stable beams that exhibit high intensity and high field gradient at the focal position in complex environments, Kolmogorov turbulence theory is used to simulate the propagation of beams in atmospheric turbulence based on the multi-phase screen method. We systematically analyzed the intensity fluctuations, the variation of the coherence factor, and the change of the scintillation index (SI) with the propagation distance. The analysis reveals that the intensity fluctuations of autofocusing beams are significantly smaller than that of Gaussian beams, and the coherence of autofocusing beams is better than that of Gaussian beams under turbulence. Moreover, autofocusing beams exhibit less oscillation than Gaussian beams, indicating that autofocusing beams propagate in complex environments with less distortion and intensity fluctuation. Overall, this work clearly demonstrates that autofocusing beams exhibit higher stability in propagation compared with the Gaussian beams, showing great promise for applications such as optical trapping and manipulation in complex environments.

Distribution of intensity and M2 factor for a partially coherent flat-topped beam in bidirectional turbulent atmosphere and plasma connection

This study investigates the bidirectional transmission of a partially coherent flat-topped beam in a turbulent atmosphere and plasma. Analytical formulas for the intensity distribution and M2 factor are derived based on the optical transmission matrix, Collins formula, and second moment theory with Wigner distribution function. Numerical results show that the beam order and transverse spatial coherence width can be selected appropriately to mitigate turbulence and plasma induced evolution properties. The partially coherent flat-topped beam propagation through a turbulent atmosphere and plasma of the forward transmission effect on the intensity distribution and M2 factor are smaller than that of the reverse transmission. Under the same conditions, the M2 factor of a partially coherent flat-topped beam is smaller than the Gaussian beam in bidirectional transmission. Our results can be used in long-distance free-space optical communications.

Propagation properties of partially coherent radially polarized rotationally-symmetric power-exponent-phase vortex beams in turbulent atmosphere

In this paper, the propagation properties of partially coherent radially polarized rotationally-symmetric power-exponent-phase vortex beams (RP-RSPEPVBs) in turbulent atmosphere were investigated. Based on the extended Huygens-Fresnel principle and unified theory of coherence and polarization, the theoretical propagation model was established. Then, the numerical simulations were carried out to reveal the evolution of intensity distribution, spectral degree of coherence (DOC) and spectral degree of polarization (DOP) in turbulent atmosphere. The results showed that although the partially coherent RP-RSPEPVBs diverged during the propagation, the spatial structure remains analogous, and the relatively larger waist widths gain smaller divergence. Moreover, the optical pattern can be evidently modulated by optical parameters, as the number of sidelobes can be changed with topological charge l, and the continuity of the light spot as well as the rotating speed around the optical axis can be influenced by power exponent n. Besides, the spectral DOC and DOP would decrease with larger propagation distance and refractive-index structure constant, but decrease less with a shorter coherence width. This work may be helpful in fields such as remote sensing and optical communication.

Multimode beam propagation through atmospheric turbulence

The investigation focuses on studying the propagation characteristics of multimode lasers in the turbulent amosphere. By employing the Huygens-Fresnel integral, we develop analytical formulations for various propagation parameters. These include the average intensity distribution, kurtosis parameter, beam spread, and the average transmittance of multimode beams in turbulent atmosphere. Our findings reveal that as the propagation distance or the structure constant of the atmosphere increases, i.e., turbulence becomes stronger, the kurtosis parameter and the beam spread increase. The multimode beam exhibits a Gaussian like intensity profile when the propagation distance is significantly increased or when the structure constant becomes sufficiently large. For the case of the Gaussian beam, the kurtosis parameter is found to be 3. The multimode beam's kurtosis parameter rises as the turbulence becomes stronger and eventually approaches 3. Raising the mode content leads to a rise in the average transmittance; however, it leads to a decline in the Kurtosis parameter and the beam spread.

Coherent properties of partially coherent vortex beam with nonuniform polarization propagating in turbulent atmosphere

The spectral degree of coherence (SDOC) evolution of partially coherent vortex beam with radially and azimuthally polarized (RPV and APV) beams in atmospheric turbulence have been studied and the results indicate that SDOC distribution will gradually appear dark ring and finally evolve into quasi-Gaussian-like form. In addition, we have simulated this process by muti-phase screen method and the simulation results are consistent well with the theoretical predictions. What’s more, we have emphatically investigated the phase evolution of SDOC and the dynamic evolution of correlation singularities of partially coherent RPV and APV beams in turbulent atmosphere in detail. The results indicate that the correlation singularity of the beam will first split, and then generate new correlation singularity, finally vanish. Both of stronger atmospheric turbulence and lower correlation length make the beam generate a pair of correlation singularities with opposite sign. Our findings can provide reference for free space communication.

Scintillation and bit error rate analysis of zero-order Bessel–Gauss beams in atmospheric turbulence based on the extended Rytov theory

Scintillation and bit error rate analysis of zero-order Bessel–Gauss beams in atmospheric turbulence based on the extended Rytov theory

Average Intensity of a Laguerre—Gaussian Vector Vortex Beam through Inhomogeneous Atmospheric Turbulence

We investigate the evolution properties of a partially coherent Laguerre–Gaussian vector vortex (LGVV) beam through inhomogeneous atmospheric turbulence. Analytical formulae for the elements of a cross-spectral density matrix of a partially coherent LGVV beam propagating in turbulence are derived with the help of the extended Huygens–Fresnel principle. Our outcomes demonstrate that the normalized initial profile of a partially coherent beam with concentric dark rings gradually evolves into a Gaussian-like beam profile in turbulence. We also find that the beam is emitted at a large zenith angle and quickly converts to a Gaussian-like beam. Furthermore, it is also shown that a propagation beam with a large topological charge has a stronger ability to resist atmospheric turbulence. In order to confirm our numerical results, we combine the complex screen method and multi-phase screen method to simulate the propagation of a partially coherent LGVV beam in atmospheric turbulence. It is indicated that the simulation results are in good agreement with theoretical predictions. Our results will pave the way for the development of free-space optical communications and remote sensing.

Crosstalk characteristics of orbital angular momentum of focused perfect vortex beam in atmospheric turbulence

The perfect optical vortex beam (POV) is a special kind of vortex beam, whose radius is independent of its orbital angular momentum (OAM) mode, but the atmospheric turbulence (AT) causes crosstalk between different topological charges, which is a serious challenge in OAM-based communication system. We establish a theoretical model with a turbulence suppression effect for deriving the spiral spectrum of a focused perfect optical vortex beam (FPOV) after propagation through anisotropic AT. Through numerical analysis, we simulate the behavior of FPOV under different turbulence and beam parameters to better understand the effect of the received probability and its corresponding modal crosstalk under various conditions. In addition, the simulation of AT uses the multi-phase screen method to verify the theoretical results. The results show that the changes in topological charge, wavelength, receiving aperture, beam waist, and hollow radius all have an influence on the received probability. Also, some strategies for selecting turbulence parameters to reduce modal crosstalk in anisotropic AT are also discussed. The focus would reduce the effect of turbulent aberrations on the signal OAM mode received probability, and the FPOV provided better performance than the POV, which may be useful in OAM-based free space optical communication.

Propagation of radial phase modulated vortex beams in atmospheric turbulence

In practical free-space optical (FSO) communications, mitigating turbulence effects is crucial. This paper introduces radial phase modulation as a method to protect the signal's orbital angular momentum (OAM) in turbulent FSO. The results demonstrate that selecting appropriate modulation parameters can improve communication quality, particularly in stronger turbulence. However, a drawback is that radial phase modulation also increases crosstalk near the signal mode in strong turbulence. We further investigate the effects of radial phase modulation in two OAM multiplexing cases: mode broadcasting and intensity superposition. The results demonstrate that by employing radial phase modulation, both intensity and phase divergence, as well as beam wander, can be effectively reduced. In addition, the peaks in the OAM spectra enable easy identification of the signal modes. Moreover, even with a limited aperture in the detector, both channel capacity and transmission distance can be enhanced. These findings have potential applications in practical FSO communication in atmospheric turbulence.

Polarization characteristics of partially coherent radially and azimuthally polarized beams with vortex phase propagating through atmospheric turbulence

Analytical formulas for the normalized spectral Stokes parameters of the partially coherent radially and azimuthally polarized beams with vortex phase (i.e., PCRPV and PCAPV beams) propagating through the turbulent atmosphere are derived. The polarization properties of PCRPV and PCAPV beams in atmospheric turbulence have been studied in detail. Our findings show that different correlation lengths induce nonuniform distribution to degree of polarization (DOP) and the normalized spectral Stokes parameters. And different correlation lengths also cause the polarization singularity splitting. Besides, we find also that the vortex phase will lead to the rotation of distributions of orientation angles and the normalized spectral Stokes parameters of PCRPV and PCAPV beams in turbulence, and the rotation degree will become obvious with increasing topological charge number. It can be found also that larger topological charge number can reduce the speed of polarization singularities destroyed by atmospheric turbulence, meaning that PCRPV and PCAPV beams with a larger topological charge has a stronger ability to resist atmospheric turbulence. Our studies could be important for free-space optical communications and polarization lidar system.

Detection of topological charge for composite perfect vortex beams in atmospheric turbulence

Aiming at the problem of detecting the orbital angular momentum (OAM) states of the composite perfect vortex beams (CPVBs) under atmospheric turbulence (AT) channels, we propose and investigate a joint scheme of combing an optical detection method and the Gerchberg-Saxton (GS) algorithm. We firstly used the GS algorithm to pre-compensate the distorted CPVBs, and then the optical intensity distribution, together with the far-field diffraction patterns of the CPVBs after they passing through an elliptical aperture which shields part of the azimuth angle (EA-shielded), can tell us the topological charges (TCs) carried by each sub beam. The results show that the tailing direction of the bright stripes in the CPVBs intensity distribution denotes the sign of the higerh-order TC, counterclockwise is positive, clockwise is negative. The difference between the TCs of the two beams is indicated by the number of stripes, that is, the number of stripes is equal to the absolute values of differences between the two beams. After passing through the EA-shielded, the far-field diffraction intensity patterns is related to the magnitude and sign of the lower-order TC. If the bright stripes are distributed above, the TC is positive, otherwise, the TC is negative, and the number of dark stripes is equal to the lower-order TC-1. The results provide a new method for detecting the TC information of the CPVBs after phase distortion.

Self-focusing effect analysis of a perfect optical vortex beam in atmospheric turbulence.

The correlation function and the detection probability of orbital angular momentum (OAM) of a perfect optical vortex beam (POVB) were obtained under atmospheric turbulence conditions and then used to estimate the POVB propagation model through atmospheric turbulence. The POVB propagation in a turbulence-free channel can be divided into anti-diffraction and self-focusing stages. The beam profile size can be well preserved in the anti-diffraction stage as the transmission distance increases. After shrinking and focusing the POVB in the self-focusing region, the beam profile size expands in the self-focusing stage. The influence of topological charge on the beam intensity and profile size differs depending on the propagation stage. The POVB degenerates into a Bessel-Gaussian beam (BGB)-like when the ratio of the ring radius to the Gaussian beam waist approaches 1. The unique self-focusing effect of the POVB enables higher received probability compared to the BGB when propagating over long distances in atmospheric turbulence. However, the property of the POVB that its initial beam profile size is not affected by topological charge does not contribute to the POVB achieving a higher received probability than the BGB in short-range transmission application scenarios. The BGB anti-diffraction is stronger than that of the POVB, assuming a similar initial beam profile size at short-range transmission.

Spectral properties of pulsed Laguerre higher-order cosh-Gaussian beam propagating through the turbulent atmosphere

The formula for the propagation of pulsed Laguerre higher-order cosh-Gaussian (LHChG) beam in turbulent atmosphere is derived using the extended Huygens–Fresnel principle and the Fourier Transform method. The impact of atmospheric turbulence, transverse positions, and initial beam parameters on the spectral intensity of the propagated beam has been examined using graphical representations. The relative spectral shift of pulsed LHChG beam in turbulent atmosphere with different radial coordinates has also been studied and illustrated with numerical calculations. Analysis show that the spectral intensity depends on the structure constant of the refractive index, pulse duration, and beam order. On-axis spectral intensity is blue-shifted and off-axis spectral intensity is red-shifted with increasing radial coordinate. From our main results, one derive some published particular cases of the considered beam. The research results have potential applications in information coding and transmission.

Adaptive optics pre-compensation for orbital angular momentum beams transmitting through simulated atmospheric turbulence.

We propose an adaptive optics (AO) pre-compensation scheme to improve the transmission quality of orbital angular momentum (OAM) beams in atmospheric turbulence. The distortion wavefront caused by atmospheric turbulence is obtained with the Gaussian beacon from the receiver. The AO system imposes the conjugate distortion wavefront onto the outgoing OAM beams at the transmitter, tto achieve the pre-compensation. Using the scheme, we conducted transmission experiments with different OAM beams in the simulated atmospheric turbulence. The experimental results indicated that the AO pre-compensation scheme can improve the transmission quality of the OAM beams in the atmospheric turbulence in real-time. It is found that the turbulence-induced crosstalk effects on neighboring modes are reduced by an average of 6 dB, and the system power penalty is improved by an average of 12.6 dB after pre-compensation.

Scintillation index and bit error rate of partially coherent twisted Gaussian beams in turbulent atmosphere

Scintillation index and bit error rate of partially coherent twisted Gaussian beams in turbulent atmosphere

Corrigendum: The behavior of partially coherent twisted space-time beams in atmospheric turbulence

In the published article, there was an error in \textbf{Figure~3} as published. \textbf{The images displayed in Figure~3 were incorrect}. The corrected \textbf{Figure~3} and its caption \textbf{Ensemble-averaged irradiance $\Langle I\left(x,0,z,t\right)\Rangle$ turbulence results: \textbf{(A)} theory $N_{Fx} = \infty$, \textbf{(B)} theory $N_{Fx} = 10$, \textbf{(C)} theory $N_{Fx} = 5$, \textbf{(D)} theory $N_{Fx} = 1$, \textbf{(E)} simulation $N_{Fx} = \infty$, \textbf{(F)} simulation $N_{Fx} = 10$, \textbf{(G)} simulation $N_{Fx} = 5$, and \textbf{(H)} simulation $N_{Fx} = 1$} appear below. \par The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.