Optimization of the probability of orbital angular momentum for Laguerre-Gaussian beam in Kolmogorov and non-Kolmogorov turbulence

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.

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.

Set of mathematical models for Bessel-Gauss beams coupling into the parabolic-index fiber under the influence of atmospheric turbulence and random jitter

The expression of efficiency for Bessel-Gauss (BG) beams coupling into the parabolic fibers (PF) after passing through the Cassegrain antenna system is first derived. The effects of atmospheric turbulence and random jitter of the coupling lens on the efficiency are also taken into account to improve the practical applicability of our model. This article use a BG beam with a wavelength of 1550 mm and fiber with a core radius R_F of 50 μm and a relative refractive index difference ζ of 0.01 for simulation testing. The optimal parameters of the antenna system are determined: the radius of the primary mirror and the secondary mirror is 8.33 cm and 1.25 cm, respectively. The coupling efficiency of BG beams of different orders reaches above 94% simultaneously when the lens's focal length is 7.8 cm. After taking into account the transmission efficiency of the antenna system, the system's total efficiency for BG beams of different orders averages 76.33%, when the transmission distance is 1 km. The results show that the same degree of turbulence and random jitter have different influences on the coupling efficiency of BG beams of different orders, and lower-order BG beams have better resistance to turbulence and jitter during propagation and coupling. Moreover, the effect of the guided mode field on the coupling efficiency and the resistance to turbulence varies for different values of mode radial index in the fiber p. The guided mode with p = 0 not only enables the BG beams of different orders to achieve the highest transmission efficiency in the coupling system almost simultaneously but also the random jitter and turbulence have less influence on the coupling efficiency of this mode. It means that the BG beams can have higher efficiency when coupled to the mode with p = 0 after long-distance transmission. This property of the fiber mode at p = 0 provides conditions for the simultaneous propagation of multiple BG beams in a parabolic fiber, which provides a theoretical basis for higher transmission capacity. This research work provides a theoretical model for the theoretical study of vortex beams and optical communication, which is beneficial for the design and application of vortex beams and has instructive meaning for practical engineering design.

Predictive correction method based on deep learning for a phase compensation system with frozen flow turbulence

We propose a deep learning method that includes convolution neural network (CNN) and convolutional long short-term memory (ConvLSTM) models to realize atmospheric turbulence compensation and correction of distorted beams. The trained CNN model can automatically obtain the equivalent turbulent compensation phase screen based on the Gaussian beams affected by turbulence and without turbulence. To solve the time delay problem, we use the ConvLSTM model to predict the atmospheric turbulence evolution and acquire a more accurate compensation phase under the Taylor frozen hypothesis. The experimental results show that the distorted Gaussian and vortex beams are effectively and accurately compensated.

Accurate analysis of the efficiency of Bessel Gauss beams passing through two Cassegrain optical antennas in atmospheric turbulence

The Bessel Gauss beam has shown good performance in solving occlusion by the secondary mirror of Cassegrain antenna. In this work, the analytical expression for the optical field of the Bessel Gauss beam after passing through the optical communication system comprising two Cassegrain antennas in atmospheric turbulence is derived. The light filed is obtained more precisely by optimising the parameters of the hard-edged optical aperture. And the energy efficiency of the whole system is investigated more accurately taking into account the efficiency of two antennas and the reflection losses. For the 3 order Bessel Gauss beam, the optimal parameters of the system are obtained by calculation. When b = 0.1m, a = 0.0162 m, η_T of Bessel Gauss beams when l = 1 ∼ 5 are 64%, 91%, 96%, 96%, 96%, respectively. At the same time, the light field expressions we have derived allow us to easily analyze the effect of atmospheric turbulence and antenna defocus on the efficiency of the system. So the effect of turbulent atmosphere and antenna defocus on the efficiency of the system and the corresponding reasons are studied as well.

Control of orbital angular momentum of optical vortex beams with complex wandering perturbations

This work investigates how independent perturbations and cross-correlation perturbations affect optical vortex beams. Theoretical and experimental results show that both perturbations cause the intensity, average orbital angular momentum (OAM), and the OAM spectrum of the vortex beam to vary periodically with the perturbation direction, but with different periods. When the beam is subjected to independent perturbations, the average OAM changes periodically with θ in every π/2; when the beam is subjected to cross-correlation perturbations, the average OAM varies with θ in every π. The results of this work provide a method to control the OAM and regulate low-coherence vortex beams in turbulent environments.

Fiber coupling efficiency of a Bessel-Gaussian beam received by a Cassegrain antenna under atmospheric turbulence

A coupling efficiency calculation method for a Bessel-Gaussian (BG) beam in a free space optical communication system received by a parabolic Cassegrain antenna and coupled into a few-mode fiber is proposed. The system of the antenna and the coupling lens is approximate to a ring-shaped lens. The effect of the antenna in the coupling system is analyzed, and maximum coupling efficiency is increased by 76.25% on average by applying the antenna. With the application of the antenna, the configurations to generate the maximum point of coupling efficiency among BG beams of different topological charges are restricted to being almost the same, which is useful for the simultaneous propagation of multiple BG beams. The effects of radial displacement and atmospheric turbulence on coupling efficiency are researched as well. Coupling efficiency becomes more sensitive to radial displacement, while the influence of turbulence on coupling efficiency remains almost the same after applying the antenna. Our calculation method has an average absolute error of only 0.6625% while increasing the calculation speed greatly, which is practical for further studies of vortex beams.

Orbital angular momentum spectrum of pin-like optical vortex beams in turbulent atmosphere

The analytical formula of the probability density of a single orbital angular momentum (OAM) mode for pin-like optical vortex beams (POVBs) in turbulent atmosphere is derived. Its OAM spectrum in the receiving plane is obtained by the numerical calculation. For comparison, the OAM spectrum of commonly Gaussian vortex beams is showed, too. Those results show that POVBs show good performance on resisting the cross talk of the OAM mode induced by the turbulence in some cases, such as smaller radius of the receiving aperture, longer propagation distance, and stronger turbulence. Our finding has application in free-space optical communication based on the OAM mode.

Mitigating the effect of atmospheric turbulence on orbital angular momentum-based quantum key distribution using real-time adaptive optics with phase unwrapping

Quantum key distribution (QKD) employed orbital angular momentum (OAM) for high-dimensional encoding enhances the system security and information capacity between two communication parties. However, such advantagesare significantly degraded because of the fragility of OAM states in atmospheric turbulence. Unlike previous researches, we first investigate the performance degradation of OAM-based QKD by infinitely long phase screen (ILPS), which offers a feasible way to study how adaptive optics (AO) dynamically corrects the turbulence-induced aberrations in real time. Secondly, considering the failure of AO while encountering phase cuts, we evaluate the quality enhancement of OAM-based QKD under a moderate turbulence strength by AO after implementing the wrapped cuts elimination. Finally, we simulate that, with more realistic considerations; real-time AO can still mitigate the impact of atmospheric turbulence on OAM-based QKD even in the large wind velocity regime.

Spiral spectrum of high-order elliptic Gaussian vortex beams in a non-Kolmogorov turbulent atmosphere

In a free space optical communication system based on vortex beams, the effects of spread and crosstalk caused by atmospheric turbulence should not be ignored. The orbital angular momentum (OAM) spectrum of the signal based on elliptic Gaussian beam (EGB) after propagation through non-Kolmogorov turbulent atmosphere are deduced, and a theoretical model of the spiral spectrum of EGB propagating through turbulent atmosphere is obtained. Numerically calculated OAM modes detection and crosstalk probability under different ellipticity parameters. The results show that the ellipticity parameter has a significant impact on the OAM spectral distribution of EGB and the transmission characteristics after turbulent atmosphere. The selection of appropriate ellipticity parameter can correspondingly reduce the degradation and crosstalk caused by turbulent atmosphere. We also compared a Laguerre-Gaussian beam (LGB) with EGB and pointed out the advantages and limitations of these two kinds of beams. The research results may be useful in the field of short distance optical communication and OAM-based multiplex communication.

Capacity analysis of oceanic channels with localized Lommel-Gaussian vortex beams

The correlation function of localized Lommel-Gaussian vortex beams is obtained in oceanic turbulence and used to estimate the channel capacity of underwater wireless optical communication systems (UWOCS). The effects of laser source and oceanic turbulence on the channel capacity are discussed. Results show that the choices of appropriate light parameters, such as input pulse half-width, beam waist, and orbital angular momentum number, are essential to achieve high channel capacity in UWOCS. Another important factor that affects channel capacity is oceanic turbulence. Scaling analysis shows that inner scale has a more significant effect on the channel capacity than the outer scale does.

Airy transform of Laguerre-Gaussian beams

Airy transform of Laguerre-Gaussian (LG) beams is investigated. As typical examples, the analytic expressions for the Airy transform of LG₀₁, LG₀₂, LG₁₁, and LG₁₂ modes are derived, which are special optical beams including the Airy and Airyprime functions. Based on these analytical expressions, the Airy transform of LG₀₁, LG₀₂, LG₁₁, and LG₁₂ modes are numerically and experimentally investigated, respectively. The effects of the control parameters α and β on the normalized intensity distribution of a Laguerre-Gaussian beam passing through Airy transform optical systems are investigated, respectively. It is found that the signs of the control parameters only affect the location of the beam spot, while the sizes of the control parameters will affect the characteristics of the beam spot. When the absolute values of the control parameters α and β decrease, the number of the side lobes in the beam spot, the beam spot size, and the Airy feature decrease, while the Laguerre-Gaussian characteristic is strengthened. By altering the control parameters α and β, the performance of these special optical beams is diversified. The experimental results are consistent with the theoretical simulations. The Airy transform of other Laguerre-Gaussian beams can be investigated in the same way. The properties of the Airy transform of Laguerre-Gaussian beams are well demonstrated. This research provides another approach to obtain special optical beams and expands the application of Laguerre-Gaussian beams.

Research for propagation properties of LG beam through Cassegrain antenna system in a turbulent atmosphere

In this paper, the propagation properties of the Laguerre-Gaussian (LG) beam passing through Cassegrain antenna system in a turbulent atmosphere have been researched. The accurate analytical function for the diffraction field of LG beam passing through Cassegrain antenna, the average intensity, and the cross-talk among different orbital angular momentum (OAM) modes of LG beam passing through Cassegrain antenna in Kolmogorov turbulent have been derived. The simulation results show that LG beam with ring-like distribution is selected to enhance the emission efficiency of Cassegrain antenna. The cross-talk among different OAM modes can remarkably reduce through using Cassegrain antenna. The analysis process can also apply to accurately analyzing the propagation properties of other kinds of beams through different optical systems in turbulent atmosphere.

Spiral spectrum of a Laguerre-Gaussian beam propagating in anisotropic non-Kolmogorov turbulent atmosphere along horizontal path

Close to the ground, it is generally known that atmospheric turbulence exhibits strong anisotropy, which affects the performance of applications such as free-space optical (FSO) communication. In this paper, we establish a theoretical model for calculating the spiral spectrum, also called the orbital angular momentum (OAM) spectrum, of a Laguerre-Gaussian (LG) beam after propagation through anisotropic turbulence along a horizontal link. This model isolates the effects of anisotropy from other parameters of the turbulence. On the basis of this model, the effects of the anisotropy on the probability density of the OAM spectrum and its corresponding modal crosstalk are studied through numerical examples. Our simulation results show that the width of the OAM spectrum will increase or slightly decrease depending on the specific nature of the anisotropy. In addition, it is demonstrated that the inner scale is more likely to cause modal crosstalk than the outer scale. Some strategies to reduce modal crosstalk in anisotropic turbulence are also discussed. Our results may be useful in OAM-based FSO communication at ground level.

Propagation of Optical Coherence Vortex Lattices in Turbulent Atmosphere

Propagation properties in the turbulence atmosphere of the optical coherence vortex lattices (OCVLs) are explored by the recently developed convolution approach. The evolution of spectral density distribution, the normalized M 2 -factor, and the beam wander of the OCVLs propagating through the atmospheric turbulence with Tatarskii spectrum are illustrated numerically. Our results show that the OCVLs display interesting propagation properties, e.g., the initial Gaussian beam distribution will evolve into hollow array distribution on propagation and finally becomes a Gaussian beam spot again in the far field in turbulent atmosphere. Furthermore, the OCVLs with large topological charge, large beam array order, large relative distance, and small coherence length are less affected by the negative effects of turbulence. Our results are expected to be used in the complex system optical communications.

Feature issue introduction: Topological Photonics and Materials

Photonic crystals have become a very common and powerful concept in optics since its introduction in the 1980s by Eli Yablonovitch and Sajeev John. It is in fact a concept borrowed from condensed matter physics. The discussion of photonic bands and bandgaps allows us to manipulate light on an optical chip, along a photonic crystal fiber and even in the quantum optics regime. Now, we are witnessing another round of concept translation again from condensed matter physics to optics about topology. Describing photonic bands by using their topology in the reciprocal space gives us a new tool to understand wave propagation and to design optical components. Topology is also an important aspect in light-matter interaction in the field of metamaterials and 2D materials.