汉克-贝塞尔光束在海洋湍流信道中的螺旋相位谱分析

携带轨道角动量的汉克-贝塞尔(Hankel-Bessel,HB)光束具有无衍射和自聚焦特性,用来作为信息传输的载体有望增大信息传输容量.基于Rytov近似理论,推导得到了HB涡旋光束经过海洋水平弱湍流信道后的螺旋相位谱的解析表达式,并利用数值仿真方法研究了海洋湍流参数对轨道角动量模式探测概率的影响.结果表明,海洋湍流导致发射轨道角动量模式的探测概率下降,出现模式串扰和螺旋相位谱扩展.海洋湍流对HB涡旋光束的负面影响随着轨道角动量模式数、传输距离、温度方差耗散率的增加而增强,随湍流动能耗散率的增加而减弱.HB涡旋光束受以盐度波动驱动的海洋湍流的负面影响更大.另外,在弱湍流及几十米传输距离条件下,HB涡旋光束的传输性能要差于最佳束腰大小设置的拉盖尔-高斯涡旋光束.这些结果有望为海洋环境水下光通信链路的实现提供一定的参考价值.     

高斯涡旋光束在大气湍流传输中的特性研究

为了研究大气湍流对高斯涡旋光束传递信息的影响,理论分析了经过大气湍流的高斯涡旋光束轨道角动量(OAM)模式的径向平均功率和归一化平均功率分布、固有模式指数、初始光束半径和湍流强度;采用纯相位扰动逼近的有效性,数值模拟高斯涡旋光束在传输中的OAM模式径向平均功率分布的变化。建立传输模型并进行外场激光大气传输实验,对比分析了模拟和实测的OAM归一化平均功率分布,结果表明在弱湍流条件下,OAM模式的径向平均功率随着接收器孔径尺寸的增加而变化,逐渐趋于稳定值。对于一般常用的接收孔径,在强湍流或较小的初始光束半径条件下对OAM模式干扰十分严重。验证了用数值方法模拟OAM在湍流介质中的模式变化过程的可靠性。     

Angle-of-arrival fluctuations for wave propagation through non-Kolmogorov turbulence

Recently the increasing experimental evidences have shown that atmospheric turbulence statistics does not obey Kolmogorov’s power spectrum model in portions of the troposphere and stratosphere. These experiments have prompted the investigations of optical wave propagation through atmospheric turbulence described by non-classical power spectra. In this paper, using an original approach and considering a non-Kolmogorov power spectrum which uses a generalized power law instead of constant standard power law value 11/3 and a generalized amplitude factor instead of constant value 0.033, the variances of the angle-of-arrival fluctuations of the plane and spherical waves are derived in weak turbulence for a horizontal path. The concise closed-form expressions are obtained and used to analyze the influence of spectral power law variation on the angle-of-arrival fluctuations.     

The probability of orbital angular momentum states of single photons with Z-tilt corrected residual aberration in a slant path turbulent atmosphere

With Rytov approximation and Kolmogorov spectrum model of index-of-refraction fluctuation, we study the effects of turbulence aberration on the orbital angular momentum of single photons in atmospheric communication channel. A theoretical model of measurement probabilities of orbital angular momentum states for single photons propagation under the Zernike tilt corrected slant path turbulent atmosphere channel is established. Our research shows that tilt-corrected residual aberration not only damage the initial OAM, but also induce new OAM. With the increasing of D/ρ₀, the number of the initial OAM photons will go down while the effective number of new OAM ascends. Meanwhile, the receiving probability of initial OAM photons declines, as the turbulence shifts from weak to strong. For Zernike tilt-corrected residual aberration, the receiving probability of initial OAM photons declines as the diameter of detector increases. The effect of Zernike tilt-corrected residual aberration on OAM of the photons is more larger than the effect of Zernike tilt turbulent aberration.     

Effect of the outer scale on the angle of arrival variance for free-space-laser beam corrugated by non-Kolmogorov turbulence

It is well known that atmospheric turbulence causes significant variations of the arrival angle of laser beams used in free-space communications. Usually, angle-of-arrival fluctuations of an optical wave in the plane of the receiver aperture is calculated by Kolmogorov’s power spectral-density model. Unfortunately, recently increasing experimental evidence has shown that atmospheric turbulence statistics does not obey Kolmogorov’s power spectrum model in some parts of the troposphere and stratosphere. These experiments have prompted investigations of the optical-wave propagation through atmospheric turbulence described by nonclassical power spectra. In this paper, employing a new approach and considering a non-Kolmogorov power spectrum with a generalized power law instead of the constant standard power-law value 11/3 and a generalized amplitude factor instead of the constant value 0.033, we derive the variances of the angle-of-arrival fluctuations of the plane and spherical waves in a weak turbulence for the horizontal path. The concise closed-form expressions are obtained and used to analyze the influence of spectral power-law variations on the angle-of-arrival fluctuations. In addition, the outer scale effect is also analyzed.     

光纤布拉格光栅及其构成的法布里-珀罗腔的相位谱特性研究

光纤光栅的相位谱对光纤光栅法布里-珀罗(F-P)腔的光谱特性有重要影响.对光纤布拉格光栅(FBG)光谱,特别是FBG相位谱进行了深人分析,推导了低反射率FBG的线性相位谱的一般表达式,提出了高反射率FBG的三段线性相位近似方法,得到了简洁直观的相位谱数学表达式.然后采用和普通F-P腔对比的方式,以等效腔长的概念分析了F...     

Non-Gaussian statistics of partially coherent light in atmospheric turbulence

We derive theoretically and verify experimentally a concise general expression for the normalized intensity correlations(IC) of partially coherent light in a weak atmospheric turbulence in the fast detector measurement regime. The derived relation reveals that the medium turbulence acts, in general, as an additional noise source enhancing the IC of partially coherent beams. The maximum of the beam IC is, in general, enhanced, causing the fields to exhibit super-Gaussian statistics.On the other hand, the relation indicates that turbulence-induced noise is negligible for sufficiently low coherence light,which reveals the condition for the turbulence-free correlation imaging.     

High-Rate Continuous-Variable Quantum Key Distribution with Orbital Angular Momentum Multiplexing

The secret key rate is one of the main obstacles to the practical application of continuous-variable quantum key distribution (CVQKD). In this paper, we propose a multiplexing scheme to increase the secret key rate of the CVQKD system with orbital angular momentum (OAM). The propagation characteristics of a typical vortex beam, involving the Laguerre–Gaussian (LG) beam, are analyzed in an atmospheric channel for the Kolmogorov turbulence model. Discrete modulation is utilized to extend the maximal transmission distance. We show the effect of the transmittance of the beam over the turbulent channel on the secret key rate and the transmission distance. Numerical simulations indicate that the OAM multiplexing scheme can improve the performance of the CVQKD system and hence has potential use for practical high-rate quantum communications.     

Wander of a Gaussian-Beam Wave Propagated Through a Non-Kolmogorov Turbulent Atmosphere

Both increasing experimental evidence and some results of theoretical investigation have shown that there exist two kinds of turbulence in the aerosphere, Kolmogorov and non-Kolmogorov turbulence. Thus, it is necessary to improve the theory of optical wave propagation through atmospheric turbulence, namely, study the laser-beam propagation in non-Kolmogorov turbulence, before analyzing the joint influence of the Kolmogorov turbulence and non-Kolmogorov one on satellite laser communication. The beam wander will lead to the performance degradation of satellite laser communication systems and exert an influence on the achievement and stability of its links. In this paper, we consider a theoretical power spectrum of refractive-index fluctuations with a generalized power law in order to derive the variance of Gaussian-beam wave wander in weak turbulence for a horizonal path and analyze the influence of spectral power-law variations on the beam wander. We show that the expression for the beam-wander variance is of concise closed form and independent of the optical wavelength.     

A marine atmospheric spectrum for laser propagation

Most refractive index power spectral models currently used in atmospheric optical propagation studies were developed for terrestrial or high altitude environments. The current paper presents a new atmospheric spectral model for the marine environment. An analytical marine atmospheric spectrum is formulated to fit a numerical spectrum with the help of the downhill simplex algorithm. Theoretical irradiance fluctuation expressions are derived from the new spectrum for plane and spherical waves in weak optical turbulence. Comparisons are made between the existing scintillation theory and the new expressions developed for the marine environment, and the comparative advantage of the model is discussed. The results suggest that the current models are adequate for modeling the marine atmosphere in weak optical turbulence for small values of the inner scale of turbulence.     

A marine atmospheric spectrum for laser propagation

Most refractive index power spectral models currently used in atmospheric optical propagation studies were developed for terrestrial or high altitude environments. The current paper presents a new atmospheric spectral model for the marine environment. An analytical marine atmospheric spectrum is formulated to fit a numerical spectrum with the help of the downhill simplex algorithm. Theoretical irradiance fluctuation expressions are derived from the new spectrum for plane and spherical waves in weak optical turbulence. Comparisons are made between the existing scintillation theory and the new expressions developed for the marine environment, and the comparative advantage of the model is discussed. The results suggest that the current models are adequate for modeling the marine atmosphere in weak optical turbulence for small values of the inner scale of turbulence.     

Influence of atmospheric turbulence on states of light carrying orbital angular momentum

We have experimentally studied the degradation of mode purity for light beams carrying orbital angular momentum (OAM) propagating through simulated atmospheric turbulence. The turbulence is modeled as a randomly varying phase aberration, which obeys statistics postulated by Kolmogorov turbulence theory. We introduce this simulated turbulence through the use of a phase-only spatial light modulator. Once the turbulence is introduced, the degradation in mode quality results in crosstalk between OAM modes. We study this crosstalk in OAM for 11 modes, showing that turbulence uniformly degrades the purity of all the modes within this range, irrespective of mode number.     

Aperture-averaged scintillation index and fade statistics in weak oceanic turbulence

With the rapid demand for underwater optical communication(UOC), studies of UOC degradation by oceanic turbulence have attached increasing attention worldwide and become a research hot-spot in recent years. Previous studies used a simplified and inaccurate oceanic turbulence spectrum, in which the eddy diffusivity ratio between temperature and salinity is assumed to be unity and the outer scale of turbulence is assumed to be infinite. However, both assumptions are not true in most of the actual marine environments. In this paper, based on the Rytov theory in weak turbulence, we derive analytical expressions of "the aperture-averaged scintillation index"(SI) for both plane and spherical waves, which can clearly demonstrate how SI is influenced by several key factors in UOC. Then, typical fade statistics of the UOC system in weak turbulence is discussed including the probability of fade, the expected number of fades per time, the mean fade time,signal-to-noise ratio and bit error rate. Our results show that spherical wave is preferable in the UOC system in weak turbulence compared to plane wave, and the aperture-averaged effect has a significant impact on UOC system's performance.Our results can be used to determine those key parameters for designing the UOC system over reasonable ranges.     

光束在强湍流区中传播的到达角起伏

 基于修正Rytov理论，导出了适用于强湍流区的无限平面波和球面波的到达角起伏方差表达式及其功率谱表达式，分析了散射盘对到达角起伏的影响。研究结果表明：导出的方差表达式在弱湍流区也适用，随着Rytov方差的增加到达角起伏趋于饱和；高频功率谱的下降速度随着散射盘尺度的增加而增加。     

光束在强湍流区中传播的到达角起伏

基于修正Rytov理论,导出了适用于强湍流区的无限平面波和球面波的到达角起伏方差表达式及其功率谱表达式,分析了散射盘对到达角起伏的影响。研究结果表明：导出的方差表达式在弱湍流区也适用,随着Rytov方差的增加到达角起伏趋于饱和;高频功率谱的下降速度随着散射盘尺度的增加而增加。     

Angle of Arrival Fluctuations for Optical Waves Propagating Through Joint Moderate to Strong Atmospheric Turbulence

Satellite laser communication has gained wide attention both at home and abroad. The pointing, acquisition, and tracking (PAT) technology is the kernel of satellite laser communication systems, and the atmospheric layer is a part of the communication channel for satellite-to-ground links. Thus, angle of arrival (AOA) fluctuations caused by atmospheric turbulence inevitably influence long-distance satellite laser communication. Therefore, it is very important to analyze the impact of AOA fluctuations in satellite laser communication systems. According to the actual situation of satellite-to-ground links, a joint atmospheric turbulence power spectrum model is defined that includes Kolmogorov turbulence from the ground to 6 km in portions of the troposphere and non-Kolmogorov turbulence above 6 km in the stratosphere. Based on the extended Rytov theory, we derive the large-scale and small-scale variances of AOA fluctuations propagating in the uplink and downlink channels for a satellite laser communication system and analyze the influence of large zenith angle variations on the AOA fluctuations. It has long been a focus of concern that the expressions for the AOA variance obtained must be concise and of closed form.     

Effects of low-order atmosphere-turbulence aberrations on the entangled orbital angular momentum states

Based on Zernike-model expansion of turbulence phase aberrations and non-Kolmogorov spectrum model of index-of-refraction fluctuation, we analyze the effects of low-order Zernike turbulence aberrations on orbital angular momentum (OAM) entanglement states in a weak fluctuation region. The signal photon detection probability of OAM entanglement states propagating in a slant turbulence channel with non-Kolmogorov turbulence Z-tilt, defocus, astigmatism, and coma aberrations are modeled, respectively. The results demonstrate that turbulence Z-tilt aberration is the dominant aberration, coma is the second, and astigmatism is the third, but that the defocus aberration has no impact on the detection probability. As the power-law exponent of the non-Kolmogorov spectrum increases from 3 to 4, the detection probability decreases.     

Beam alignments based on the spectrum decomposition of orbital angular momentums for acoustic-vortex communications

Given the enhanced channel capacity of wave chirality, acoustic communications based on the orbital angular momentum (OAM) of acoustic-vortex (AV) beams are of significant interest for underwater data transmissions. However, the stringent beam alignment is required for the coaxial arrangement of transceiver arrays to ensure the accuracy and reliability of OAM decoding. To avoid the required multiple measurements of the traditional orthogonality based algorithm, the beam alignment algorithm based on the OAM spectrum decomposition is proposed for AV communications by using simplified ring-arrays. Numerical studies of the single-OAM and OAM-multiplexed AV beams show that the error of the OAM spectrum increases with the translation distance and the deflection angle of the transceiver arrays. To achieve an ideal arrangement, two methods of the single-array translation alignment and the dual-array deflection alignment are developed based on the least standard deviation of the OAM spectrum (SD-OAM). By decreasing the SD-OAM towards zero using transceiver arrays of 16 transmitters and 16 receivers, accurate beam alignments are accomplished by multiple adjustments in three dimensions. The proposed method is also demonstrated by experimental measurements of the OAM dispersion and the SD-OAM for misaligned beams. The results demonstrate the feasibility of the rapid beam alignment based on the OAM spectrum decomposition by using simplified transceiver ring-arrays, and suggest more application potentials for acoustic communications.     

Measuring orbital angular momentum of vortex beams in optomechanics

Measuring the orbital angular momentum (OAM) of vortex beams, including the magnitude and the sign, has great application prospects due to its theoretically unbounded and orthogonal modes. Here, the sign-distinguishable OAM measurement in optomechanics is proposed, which is achieved by monitoring the shift of the transmission spectrum of the probe field in a double Laguerre–Gaussian (LG) rotational-cavity system. Compared with the traditional single LG rotational cavity, an asymmetric optomechanically induced transparency window can occur in our system. Meanwhile, the position of the resonance valley has a strong correlation with the magnitude and sign of OAM. This originally comes from the fact that the effective detuning of the cavity mode from the driving field can vary with the magnitude and sign of OAM, which causes the spectral shift to be directional for different signs of OAM. Our scheme solves the shortcoming of the inability to distinguish the sign of OAM in optomechanics, and works well for high-order vortex beams with topological charge value±45, which is a significant improvement for measuring OAM based on the cavity optomechanical system.     

基于拉盖尔-高斯光束的通信系统在非Kolmogorov湍流中传输的系统容量

涡旋波束在大气湍流中的传输有非常重要的理论研究和实际应用意义. 本文基于利托夫近似和广义惠更斯-菲涅耳原理, 推导出拉盖尔-高斯(LG)光束在非Kolmogorov湍流中斜程传输时的螺旋谱, 并进一步推导出系统的容量. 对基于LG光束的通信系统容量进行了数值计算, 并对指数参数、光束波长、天顶角、湍流内尺度、外尺度、结构常数对系统容量的影响进行了分析比较. 本文的结论能够为LG光束在非Kolmogorov湍流中的通信提供一定的参考价值. 关键词： 拉盖尔-高斯光束 非Kolmogorov湍流 平均容量