Modified Von Karman Spectrum Research Articles

Modulation effect of focusing mirror on beam propagation through anisotropic turbulence

In this study, we modulated the Bessel-Gaussian (BG) beam using a focusing mirror to enhance the performance of wireless optical communication (WOC) while considering the angles between turbulence cells and the transmitted direction when beams propagate through anisotropic atmospheric turbulence along a slant path. Numerical results reveal that when the BG beam is modulated by a focusing mirror with a focusing length of 1 km, the detection probability of orbital angular momentum (OAM) is increased by 9.06% compared with the unmodulated BG beam when the OAM quantum number is 1. Simultaneously, this modulation method effectively reduces the bit error rate and enhances the channel capacity in OAM-based WOC. Furthermore, we observed that the smaller the OAM number, the better the effect of the modulation. Through our analysis, we identified that the most significant distortions in OAM mode propagation occur at the exponential parameter approximately 3.1 in the modified von Karman spectrum. Moreover, we demonstrated that the effects of the anisotropic tilt angle can not be negligible for beams through a slant path. Therefore, the modulation of the focusing mirror, in combination with a well-designed propagation direction that takes appropriate angles into account, can significantly improve the overall quality and performance of optical communication systems.

The spiral phase spectrum of the composite power Gaussian vortex beam in plasma sheath turbulence

This paper establishes an evolution model for the spiral phase spectrum of a composite power Gaussian (CPG) vortex beam in plasma sheath turbulence (PST) based on the Rytov approximation theory and the modified von Karman spectrum. The impact of various parameters, including turbulence and beam attributes, on the spiral phase spectrum of the CPG vortex beam in PST is investigated through numerical simulations. Our numerical results reveal that the spiral phase spectrum of beam exhibits asymmetry which modulated by the structural parameter. Meanwhile, the resistance of the CPG vortex beam against turbulence strengthens as the wavelength increases and the topological charge decreases. The findings also demonstrate that the spiral phase spectrum of the CPG vortex beam incorporates a broader range of modes in isotropic PST compared to anisotropic PST. Furthermore, the impact of PST on the beam is intensified with a higher refractive index undulation variance and a smaller outer scale parameter.

Anisotropic plasma sheath turbulence effects on the mode states of Whittaker–Gaussian beams

In this paper detection probability and crosstalk probability variance of the orbital angular momentum states of the diffraction-free Whittaker–Gaussian (WG) beams passing through an anisotropic plasma sheath turbulence (PST) are theoretically formulated. In this regard, using modified von Karman spectrum in the frame of Rytov theory the spiral spectrum of the WG beams is derived, and the role of the anisotropy parameters, refractive index fluctuation variance, initial topological charge, receiving aperture radius, the outer scale of turbulence, beam wavelength and waist in the mitigation of the turbulence-induced disturbance is numerically explored. The remarkable findings indicate that WG beams in anisotropic PST are less influenced than isotropic one, and increasing the anisotropy feature of plasma medium leads to alleviate modulated distortion. Furthermore, it is found out that the propagation performance of WG vortex beams with high-order initial topological charge is significantly better than those with lower order. We expect that our results will be helpful for designing optimal free-space communication systems.

Orbital angular momentum state variation of vortex beams propagating in a plasma sheath turbulence

The presence of turbulent media is one of the major problems in the free-space communications. This arises from the sever distortion of spatial modes which leads to data degradation. In recent years, utilizing pseudo-nondiffracting beams has been proposed as an efficient way for mitigating the disturbance induced by turbulence. In this regard, this paper is intended to theoretically investigate anisotropic plasma turbulence (PT) effects on the orbital angular momentum (OAM) spectra and phase evolutions of different kinds of pseudo-nondiffracting vortex beams (VB), including Bessel-Gaussian (BG) and Hypergeometric-Gaussian (HGG) beams. For this purpose, using the modified von Karman spectrum in the frame of Rytov theory, the orbital OAM-spectra of VBs propagating in anisotropic PT are derived, and the effects of anisotropy and source beams parameters on the mode probability of transmitted VBs are studied. Our numerical analysis reveals that when propagating VBs carrying OAM come across PT, under influences of such random medium, their OAM-spectra spread, and several side-band modes which induce phase perturbations are generated. As well as, the propagation performance of pseudo-nondiffracting VBs in an anisotropic PT is better than isotropic one. Furthermore, it is found out that under the equivalent PT conditions BG beams are less influenced by PT in comparison with HGG beams. We expect our results to provide advances on turbulence-resilient communications, free-space optical data transmissions, and imaging.

Generation of homogeneous 3D Gaussian noise with spherically symmetric covariance.

In this paper, an approach for 3D noise generation is presented. The proposed algorithm might be a useful tool for the generation of correlated phase screens. These phase screens can be used for the simulation and modeling of optical wave propagation through atmospheric turbulence. Arbitrary user-defined covariance functions between voxel pairs can be achieved. Correlated 3D noise is formed by superposition of multiple uncorrelated 3D Gaussian noise patterns. These uncorrelated input noise patterns are of different dimensions. They are upsampled to the same target dimensions by linear interpolation. Each input pattern then contributes to total covariance on different spatial scales. The covariances between different voxels are expressed analytically by propagation of error. For a subset of randomly chosen voxels in the entire voxel space, relative deviations between the analytical and user-defined covariances are calculated. A sum of squares of these relative deviations is then minimized by machine learning methods. The optimized parameters are the weighting factors of individual uncorrelated 3D noise patterns. Corresponding covariance functions are numerically evaluated for two current atmospheric turbulence spectra. The first one is the generalized modified atmospheric spectrum. The second one is the generalized modified von Karman spectrum. Based on these covariance functions, optimal superpositions are calculated. Finally, statistical properties of these patterns are validated by ensemble sample covariance analysis.

Power Spectrum of Refractive-Index Fluctuation in Hypersonic Plasma Turbulence

Anisotropic spatial distribution data of refractive-index fluctuation in hypersonic turbulence are obtained based on the experimental images of hypersonic turbulence. Furthermore, taking re-entry turbulent plasma fluctuation into consideration, the variance of the refractive-index fluctuation in hypersonic plasma is calculated based on the Saha equation and the expression of refractive index in hypersonic plasma. On this basic, the anisotropic power-spectral model of hypersonic plasma turbulence is established by introducing the orientation factor to the modified von Karman spectrum. Finally, the mutual coherence function (MCF) and the angle-of-arrival fluctuations of electromagnetic (EM) waves propagation in hypersonic plasma turbulence are calculated. Results show that the angle-of-arrival fluctuations have obvious differences between the directions of vertical to turbulent plasma flow field and parallel to it. The various gradients of the electron density along the direction of vertical to turbulent plasma flow field are far greater than the parallel to it, which causes the horizontal scale is larger than perpendicular scale of plasma eddies. Therefore, when EM waves propagating through plasma turbulence, the refractive effect of plasma eddies show obvious anisotropy. The results of this paper can be used to analyze the EM waves propagation characteristics in hypersonic plasma turbulence.

高斯阵列光束自耦合特性的实验研究

Based on the generalized Huygens-Fresnel principle and the modified von Karman spectrum model, the analytic expressions for intensity distribution of radial Gaussian array beams after incoherent combination that propagation in the atmospheric turbulence were derived. And the self-coupling characteristics of array beams was analyzed numerically with the change of transmission distance and the radial radius. Finally self-coupling characteristics of array beam of different radial radius with the change of the transmission distance had been measured by using a beam analyzer. The experimental results show that when Gaussian array beams propagate in atmospheric turbulence horizontaly, array beam will combine a beam from a certain distance with the increasing of transmission distance. And the average intensity of the combined beam is like-Gaussian distribution; under the same transmission conditions, the smaller the radial radius, the better the self-coupling characteristics of the array beams is.

Split-step approach to electromagnetic propagation through atmospheric turbulence using the modified von Karman spectrum and planar apertures

The impact of atmospheric phase turbulence on Gaussian beam propagation along propagation paths of varying lengths is examined using multiple random phase screens. The work is motivated by research involving generation and encryption of acousto-optic chaos, and the interest in examining propagation of such chaotic waves through atmospheric turbulence. A phase screen technique is used to simulate perturbations to the refractive index of the medium through the propagation path. A power spectral density based on the modified von Karman spectrum model for turbulence is used to describe the random phase behavior of the medium. In recent work, results for the numerical simulation of phase turbulence over a narrow region of space implemented by placing a planar aperture representing a (narrow) random phase screen were presented. Results are presented pertinent to extended phase screens (via multiple random-phase apertures) through which an incident Gaussian beam propagates incrementally via alternate phase transmission and diffraction along the propagation path. Additionally, for profiled electromagnetic waves (such as Gaussian), the scintillation index is evaluated for extended phase turbulence, and finally, fringe visibility due to the interference of double-Gaussian beams passing through extended turbulence is examined.

Beam Spreading of Partially Coherent Beams Propagating through Turbulence Atmospheric in Boundary Layer

The cross-spectral density function of the partially coherent beam on 1.06μm is extended based on the generalized Huygens-Fresnel principle by using the Gaussian Schell-mode(GSM) and the modified Frehlich spectrum. And on the analysis of variation of the beam spreading radius w with the initial emission radius w0, zenith angle θ and propagating distance z, the intensity distribution and beam spreading of GSM beam through atmospheric boundary layer turbulence are obtained under different distance. The results show that the beam spreading can be reduced at long distance for the suitable w0 according to the inflexion value of the curve. As well as, simulation results demonstrate that the modified Frehlich spectrum and the modified von Karman spectrum have little difference on the beam spreading for partially coherent beam propagating in atmospheric boundary layer turbulence.

Detection probability of single photons in a slant path atmospheric turbulence communication channel

Using Rytov approximation and modified von Karman spectrum model of the index-of-refraction, the detection probability of single-photon beam propagation in a atmospheric turbulence communication channel is investigated and developed. In this research, the single-photon beam is assumed as a pulse beam which has an initial Gaussian temporal shape of the pulse and a Laguerre–Gaussian fundamental-model spatial distribution. It is found that in order to obtain the messages probability greater than or equal 0.1, we should encode and dispatch 66680 photons in identical information carriers at the transmitting side, and the radius of the detector at the receiving plane must be at least up to 0.4 m when the photons propagate in a turbulent atmosphere communication channel.

Optical pulse propagation through a slab of random medium

Tractable analytic expressions are developed for the expected broadening that a Gaussian space-time optical pulse experiences as it propagates through a slab of random medium confined to a portion of the propagation path between the input and output planes. The analytic results developed in this paper are based on the modified von Karman spectrum for refractive index fluctuations and the Rytov method which restricts the validity of the results to the weak optical turbulence regime. It is further assumed that the Gaussian beam is collimated and that the Gaussian pulse is narrowband with respect to the carrier frequency which, for optical frequencies, requires pulse widths greater than 20 fs. The results in this paper are given for both near and far fields and it is shown that when the thickness of the slab of random medium is the total propagation distance, the results given in this paper agree with the results for an extended random medium. Examples are given for unmanned air vehicle (UAV) to low Earth orbit (LEO) satellite and LEO-to-LEO crosslinks.

Two-frequency mutual coherence function of a Gaussian beam pulse in weak optical turbulence: an analytic solution

Pulse propagation in a random medium is studied through the calculation of the two-frequency mutual coherence function. An exact integral representation is formulated for the two-frequency mutual coherence function of a Gaussian beam pulse propagating in a weakly fluctuating random medium. Based on the modified von Karman spectrum for refractive-index fluctuations, an analytic approximation to the integral representation is presented and compared with exact numerical results.

Spatial coherence of a Gaussian-beam wave in weak and strong optical turbulence

A generalized Huygens–Fresnel integral, valid for optical wave propagation through random inhomogeneities in the presence of any complex optical system characterized by an ABCD ray matrix, is used to derive a general expression for the mutual coherence function (MCF) associated with a Gaussian-beam wave in the weak-fluctuation regime. The mean irradiance obtained from this expression shows excellent agreement with all known asymptotic relations. By introducing a pair of effective beam parameters Θt and Λt that account for additional diffraction on the receiving aperture, resulting from turbulence, the normalized MCF and the related degree of coherence are formally extended into the regime of strong fluctuations. Results for the normalized MCF from this heuristic approach compare well with numerical calculations obtained directly from the formal solution of the parabolic equation. Also, the implied spatial coherence length from this analysis in moderate-to-strong-fluctuation regimes generally agrees more closely with numerical solutions of the parabolic equation than do previous approximate solutions. All calculations are based on the modified von Karman spectrum for direct comparison with established results.

Analytic Expressions for the Wave Structure Function Based on a Bump Spectral Model for Refractive Index Fluctuations

Abstract A recently developed analytical spectral model for refractive index fluctuations, showing the characteristic ‘bump’ at high wave-numbers, is used to derive new expressions for the wave structure function associated with the propagation of infinite plane waves and spherical waves through isotropic and homogeneous turbulence. For computational ease, simple interpolation formulae are also developed for the wave structure function based on this new spectral model as well as on the more familiar modified von Karman spectrum. These interpolation formulae permit accurate numerical estimates for the wave structure function at all transverse separation distances up to the outer scale. Results based on the new bump spectrum are in excellent agreement with numerical values generated by the Hill spectrum.

Numerical evaluation of the mutual coherence function of a laser beam in atmospheric turbulence

Using transport methods we have computed the mutual coherence function of a laser beam propagating in turbulence with a modified von Karman spectrum for the index of refraction fluctuations, including a parametric study of the effect of varying beam size, focal length, and the properties of the turbulence.

Beam Spreading in a Turbulent Medium

The Kolmogorov spectrum with its associated structure functions is generally used to study wave propagation in turbulent media. It is known, however, that this spectrum does not accurately represent the real atmosphere outside the inertial range. In this paper, the broadening of a focused gaussian beam is calculated, using instead a modified von Karman spectrum better to describe the medium. The Born approximation is also used, because it follows naturally from the use of this spectrum. The dependence of beam spreading on the outer scale of turbulence is obtained and the results generally reduce to those corresponding to the Kolmogorov spectrum and the Rytov approximation, which in fact do not depend on the outer scale of turbulence. The results can be applied to arbitrary source configurations or extended to include the calculation of other field quantities of interest.