scholarly journals Influence of a Turbulent Jet Engine Exhaust on Laguerre-Gaussian Correlated Shell-Model Beams

2021 ◽  
Author(s):  
Hassan Nabil ◽  
Adil A. Balhamri ◽  
Abdelmajid Belafhal
Keyword(s):  
Spectral Density ◽  
Shell Model ◽  
Wigner Distribution ◽  
Beam Width ◽  
Propagation Distance ◽  
Spectral Density Function ◽  
Engine Exhaust ◽  
Jet Engine ◽  
Degree Of Coherence ◽  
Analytical Formulae

Abstract In this paper, we investigated the influence of a turbulence jet engine exhaust on Laguerre-Gaussian correlated shell-model beams (LGSMBs). The analytical formulae of the cross-spectral density function as well as the beam width are derived based on the Huygens-Fresnel diffraction principle and the second-order moments of the Wigner distribution function, respectively. From our main results, the spectral density, the degree of coherence and beam width of a LGSMB are analyzed numerically. It is found that for high source coherence width, the spectral density changes gradually its profiles from circular to elliptical shape at short propagation distance, then the beam transforms into a well like Gaussian at long propagation distance. Although, at very short propagation distance, the beam becomes an elliptical dark hollow if the source coherence is very lower. Also, the numerical results show that the LGSMB spreads more rapidly than the GSMB in the same conditions.

scholarly journals Statistical Characteristics of a Twisted Anisotropic Gaussian Schell-Model Beam in Turbulent Ocean

Photonics ◽  
2020 ◽  
Vol 7 (2) ◽  
pp. 37
Author(s):  
Yonglei Liu ◽  
Yuefeng Zhao ◽  
Xianlong Liu ◽  
Chunhao Liang ◽  
Lin Liu ◽  
...  
Keyword(s):  
Spectral Density ◽  
Communication Systems ◽  
Beam Width ◽  
Propagation Distance ◽  
Spectral Density Function ◽  
Statistical Characteristics ◽  
Beam Spot ◽  
Beam Shape ◽  
Oceanic Turbulence ◽  
Twist Factor

The analytical expression of the cross-spectral density function of a twisted anisotropic Gaussian Schell-model (TAGSM) beam transmitting in turbulent ocean is derived by applying a tensor method. The statistical properties, including spectral density, the strength of twist and beam width of the propagating beam are studied carefully through numerical examples. It is demonstrated that the turbulence of ocean has no effect on the rotation direction of the beam spot during propagation. However, the beam shape will degrade into a Gaussian profile under the action of oceanic turbulence with sufficiently long propagation distance, and a beam with a larger initial twist factor is more resistant to turbulence-induced degeneration. As oceanic turbulence becomes stronger, the beam spot spreads more quickly while the twist factor drops more rapidly upon propagation. The physical mechanisms of these phenomena are addressed in detail. The obtained results will be helpful in optical communication systems underwater.

scholarly journals Propagation of a Modified Complex Lorentz–Gaussian-Correlated Beam in a Marine Atmosphere

Photonics ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 82
Author(s):  
Baoyin Sun ◽  
Han Lü ◽  
Dan Wu ◽  
Fei Wang ◽  
Yangjian Cai
Keyword(s):  
Spectral Density ◽  
Wigner Distribution ◽  
Structure Constant ◽  
Beam Width ◽  
Intensity Pattern ◽  
Second Order Statistics ◽  
Scale Size ◽  
New Type ◽  
Inner Scale ◽  
Analytical Expressions

In this paper, we study the second-order statistics of a modified complex Lorentz–Gaussian-correlated (MCLGC) beam, which is a new type of partially coherent beam capable of producing an Airy-like intensity pattern in the far field, propagation through marine atmospheric turbulence. The propagation formula of spectral density is derived by the extended Huygens–Fresnel integral, which could explicitly indicate the interaction of turbulence on the beams’ spectral density under propagation. The influences of the structure constant of the turbulence, initial coherence width and wavelength on the spectral density are investigated in detail through numerical examples. In addition, analytical expressions for the r.m.s beam width, divergence angle and M2 factor of the MCLGC beam in the marine turbulence are also derived with the help of the Wigner distribution function. The results reveal that the beam spreads much faster, and the M2 factor deteriorates severely with the increase of the structure constant and the decrease of the inner scale size, whereas the outer scale size has little effect on these two quantities.

ON THE SPECTRAL MEASURES OF SOME WEAKLY STATIONARY SEQUENCES INVOLVING RANDOMLY SPACED OBSERVATIONS

2012 ◽  
Vol 12 (01) ◽  
pp. 1150004
Author(s):  
RICHARD C. BRADLEY
Keyword(s):  
Spectral Density ◽  
Density Function ◽  
Spectral Density Function ◽  
Strong Mixing ◽  
Spectral Measures ◽  
Mixing Conditions ◽  
Stationary Sequences ◽  
Second Moments ◽  
The Central Limit Theorem ◽  
Complex Valued

In an earlier paper by the author, as part of a construction of a counterexample to the central limit theorem under certain strong mixing conditions, a formula is given that shows, for strictly stationary sequences with mean zero and finite second moments and a continuous spectral density function, how that spectral density function changes if the observations in that strictly stationary sequence are "randomly spread out" in a particular way, with independent "nonnegative geometric" numbers of zeros inserted in between. In this paper, that formula will be generalized to the class of weakly stationary, mean zero, complex-valued random sequences, with arbitrary spectral measure.

scholarly journals Characterization and Design of Functional Quasi-Random Nanostructured Materials Using Spectral Density Function

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Shuangcheng Yu ◽  
Yichi Zhang ◽  
Chen Wang ◽  
Won-kyu Lee ◽  
Biqin Dong ◽  
...  
Keyword(s):  
Spectral Density ◽  
Density Function ◽  
Design Methodology ◽  
Light Trapping ◽  
Spectral Density Function ◽  
Particle Type ◽  
Bottom Up ◽  
Design Representation ◽  
Material Systems ◽  
Channel Type

Quasi-random nanostructures are playing an increasingly important role in developing advanced material systems with various functionalities. Current development of functional quasi-random nanostructured material systems (NMSs) mainly follows a sequential strategy without considering the fabrication conditions in nanostructure optimization, which limits the feasibility of the optimized design for large-scale, parallel nanomanufacturing using bottom-up processes. We propose a novel design methodology for designing isotropic quasi-random NMSs that employs spectral density function (SDF) to concurrently optimize the nanostructure and design the corresponding nanomanufacturing conditions of a bottom-up process. Alternative to the well-known correlation functions for characterizing the structural correlation of NMSs, the SDF provides a convenient and informative design representation that maps processing–structure relation to enable fast explorations of optimal fabricable nanostructures and to exploit the stochastic nature of manufacturing processes. In this paper, we first introduce the SDF as a nondeterministic design representation for quasi-random NMSs, as an alternative to the two-point correlation function. Efficient reconstruction methods for quasi-random NMSs are developed for handling different morphologies, such as the channel-type and particle-type, in simulation-based microstructural design. The SDF-based computational design methodology is illustrated by the optimization of quasi-random light-trapping nanostructures in thin-film solar cells for both channel-type and particle-type NMSs. Finally, the concurrent design strategy is employed to optimize the quasi-random light-trapping structure manufactured via scalable wrinkle nanolithography process.

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