Propagation characteristics of partially coherent anomalous elliptical hollow Gaussian beam propagating through atmospheric turbulence along a slant path

Based on the extended Huygens–Fresnel principal and the Wigner distribution function, the root mean square (rms) angular width and propagation factor (M²-factor) of partially coherent anomalous elliptical hollow Gaussian (PCAEHG) beam propagating through atmospheric turbulence along a slant path are studied in detail. Analytical formulae of the rms angular width and M²-factor of PCAEHG beam are derived. Our results show that the rms angular width increases with increasing of wavelength and zenith angle and with decreasing of transverse coherence length, beam waist sizes and inner scale. The M²-factor increases with increasing of zenith angle and with decreasing of wavelength, transverse coherence length, beam waist sizes and inner scale. The saturation propagation distances (SPDs) increase as zenith angle increases. The numerical calculations also indicate that the SPDs of rms angular width and M²-factor for uplink slant paths with zenith angle of π/12 are about 0.2 and 20 km, respectively.     

Propagation properties of partially coherent dark hollow beam in inhomogeneous atmospheric turbulence

Abstract

Propagation properties of a partially coherent dark hollow beam (PC-DHB) in inhomogeneous atmospheric turbulence are studied in detail. Analytical formulae for the root-mean-square (rms) spatial width, rms angular width, M²-factor of PC-DHB in inhomogeneous turbulence are derived based on the extended Huygens–Fresnel integral. It is found that PC-DHB spreads in inhomogeneous turbulence more rapidly than the free space, and the saturation propagation distances (SPDs) of relative spatial and angular spreadings for uplink slant paths with zenith angles of 45° or less are about 5 and 0.6 km, respectively. M²-factor of PC-DHB in turbulence depends on beam order, waist width, inner scale of the turbulence and the SPD of the normalized M²-factor for the propagation with zenith angles of 45° or less is about 30 km. Our results are useful for the free space optical communications and the beam propagation in the slant path.     

Kurtosis parameter K of arbitrary electromagnetic beams propagating through non-Kolmogorov turbulence

General analytical formulae for the kurtosis parameters K (K parameters) of the arbitrary electromagnetic (AE) beams propagating through non-Kolmogorov turbulence are derived, and according to the unified theory of polarization and coherence, the effect of degree of polarization (DOP) of an electromagnetic beam on the K parameter is studied. The analytical formulae can be given by the second-order moments and fourth-order moments of the Wigner distribution function for AE beams at source plane, the two turbulence quantities relating to the spatial power spectrum, and the propagation distance. Our results can also be extended to the arbitrary beams and the arbitrary spatial power spectra of Kolmogorov turbulence or non-Kolmogorov turbulence. Taking the stochastic electromagnetic Gaussian Schell-model (SEGSM) beam as an example, the numerical examples indicate that the K parameters of a SEGSM beam in non-Kolmogorov turbulence depend on propagation distance, the beam parameters and turbulence parameters. The K parameter of a SEGM beam is more sensitive to effect of turbulence with smaller inner scale and generalized exponent parameter. A non-polarized light has the strongest ability of resisting turbulence (ART), however, a fully polarized SEGSM beam has the poorest ART.     

Evolution properties of partially coherent four-petal Gaussian beams in oceanic turbulence

Based on the extended Huygens–Fresnel integral formula, the analytical expressions for partially coherent four-petal Gaussian beam propagating in oceanic turbulence are derived, and the influences of coherence length, beam order N and the parameters of oceanic turbulence (the rate of dissipation of turbulent kinetic energy per unit mass of fluid, the rate of dissipation of mean square temperature and the relative strength of temperature and salinity fluctuations) on average intensity properties are investigated using numerical examples in detail. The results show that the beam with the higher beam order N or coherence length will lose its initial four-petal profiles slower. It is also indicated that the beam will evolve into a Gauss-like beam more rapidly with increasing oceanic turbulence strength. The results have the potential application in underwater laser communication using a partially coherent four-petal Gaussian beam.     

Analysing the behaviour of partially coherent divergent Gaussian beams propagating through oceanic turbulence

Theoretical study of propagation behaviour of partially coherent divergent Gaussian beams through oceanic turbulence has been performed. Based on the previously developed knowledge of propagation of a partially coherent beam in atmosphere, the spatial power spectrum of the refractive index of ocean water, extended Huygens–Fresnel principle and the unified theory of coherence and polarization, analytical formulas for cross-spectral density matrix elements are derived. The analytical formulas for intensity distribution, beam width and spectral degree of coherence are determined by using cross-spectral density matrix elements. Then, the effects of some source factors and turbulent ocean parameters on statistical properties of divergent Gaussian beam propagating through turbulent water are analysed. It is found that beam’s statistical propagation behaviour is affected by both environmental and source parameters variations.     

Propagation properties of a partially coherent radially polarized beam in atmospheric turbulence

Based on the extended Huygens–Fresnel integral, second-order moments of the Wigner distribution function of a partially coherent radially polarized beam propagating through atmospheric turbulence are derived. Besides, propagation properties such as the mean-squared beam width, angular width, effective radius of curvature, beam propagation factor and Rayleigh range can also be obtained and calculated numerically. It is shown that the propagation properties are dependent on the spatial correlation length, refraction index structure constant and propagation distance.     

M2-factor of truncated partially coherent beams propagating through atmospheric turbulence

A method of studying the M2-factor of truncated partially coherent beams both in free space and in turbulence is proposed, i.e., the method of the window function being expanded into a finite sum of complex-valued Gaussian functions. Taking the Gaussian Schell-model (GSM) beam as a typical example of partially coherent beams, the analytical formula of the M2-factor of truncated GSM beams propagating through atmospheric turbulence is derived. It is shown that the M2-factor decreases as the truncation parameter δ and the coherence parameter α increase. However, the M2-factor in turbulence is more sensitive to δ than that in free space. On the other hand, the M2-factor of truncated partially coherent beams with smaller δ is more affected by turbulence. In addition, the effect of turbulence on the M2-factor of truncated GSM beams is less sensitive to the coherence parameter α than that of nontruncated GSM beams.     

Focal shift of a focused partially coherent Laguerre-Gaussian beam of all orders

Abstract

We explore the focusing properties of a partially coherent Laguerre–Gaussian (LG) beam of all orders, particularly the focal shift (i.e. the shift of the actual focal plane away from the geometrical focal plane). We derive the analytical expressions for the average intensity and the effective beam width of a focused partially coherent LG beam, and we adopt the minimum effective beam width instead of the conventional maximum on-axis intensity to determine the actual focal plane. It is found that the focused beam shape, minimum effective beam width and the focal shift of a focused partially coherent LG beam are determined by its initial coherence width, radial mode order and azimuthal mode order (i.e. topological charge) together. Our results may be useful for optical trapping and micro-fabrication, where precise focal position and prescribed beam shape are required.     

Propagation properties of a partially coherent anomalous hollow vortex beam in uniaxial crystal orthogonal to the optical axis

The concept of a partially coherent anomalous hollow vortex beam generated by a Schell-model source was introduced in this paper. Next, the analytical expressions of a partially coherent anomalous hollow vortex beam propagating in a uniaxial crystal orthogonal to the optical axis were derived, and the evolution properties of a partially coherent anomalous hollow vortex beam propagating in a uniaxial crystal were illustrated using numerical examples. Finally, the influences of the uniaxial crystal and the beam parameters on the spreading properties of partially coherent anomalous hollow vortex beam were analysed in detail.     

多束部分相干光通过强湍流对光强闪烁的影响

在Rytov方差的基础上,利用Andrews的唯像闪烁模型,推导出部分相干光通过强大气湍流后其对数光强起伏方差的公式,并用此公式对部分相干光通过强湍流后给光强闪烁造成的影响进行了仿真。其结果表明,当光源的相干性变差,即变为部分相干光后,对数光强起伏方差变小;当采用多束部分相干光时,接收面上光强起伏方差得到明显改善,而且光束越多,改善越明显。     

Coupling characteristics and kurtosis parameter of partially coherent beams in turbulent atmosphere

Coupling properties and kurtosis parameter (K parameter) of arbitrary beams propagating through atmospheric turbulence are investigated. A correlation factor (C⁴-factor) is introduced to describe the influence of turbulence on coupling characteristics. The general analytical expression for C⁴-factor of arbitrary beams in atmospheric turbulence is derived. It is shown that C⁴-factor of arbitrary beams in the turbulent atmosphere depends on the initial second-order moments and fourth-order moments and turbulence quantities. Taking the partially coherent anomalous elliptical hollow Gaussian (PCAEHG) beam as an example, we can obtain that C⁴-factor decreases as structure constant of the refractive index fluctuations and inner scale increase, and waist width and transverse coherence length decrease when z?>?5?km. Moreover, K parameter of PCAEHG beam in turbulent atmosphere converges to 2 when propagation distance is large enough. It indicates that the profile of PCAEHG beams in turbulent atmosphere finally evolves into fundamental Gaussian distribution.     

Scintillation index and bit error rate of hollow Gaussian beams in atmospheric turbulence

Based on the Huygens–Fresnel principle and Rytov method, the on-axis scintillation index is derived for hollow Gaussian beams (HGBs) in weak turbulence. The relationship between bit error rate (BER) and scintillation index is found by only considering the effect of atmosphere turbulence based on the probability distribution of intensity fluctuation, and the expression of the BER is obtained. Furthermore, the scintillation and the BER properties of HGBs in turbulence are discussed in detail. The results show that the scintillation index and BER of HGBs depend on the propagation length, the structure constant of the refractive index fluctuations of turbulence, the wavelength, the beam order and the waist width of the fundamental Gaussian beam. The scintillation index, increasing with the propagation length in turbulence, for the HGB with higher beam order increases more slowly. The BER of the HGBs increases rapidly against the propagation length in turbulence. For propagating the same distance, the BER of the fundamental Gaussian beam is the greatest, and that of the HGB with higher order is smaller.     

Synthesis and characterization of ZrO2 hollow spheres

ZrO₂ hollow microspheres with the average diameter of about 500 nm and the shell thickness of about 50 nm were synthesized by a facile technique using carbon spheres as templates. The corresponding ZrO₂ hollow microspheres were obtained by calcining the precursors of C-Zr(OH)₄ core-shell heterostructures, which were synthesized with the precipitation of ZrCl₄ solution with aqueous ammonia on the surface of colloid carbons. SEM, XRD, TGA and BET were used to characterize the composition, morphology, size and crystal structure of synthesized products. The effects of ultrasonic dispersion and separation process on the hollow spheres were studied, and the surfactant PEG-1000 was added to tune the shell structure of synthesized ZrO₂ hollow spheres.     

Growth and characterization of group-III impurity-doped semiconducting BaSi2 films grown by molecular beam epitaxy

Ga- or In-doped BaSi₂ films were grown on Si(111) by molecular beam epitaxy (MBE). The Ga-doped BaSi₂ showed n-type conductivity. The electron concentration and resistivity of the Ga-doped BaSi₂ depended on the Ga temperature; however, the electron concentration and resistivity could not be controlled properly. In contrast, the In-doped BaSi₂ showed p-type conductivity and its hole concentration was controlled in the range between 10¹⁶ and 10¹⁷ cm^− 3 at RT.     

钴铁氧体/聚吡咯复合材料的制备及电磁性能

首先采用溶胶-凝胶法制备钴铁氧体,再使用水热原位合成钴铁氧体(CoFe₂O₄,CFO)/聚吡咯(polypyrrole,PPy)新型复合材料。采用X射线衍射仪(XRD)分析样品的相结构、扫描电子显微镜(SEM观察样品微观形貌、振动样品磁场计(VSM)测试样品磁性能表征样品磁性能、样品的电磁参数采用矢量网络分析仪分析,计算获得样品在(8～12)GHz频率范围内的反射损耗。结果表明:在以酒石酸为络合剂、pH=5左右、经650 ℃热处理,得到结晶度良好的尖晶石结构钴铁氧体,平均粒径为350 nm;原位聚合后得到的钴铁氧体/聚吡咯复合材料表现出良好的吸波性能,在涂层厚度1.5 mm,PPy含量为6%时,吸波性能最佳,在频率为8.66 GHz处达到-11.05 dB,小于-5 dB的频段范围为(7.49~11.43)GHz,其可作为一种轻质、宽频的雷达波吸收剂来使用。     

Synthesis and characterization of Al2O3 hollow spheres

This paper presents a novel technique to create Al₂O₃ hollow spherical nanoparticles. It used Al(OH)₃ which was synthesized with Al₂(SO₄)₃ and NaOH, and the C-Al(OH)₃ core-shell nanoparticle as intermediate phases. The Al₂O₃ hollow spheres were achieved by the calcination of the carbon cores and the dehydration of Al(OH)₃. The chemical composition, morphology, size and superficial crystal structure of the nanoparticles were characterized with TEM, XRD, TGA, FTIR and BET. The result shows that the average diameter of the C-Al(OH)₃ core-shell nanoparticles is about 25 nm, the thickness of the Al₂O₃ shell is about 5 nm and the surface area is 215.2 m²/g. The procedure for the formation of Al₂O₃ hollow nanoparticles is discussed in details.     

Effect of assist ion beam voltage on intrinsic stress and optical properties of Ta2O5 thin films deposited by dual ion beam sputtering

The optical properties and intrinsic stress of Ta₂O₅ thin films deposited by dual ion beam sputtering (DIBS) were studied as a function of the assist ion beam voltage (250-650 V). When the assist ion beam voltage was in the range of 350-450 V, the transmittance at the quarter-wave point reached its highest value (lowest absorption). The refractive index increased to 2.185 as the assist ion beam voltage increased from 250 to 350 V, but decreased as the assist ion beam voltage was further increased from 350 to 650 V.     

Promotion effect of nanosized Pt,RuO2 and NiOx loading on visible light-driven photocatalysts K4Ce2M10O30 (M = Ta,Nb) for hydrogen evolution from water decomposition

Metal oxide photocatalysts K₄Ce₂M₁₀O₃₀ (M = Ta, Nb) capable of responding to visible light were synthesized by conventional high temperature solid-state reaction. The photocatalysts have an appropriate band gap energy ca. 1.8–2.3 eV and excellent chemical potential level to evolve H₂ from aqueous solutions containing a sacrificial electron donor (Na₂SO₃) under visible light irradiation (λ>420 nm) without any co-catalyst. When they were loading with Pt, RuO₂ and NiO_x, the activities for evolving H2 were prompted markedly. By SEM and TEM investigations, it can be seen that these loading K₄Ce₂M₁₀O₃₀ (M = Ta, Nb) in diameter of about 10–30nm particles, especially the NiO_x loading even formed double layered structure with metal nickel (Ni) and metal oxide (NiO). The reasons for the increasing activities after these loading electron migrating from the conduction band of K₄Ce₂M₁₀O₃₀ (M =Ta, Nb) to the Pt, RuO₂ and NiO_x nanoparticles, which function as H₂ production sites on the surface of catalysts. The same phenomenon appears on the solid solution K₄Ce₂Ta_{10 –x}Nb_xO30 (x = 0–10) with loading RuO₂.