Partially coherent elegant Hermite–Gaussian beam in turbulent atmosphere

Based on the extended Huygens–Fresnel integral, analytical formulas for the cross-spectral density, mean-squared beam width and angular spread of a partially coherent elegant Hermite–Gaussian (HG) beam in turbulent atmosphere are derived. The evolution properties of the average intensity, spreading and directionality of a partially coherent elegant HG beam in turbulent atmosphere are studied numerically. It is found that the partially coherent elegant HG beam with smaller initial coherence width, larger beam order and longer wavelength is less affected by the atmospheric turbulence. Compared to the partially coherent standard HG beam, the partially coherent elegant HG beam is less affected by turbulence under the same condition. Furthermore, it is found that there exist equivalent partially coherent standard and elegant HG beams, equivalent fully coherent standard and elegant HG beams, and an equivalent Gaussian–Schell-model beam may have the same directionality as a fully coherent Gaussian beam whether in free space or in turbulent atmosphere. Our results can be utilized in short and long atmospheric optical communication systems.     

Intensity fluctuations of partially coherent laser beam arrays in?weak atmospheric turbulence

The intensity fluctuation of a partially coherent laser beam array is examined. For this purpose, the on-axis scintillation index at the receiver plane is analytically formulated via the extended Huygens–Fresnel diffraction integral in conditions of weak atmospheric turbulence. The effects of the propagation length, number of beamlets, radial distance, source size, wavelength of operation and coherence level on the scintillation index are investigated for a horizontal propagation path. It is found that, regardless of the number of beamlets, the scintillation index always rises with an increasing propagation length. If laser beam arrays become less coherent, the scintillation index begins to fall with growing source sizes. Given the same level of partial coherence, slightly less scintillations will occur when the radial distance of the beamlets from the origin is increased. At partial coherence levels, lower scintillations are observed for larger numbers of beamlets. Both for fully and partially coherent laser beam arrays, scintillations will drop on increasing wavelengths.     

Generalized expression for optical source fields

A generalized optical beam expression is developed that presents the majority of the existing optical source fields such as Bessel, Laguerre–Gaussian, dark hollow, bottle, super Gaussian, Lorentz, super-Lorentz, flat-topped, Hermite–sinusoidal-Gaussian, sinusoidal-Gaussian, annular, Gauss–Legendre, vortex, also their higher order modes with their truncated, elegant and elliptical versions. Source intensity profiles derived from the generalized optical source beam fields are checked to match the intensity profiles of many individual known beam types. Source intensities for several interesting beam combinations are presented. Our generalized optical source beam field expression can be used to examine both the source characteristics and the propagation properties of many different optical beams in a single formulation.     

Nucleophilic Iron Complexes in Proton‐Transfer Catalysis: An Iron‐Catalyzed Dimroth Cyclocondensation

The nucleophilic iron complex Bu₄N[Fe(CO)₃(NO)] (TBA[Fe]) is an active catalyst in C?H‐amination but also in proton‐transfer catalysis. Herein, we describe the successful use of this complex as a proton‐transfer catalyst in the cyclocondensation reaction between azides and ketones to the corresponding 1,2,3‐triazoles. Cross‐experiments indicate that the proton‐transfer catalysis is significantly faster than the nitrene‐transfer catalysis, which would lead to the C?H amination product. An example of a successful sequential Dimroth triazole–indoline synthesis to the corresponding triazole‐substituted indolines is presented.     

Synthesis and magnetic characterization of Zn0.6Ni0.4Fe2O4 nanoparticles via a polyethylene glycol-assisted hydrothermal route

Zn-doped nickel ferrite nanoparticles (Zn_0.6Ni_0.4Fe₂O₄) have been prepared via a surfactant, polyethylene glycol assisted hydrothermal route. X-ray powder diffractometry (XRD), Fourier transform infrared spectroscopy, transmission electron microscopy (TEM), and vibrating scanning magnetometry (VSM) were used for the structural, morphological, and magnetic characterizations of the product, respectively. TEM analysis revealed that the nanoparticles have a narrow size distribution, with average particle size of 15±1 nm, which agrees well with the XRD based estimate of 14±2 nm. The absence of saturation and remanent magnetization, and coercivity in the high temperature region of the M-H curve and non-zero magnetic moments indicate superparamagnetism of the nanoparticles with a canted spin structure. The appearance of a peak on the temperature-dependent zero-field cooling magnetization curve at ∼190 K indicates the blocking temperature of the sample.     

Arbitrary laser beam propagation in free space

The propagation of arbitrary laser beams in free space is examined. For this purpose, starting with an incident field of arbitrary field distribution, the intensity at the receiver plane is formulated via Huygens Fresnel diffraction integral. Arbitrary source field profile is produced by decomposing the source into incremental areas (pixels). The received field through the propagation in free space is found by superposing the contributions from all source incremental areas. The proposed method enables us to evaluate the received intensity originating from any type of source field. Using the arbitrary beam excitation, intensity of various laser beams such as cos-Gaussian, cosh-Gaussian, general type beams are checked to be consistent with the already existing results in literature, and the received intensity distributions are obtained for some original arbitrary beam field profiles. Our received intensity formulation for the arbitrary source field profiles presented in this paper can find application in optics communication links, reflection from rough surfaces, optical cryptography and optical imaging systems.     

Propagation properties of anomalous hollow beams in a turbulent atmosphere

Propagation of circular and elliptical anomalous hollow beams in a turbulent atmosphere is investigated in detail. Based on the extended Huygens–Fresnel integral, analytical formulae for the average irradiance of circular and elliptical anomalous hollow beams propagating in a turbulent atmosphere are derived. The irradiance and spreading properties of circular and elliptical anomalous hollow beams in a turbulent atmosphere and in free space are studied numerically. It is found that circular and elliptical anomalous hollow beams at short propagation distance in turbulent atmosphere have similar propagation properties to those of free space, while at long propagation distance, circular and elliptical anomalous hollow beams eventually become circular Gaussian beams in a turbulent atmosphere, which is much different from their propagation properties in free space. The conversion from an anomalous hollow beam to a circular Gaussian beam becomes quicker and the beam spot spreads more rapidly for a larger structure constant, a shorter wavelength and a smaller waist size of the initial beam.     

Letter: Riemannian Metric of the Invariance Quantum Group of the Fermion Algebra

We calculate the bi-invariant metric of FIO(2), the inhomogeneous invariance quantum group of the fermion algebra. We find that this metric is identical to that of the bi-invariant metric of GL(2, R) ⁺ × SU (1, 1). However, the quantum group manifold is restricted to a region of the GL(2, R) manifold.     

Low temperature synthesis and characterization of Mn3O4 nanoparticles

Heating hydrous manganese (II) hydroxide gel at 85 °C for 12 hours produces Mn₃O₄ nanoparticles. They were characterized by X-ray powder diffraction (XRD) and infrared spectroscopy (FTIR). The particle size estimated from the SEM and X-ray peak broadening is approximately 32 nm, showing them to be nanocrystalline. EPR measurements confirm a typical Mn²⁺signal with a highly resolved hyperfine structure.      

Synthesis and magnetic properties of octahedral ferrite Ni χ Co1−χ Fe2O4 nanocrystals

A series of Ni doped cobalt ferrite compounds with the formula Ni _χ Co_1−χ Fe₂O₄ where x=0, 0.2, 0.4, 0.6, 0.8, and 1.0 were prepared using a hydrothermal method and subsequently sintered/annealed at 600 °C for 3 h. The influence of the Ni content on the lattice parameter, a, stretching vibration and the magnetization of specimens were subsequently studied. XRD and FTIR were used to investigate structure and composition variations. All samples were found to have a cubic spinel structure. SEM was used to study morphological variations. The results indicate that the average particle sizes are between 30–35 nm with a narrow size distribution along with nanocrystals forming of regular octahedrons. A decrease in the peak to peak line width and increase in resonance field with increasing Ni content were observed from ESR measurements. Based on ESR results, a core-shell type of formation was proposed where the core is made up of undoped CoFe₂O₄ and the shell is Ni²⁺ doped CoFe₂O₄.