Beam quality of radial Gaussian Schell-model array beams

Taking the Rayleigh range z_R and the M²-factor as the characteristic parameters of beam quality, the beam quality of radial Gaussian Schell-model (GSM) array beams is studied. The analytical expressions for the z_R and the M²-factor of radial GSM array beams are derived. It is shown that for the superposition of the cross-spectral density function z_R is longer and the M²-factor is lower than that for the superposition of the intensity. For the two types of superposition, z_R increases and the M²-factor decreases with increase in beam coherence parameter, and both z_R and the M²-factor increase with increase in inverse radial fill-factor. For the superposition of the cross-spectral density function, z_R increases and the M²-factor decreases with increase in beam number, while for the superposition of the intensity both the z_R and M²-factor are independent of the beam number.     

Investigation on z-scan experiment by use of partially coherent beams

Z-Scan experiment using partially coherent beams is investigated theoretically. We derive the expression for the cross-spectral density of the Gaussian Schell-model (GSM) beam passing through the nonlinear thin sample. Then the influences of the aperture radius and the spatial degree of coherence on the z-scan curves are analyzed. We find that transmittance difference ΔT_p-v between the peak and valley in z-scan curves decreases gradually with the increment of the aperture radius, which is similar to the case of the fully coherent beams. It is also shown that ΔT_p-v is getting bigger with the increment of the spatial degree of coherence α₀, and when α₀ is larger than a certain value, ΔT_p-v becomes almost unchanged. The results show that the z-scan experiment with partially coherent beams may provide a feasible method for measuring the spatial degree of coherence.     

Propagation of random electromagnetic beams through axially nonsymmetrical optical systems

When random electromagnetic beams passing through axially nonsymmetrical ABCD optical systems, the analytical formula for the transformation of the elements of 2 × 2 cross-spectral density matrix is obtained with the help of vector integration. We derive analytical expressions of the spectral degree of polarization, the spectral degree of coherence, and the spectral density in any output plane z > 0. Some numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams propagating through such optical systems.     

Modulation in the statistical properties of stochastic electromagnetic beams through an electromagnetic induced transparency atomic vapor

We report analytical expressions for the elements of the 2 × 2 cross-spectral density matrix of a stochastic electromagnetic beam passing through an electromagnetic induced transparency (EIT) atomic vapor. By use of the derived formulas the changes in the spectral density, the spectral degree of coherence, and the spectral degree of polarization of such a beam on propagation can be studied in detail. Numerical examples show that the statistical properties of the stochastic electromagnetic beam can be modulated by the Rabi frequency of the control light when the beam propagates through the EIT atomic vapor.     

Steady state and transient self-interaction of a laser beam in a strongly ionized moving plasma

The steady state and transient self-interaction of a laser beam with a strongly ionized plasma flowing transverse to the direction of propagation have been investigated by a phenomenological approach using perturbation theory, WKB and paraxial ray approximations. The effect of the transverse motion of the plasma has been included by a convection term in the energy balance equation and is found to result in the non-symmetrical heating of electrons. As a result the beam is shifted towards the direction of transverse flow of the plasma by an amount that increases with the flow velocity. The extent of asymmetry in self-focusing along the transverse directions is, however very small. In a typical case of 7.6×10⁵ watt laser of ω=10⁴ GHz and initial beam widthr ₀=0.05 cm the transverse shiftx _p=0.1r ₀ is predicted in a distance of propagationz=0.34 cm in a strongly ionized plasma of electron densityN _e=10¹⁶ cm^?3 and transverse flow velocityW ₀=10⁷ cm/sec.     

Low temperature sintering of sub-stoichiometric Ni-Cu-Zn ferrites: Shrinkage, microstructure and permeability

We have studied sub-stoichiometric Ni-Cu-Zn ferrites with iron deficiency (i.e., <50mol% Fe₂O₃) of composition Ni_0.20Cu_0.20Zn_0.60+zFe_2−zO_4−(z/2) with 0≤z≤0.06. The temperature of maximum shrinkage rate is shifted from T=1000 °C for z=0 towards lower temperatures down to T=900 °C for a sub-stoichiometric ferrite with z=0.02. Dense samples are obtained after firing at 900 °C for z>0 only. Sub-stoichiometric compositions (z>0) do not form single-phase spinel ferrites after sintering at 900 °C, but rather represent mixtures of CuO and a stoichiometric ferrite with slightly modified composition. The formation of small amounts of CuO at grain boundaries is demonstrated by XRD and SEM. The permeability is increased from μ=80 for stoichiometric ferrites (z=0) to μ=660 for z=0.02. The formation of CuO during sintering of sub-stoichiometric ferrites supports densification and is a prerequisite for low temperature firing of multilayer inductors. Addition of 1 wt% Bi₂O₃ as liquid phase sintering aid is required to provide sufficient densification of the stoichiometric ferrite (z=0) at 900 °C. Addition of 0.37 wt% Bi₂O₃ to a sub-stoichiometric ferrite (z=0.02) results in dense samples after firing at 900 °C; however, the microstructure formation is dominated by heterogeneous grain growth.     

Evaluation of magnetic force distribution on a pair of superconducting bulk magnets

We study the construction of superconducting permanent magnets by RE123 bulk materials and the investigation of these industrial applications such as a magnetic separation. A bulk magnet can generate strong magnetic fields exceeding 2 T, which is the limit of ordinary iron-cored electromagnets, in a compact device with a low running cost. A magnetic field distribution of the bulk magnet is a cone shape, and it contributes to an increase of magnetic force which is proportional to the product of a magnetic field and its gradient. It is important to evaluate magnetic force when the application of the bulk magnet is discussed. In this paper, two Gd123 bulk materials of 65 mm in diameter were magnetized using a pair of superconducting bulk magnet system and three-axis components of magnetic flux density (B_x,⋅B_y, and B_z) in an open space between the magnetic poles were scanned with pitch of 2 mm in each direction. From these measured data, the axial and radial components of magnetic force factor, B_z⋅dB_z/dz and B_r⋅dB_r/dr, were calculated. At 10 mm gap, the B_z⋅dB_z/dz value reached 180.6 T²/m for a field of 2.33 T, which is comparable to B_z = 6.76 T for a common 10 T–100 mm∅ superconducting magnet.     

Nonparaxial propagation of spatially and spectrally partially coherent electromagnetic Cosh-Gaussian pulsed beams

Based on the generalized Rayleigh–Sommerfeld diffraction integral, the analytical expression for 3×3 cross-spectral density matrix of nonparaxial spatially and spectrally partially coherent electromagnetic Cosh-Gaussian (ChG) pulsed beams propagating in free space is derived, and used to formulate the spectral density and spectral degree of polarization of electromagnetic pulsed beams at the z-plane. It is found that the parameters f and f_αα are the key parameters in determining the nonparaxiality of spatially and spectrally partially coherent electromagnetic ChG pulsed beams. And the decentered parameter, pulse duration and temporal coherence length can change the nonparaxial behavior of the electromagnetic ChG pulsed beams. The effect of decentered parameter, pulse duration and temporal coherence length on the spectral density and spectral degree of polarization of electromagnetic ChG pulsed beams is illustrated through numerical calculations. Propagation of nonparaxial spatially and spectrally partially coherent electromagnetic Gaussian Schell-model pulsed beams can be treated as a special case when the decentered parameter of electromagnetic ChG pulsed beams approaches to zero.     

Mechanism of the quasi-zero axial acoustic radiation force experienced by elastic and viscoelastic spheres in the field of a quasi-Gaussian beam and particle tweezing

The present analysis investigates the (axial) acoustic radiation force induced by a quasi-Gaussian beam centered on an elastic and a viscoelastic (polymer-type) sphere in a nonviscous fluid. The quasi-Gaussian beam is an exact solution of the source free Helmholtz wave equation and is characterized by an arbitrary waist w₀ and a diffraction convergence length known as the Rayleigh range z_R. Examples are found where the radiation force unexpectedly approaches closely to zero at some of the elastic sphere’s resonance frequencies for kw₀ ? 1 (where this range is of particular interest in describing strongly focused or divergent beams), which may produce particle immobilization along the axial direction. Moreover, the (quasi)vanishing behavior of the radiation force is found to be correlated with conditions giving extinction of the backscattering by the quasi-Gaussian beam. Furthermore, the mechanism for the quasi-zero force is studied theoretically by analyzing the contributions of the kinetic, potential and momentum flux energy densities and their density functions. It is found that all the components vanish simultaneously at the selected ka values for the nulls. However, for a viscoelastic sphere, acoustic absorption degrades the quasi-zero radiation force.     

Analysis of signal-to-noise ratio and heterodyne efficiency for reference-beam laser Doppler velocimeter

Heterodyne efficiency is a very important factor in a laser Doppler velocimeter (LDV). Gaussian-Airy mode is put forward to analyze the heterodyne efficiency. By studying the distribution of the optical field, the mathematic expression and simulation results of heterodyne efficiency are given under the conditions of both exact match and mismatch. The results of numerical analysis show that heterodyne efficiency of LDV depends on Gaussian beam's parameter Q, detector's parameter X₀, angle of collimation mismatching θ_a, parameter of offset mismatching X_a and the radius of curvature of the reference beam on the detector R(z). Heterodyne efficiency can reach 83.39% when Q=4.15×10^?7, X₀=6.1×10^?7, θ_a=X_a=0, R(z)=∞. But it declines to 0.5 when Fθ_a enhances to 0.28. It decreases with the increment of the offset X_a and the diminishment of the radius of curvature R(z). Results of experiment are in good accordance with the theoretical analysis.     

Polarization changes in partially coherent electromagnetic beams propagating through turbulent atmosphere

In this paper, we study the effects of turbulent atmosphere on the degree of polarization of a partially coherent electromagnetic beam, which propagates through it. The beam is described by a 2⊗2 cross-spectral density matrix and is assumed to be generated by a planar, secondary, electromagnetic Gaussian Schell-model source. The analysis is based on a recently formulated unified theory of coherence and polarization and on the extended Huygens-Fresnel principle. We study the behaviour of the degree of polarization in the intermediate zone, i.e. in the region of space where coherence properties of the beam and the atmospheric turbulence are competing. We illustrate the analysis by numerical examples.     

Influence of turbulence on the beam propagation factor of Gaussian Schell-model array beams

The analytical expression for the beam propagation factor (M²-factor) of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the M²-factor of GSM array beams depends on the beam number, the relative beam separation distance, the beam coherence parameter, the type of beam superposition, and the strength of turbulence. The turbulence results in an increase of the M²-factor. However, for the superposition of the intensity the M²-factor is less sensitive to turbulence than that for the superposition of the cross-spectral density function. The M²-factor of GSM array beams is larger than that of the corresponding Gaussian array beams. However, the M²-factor of GSM array beams is less affected by turbulence than that of the corresponding Gaussian array beams. For the superposition of the cross-spectral density function a minimum of the M²-factor of GSM array beams may appear in turbulence, which is even smaller than that of the corresponding single GSM beams.     

The proton recoil spectrum of thermal neutrons decaying in vacuum

The decay of neutrons in an evacuated tangential reactor beam tube is considered. Due to the thermal motion of the decaying neutrons, the proton recoil spectrum in the laboratory system (z-axis parallel to the beam tube) differs from that in the c.m. system. This difference is calculated for a point at the beam tube exit, and expressed in terms of the average¯q _z and of the variance of thez-component of neutron momentum. An activation method for measuring the neutron current densityJ _z (which is closely related to¯q _z) is suggested. The distortion of the spectrum by the finite resolution of an electrostatic spectrometer is also given. The results are to be used in connection with a planned measurement of the proton recoil spectrum in neutron decay.     

The elliptical dimension of space-time atmospheric stratification of passive admixtures using lidar data

State-of-the-art airborne lidar data of passive scalars have shown that the spatial stratification of the atmosphere is scaling: the vertical extent (Δz) of structures is typically ≈Δx^H_z where Δx is the horizontal extent and H_z is a stratification exponent. Assuming horizontal isotropy, the volumes of the structures therefore vary as ΔxΔxΔx^H_z=Δx^D_s where the “elliptical dimension” D_s characterizes the rate at which the volumes of typical non-intermittent structures vary with scale. Work on vertical cross-sections has shown that 2+H_z=2.55±0.02 (close to the theoretical prediction 23/9).In this paper we extend these (x, z) analyses to (z, t). In the absence of overall advection, the lifetime Δt of a structure of size Δx varies as Δx^H_t with H_t=2/3 so that the overall space-time dimension is D_st=29/9=3.22…. However, horizontal and vertical advection lead to new exponents: we argue that the temporal stratification exponent H_t≈1 or ≈0.7 depending on the relative importance of horizontal versus vertical advection velocities. We empirically test these space-time predictions using vertical-time (z, t) cross-sections using passive scalar surrogates (aerosol backscatter ratios from lidar) at ∼3 m resolution in the vertical, 0.5-30 s in time and spanning 3-4 orders of magnitude in scale as well as new analyses of vertical (x, z) cross-sections (spanning over 3 orders of magnitude in both x, z directions). In order to test the theory for density fluctuations at arbitrary displacements in (Δz, Δt) and (Δx, Δz) spaces, we developed and applied a new Anisotropic Scaling Analysis Technique (ASAT) based on nonlinear coordinate transformations. Applying this and other analyses to data spanning more than 3 orders of magnitude of space-time scales we determined the anisotropic scaling of space-time finding the empirical value D_st=3.13±0.16. The analyses also show that both cirrus clouds and aerosols had very similar space-time scaling properties. We point out that this model is compatible with (nonlinear) “turbulence” waves, hence potentially explaining the observed atmospheric structures.     

Propagation regimes of intense circularly polarized laser beam in magnetoactive plasma

This paper presents an analytical and numerical investigation of an intense circularly polarized wave propagating along the static magnetic field parallel to oscillating magnetic field in magnetoactive plasma. In the relativistic regime such a magnetic field is created by pulse itself. The authors have studied different regimes of propagation with relativistic electron mass effect for magnetized plasma. An appropriate expression for dielectric tensor in relativistic magnetoactive plasma has been evaluated under paraxial theory. Two modes of propagation as extraordinary and ordinary exist; because of the relativistic effect, ultra-strong magnetic fields are generated which significantly influence the propagation of laser beam in plasma. The nature of propagation is characterized through the critical-divider curves in the normalized beam width with power plane For given values of normalized density (ω_p/ω) and magnetic field (ω_c/ω) the regions are namely steady divergence (SD), oscillatory divergence (OD) and self-focusing (SF). Numerical computations are performed for typical parameters of relativistic laser-plasma interaction: magnetic field B = 10-100 MG; intensity I = 10¹⁶ to 10²⁰ W/cm²; laser frequency ω = 1.1 × 10¹⁵ s⁻¹; cyclotron frequency ω_c = 1.7 × 10¹³ s⁻¹; electron density n_e = 2.18 × 10²⁰ cm⁻³. From the calculations, we confirm that a circularly polarized wave can propagate in different regimes for both the modes, and explicitly indicating enhancement in wave propagation, beam focusing/self-guiding and penetration of E-mode in presence of magnetic field.     

Application of the two-mode squeezed coherent state representation in deriving generalized optical Collins formula

We propose a new two-mode squeezed coherent state representation |z₁, z₂〉_g which is characteristic of the correlation between the squeezing and the displacement. Based on it and using the technique of integration within an ordered product of operators we obtain a generalized two-mode Fresnel operator (GTFO), which is an image of the mapping from (z₁, z₂) to in |z₁, z₂〉_g representation. The matrix element of GTFO in the coordinate representation leads to a generalized two-dimensional Collins formula (Huygens-Fresnel integration transformation describing optical diffraction) in entangled form.     

Eikonal equation for partially coherent fields

Coherence is the study of the amplitude correlations of optical fields. Its physical features can be obtained from the cross-spectral density function W(x₁,x₂,γ) which satisfies two coupled Helmholtz equations. In this article, we describe the amplitude of the optical field using the angular spectrum model. With this representation we calculate the propagation of the correlation function emerging from a transmittance plane. We show that the cross-spectral density function, can be described by just one Helmholtz equation. The treatment permits us to associate directional features to the coherence phenomena. This implies the existence of extremal trajectories of correlation, which are characterized by an eikonal equation, and the existence of a function for media fluctuations, which we term the correlation refractive index. Experimental results are shown for the synthesis of partially coherent focusing regions, which are described by an ensemble of extreme correlation trajectories.     

Cross-polarization properties of two Gaussian Schell-model beams through non-Kolmogorov turbulence

General expressions are derived for the spectral degree of cross-polarization (SDCP) of a beam generated by the superposition of two Gaussian Schell-model (GSM) beams, which illuminated with the same Gaussian Schell-mode source propagating in non-Kolmogorov turbulent atmosphere by adopting beam cross-spectral density matrix and Young's interference theory. In particular, through numerical examples based on our analytical formal the SDCP of two GSM beams is analyzed. Detailed analysis demonstrate that the SDCP is closely to the spacing of two beams on source plane as well as the strength of the atmospheric turbulent, but the fractal constant α has no affect on the SDCP.     

Lifetime measurements of levels in 34Ar: Isoscalar and isovector matrix elements for E2 analogue transitions

Mean lifetimes have been measured for the low-lying levels in ³⁴Ar(T_z = ? 1) excited by the bombardment of ³He-implanted Au targets with a beam of 80 MeV ³²S. The lifetimes determined by fitting Doppler-broadened γ-ray lineshapes are as follows (E_x in keV, τ in fs): 2091, 460 ± 60; 3288, 280 ± 50; 3871, > 270 and 4128, 1301⁺¹⁷⁰_?130. The resulting transition matrix elements for the 2⁺₁ → 0⁺₁ and 2⁺₂ → 0⁺₁ transitions are compared with those for the analogue transitions in ³⁴S (T_z = + 1) and ³⁴Cl(T_z = 0) to determine the isoscalar and isovector components. The component values are compared with theoretical calculations and with values of the ratio of neutron to proton matrix elements determined by inelastic scattering with strongly interacting probes.     

Longitudinal polarization transfer in the T→p, →n)3He reaction

The longitudinal polarization of neutrons has been measured for the reaction $\text{T}\text{→p}\text{,}\text{→n}\text{)}{}^3\text{He}$ with the incident proton beam longitudinally polarized. Measurements were performed at 0° for proton energies from 4 to 15 MeV and an angular distribution was measured at 10 MeV. The data determine the polarization transfer coefficient K_z^z′, which is equivalent to the Wolfenstein A′ parameter for nucleon-nucleon scattering. The quantity K_z^z′ at 0° increases from about 0.3 at 3 MeV incident energy to 0.9 at 9 MeV, and then decreases to 0.5 at 15 MeV. The data are computed with R-matrix calculations which reproduce the qualitative shape of the data at 0° and the angular distribution at 10 MeV.