Effective radius of curvature of partially coherent Hermite–Gaussian beams propagating through non-Kolmogorov turbulence

Based on the extended Huygens–Fresnel principle and non-Kolmogorov spectrum, the analytical expression for the effective radius of curvature of partially coherent Hermite–Gaussian (PCHG) beams propagating through non-Kolmogorov turbulence is derived, and the relative effective radius of curvature is used to describe the effect of turbulence on the effective radius of curvature. It is shown that the effective radius of curvature of PCHG beams depends on the beam and non-Kolmogorov turbulence parameters and on the propagation distance. The variation of relative effective radius of curvature with increasing generalized exponent parameter α of non-Kolmogorov turbulence is non-monotonic. The longer the propagation distance is, the larger the effect of turbulence on the effective radius of curvature of PCHG beams is. The effective radius of curvature of PCHG beams with shorter wavelength, smaller beam order, larger beam waist width or better spatial coherence is more affected by the non-Kolmogorov turbulence. The results are interpreted physically.     

A comparative study of standard and elegant Hermite–Gaussian beams propagating through turbulent atmosphere

Based on the extended Huygens–Fresnel principle and the definition of the second-order moments of the Wigner distribution function (WDF), the analytical expressions for the root-mean-square (rms) beam width and far-field divergence angle, curvature radius and M ²-factor of standard Hermite–Gaussian (SHG) and elegant Hermite–Gaussian (EHG) beams passing through turbulent atmosphere are derived and compared. It is shown that in turbulent atmosphere the far-field divergence angle of SHG and EHG beams is equal under the same conditions, but the rms beam width, curvature radius and the M ²-factor of SHG and EHG beams are different except for beam orders m?=?0 and m?=?1. The relative rms beam width, relative curvature radius and relative M ²-factor of SHG beams are less than those of EHG beams. Therefore, the conclusion that SHG beams are less influenced by turbulence than EHG beams can be drawn if we examine one of the above three relative beam parameters.     

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.     

Beam wander and M2-factor of partially coherent electromagnetic hollow Gaussian beam propagating through non-Kolmogorov turbulence

Propagation formulae for M²-factor and beam wander of partially coherent electromagnetic hollow Gaussian (PCEHG) beam in non-Kolmogorov turbulence are derived based on the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function. Our results indicate that the normalized M²-factors of PCEHG beam with larger beam order, waist width, inner scale of turbulence, the generalized exponent parameter, and smaller transverse coherent widths, outer scale of turbulence, the generalized structure parameter are less affected by the turbulence. The root mean square beam wander and relative beam wander are more obvious for PCEHG beam with smaller beam order, larger inner and outer scales of turbulence, exponent parameter, transverse coherent widths, and the generalized structure parameter. What is more, the beam wander properties of PCEHG beam in non-Kolmogorov turbulence are very different from M²-factor and spreading properties of beam in turbulence.     

Method for stabilizing beam intensity and energy in the SPring-8 linac

In any electron accelerator facilities, radio frequencies (RF) for a linear accelerator and a circular accelerator that includes a booster synchrotron ring and a storage ring are completely different. There is not necessarily a sub-harmonic relation of two RFs between a linear accelerator and a circular accelerator. It is, however, indispensable to obtain a synchronous relation between both RFs and the timing of the gun trigger signal with the increasing beam current and shortening of beam time width from an electron gun in a linear accelerator. For a synchronous timing system in any electron accelerator facilities, there is no choice but to assemble a complicated system with the frequency dividers and multipliers in order to realize the synchronous relation between both RFs and the gun trigger signal. To simplify the complicated synchronous timing system, we have developed a new synchronization method for the RFs of both linear and circular accelerators. The new synchronization system has been installed into the synchrotron radiation facility, SPring-8 (Super Photon ring 8 GeV), which consists of a 1-GeV linac, an 8-GeV booster synchrotron and an 8-GeV storage ring. A 2856 MHz RF for the 1-GeV linac was generated by the 508.58 MHz RF of the 8-GeV storage ring with the new synchronous timing system, and the emission and acceleration under the condition of the shortening the beam time width in the linac was carried out. Since the synchronous relation between both the RFs and the gun trigger signal was realized by using the new synchronous timing system, the time jitter between the gun trigger signal and the RF phase of 2856 MHz was significantly reduced and resulted in beam energy stabilization. The new synchronous timing system has been used for usual beam operations at SPring-8. This timing system has achieved time jitters of 3.5 ps (rms) and beam energy stability of 0.009% (rms) under the condition of completely synchronized two RFs and the gun trigger signal.     

RC环梁连接的钢管混凝土柱-RC梁框架计算模型研究

RC环梁连接的钢管混凝土柱-RC梁框架在竖向荷载和水平荷载作用下,在环梁一定高度范围内,环梁与柱之间会有很窄的缝隙。通过有限元分析研究了环梁连接的转角刚度和环梁区域框架梁等效宽度以及它们的影响因素,结果表明环梁宽度和框架梁宽度对转角刚度和等效宽度影响较大。框架内力、位移计算以及两层两跨框架结构的静力试验和拟动力试验表明,环梁连接的钢管混凝土柱-RC梁框架可以采用梁柱直接刚性连接的模型进行弹性分析。     

Optimum design of an extended octagonal ring by goal programming

Extended octagonal rings are used in metal cutting dynamometers to measure cutting forces and torque. The controllable design variables are the thickness, radius and width of the ring. Normally the objectives of the design are to achieve high sensitivity and high rigidity which arc conflicting in nature. Therefore, both requirements cannot be achieved simultaneously. The goal programming technique is used to determine the optimum size of extended octagonal ring for various goal priorities with respect to sensitivity and rigidity     

Two-dimensional multiplexing scheme both with ring radius and topological charge of perfect optical vortex beam

Perfect optical vortex (POV) beam is a special kind of vortex beam, whose radius is independent of its topological charge. In this paper, we propose a two-dimensional multiplexing scheme with a ring radius and topological charge of POV beam. A communication system using the proposed multiplexing scheme with a two-step detection method is presented, and on–off keying modulation is applied to demonstrate the bit error rate (BER) performance under atmospheric turbulence. The numerical results show that the BER performance of the proposed scheme is better than that when only topological charge is multiplexed with the same conditions. The two-dimensional multiplexing scheme has an anti-interference capability since the ring radius is only concerned in magnitude. At the same time, the capacity and the spectral efficiency of the system are improved since both ring radial and topological charge of POV beam are used.     

Rays and fields in general astigmatic resonators

General astigmatic (GA) resonators are discussed in detail. Eigenrays, eigenmodes and eigenvalues (Gouy-factors) of this resonator are evaluated. A stability diagram for such resonators is introduced, which clearly depicts the stable and unstable regions for rays as well as for fields. Eigenrays and their stability regions are evaluated using the ABCD-law. For the beam propagation Collins' integral and the second moment method are applied. The eigenfunctions for rectangular symmetry are the generalized Hermite polynomials multiplied by the Gaussian exponential factor. It is shown that for general astigmatic resonators these polynomials are the product of normal Hermite polynomials. The generating function of the eigenfunctions depends on the special resonator. It is a useful tool for all calculations and it is determined. Furthermore it is shown that the second moment characterization of the modes is a useful and easy to handle procedure to evaluate beam width, beam divergence, radius of curvature and twist of the generalized Gauss–Hermite functions.     

Beam loss rates with an internal gas target in an electron-cooled storage ring Implications for luminosity optimization

Measurements have been made in the Cooler ring at the Indiana University Cyclotron Facility (IUCF) of the mean lifetime of stored and electron-cooled proton beams in the presence of various target gas species at two ring locations differing in dispersion. A broad range of beam energy T_b, target atomic number Z_t and thickness x_t was employed. The loss (removal) cross sectionσ_L per target atom, extracted from the lifetime measurement, exhibits a minimum for small x_t which is found to scale with . This behavior is expected because forward Coulomb scattering from target nuclei should be the dominant loss mechanism under the conditions of measurement. A marked increase in σ_L for larger x_t is attributed to emittance growth arising from multiple scattering in competition with the transverse cooling rate. Lattice dispersion at the target increases the contribution to beam heating by electrons in the target atoms and introduces an additional loss mechanism. From the measured σ_L and beam lifetime, a time cycle may be selected which gives the optimum time-averaged luminosity for a given experiment. Scaling of σ_L allows prediction of the optimum luminosity over the full operating regime of the cooling ring.     

Focal shift in focused truncated pulsed-laser beam

The focal shift of a focused truncated pulsed-laser beam is investigated. In the case of the Fresnel approximation, the analytic expression of the time-averaged intensity distribution along the axis is derived based on the series expansion. It shows that the focal shift of the pulsed beam can be completely determined by a series of normalized spectrum moments and the central Fresnel number defined according to the central frequency of the pulse. The absolute value of the focal shift of the pulsed beam decreases monotonously and slowly with the normalized spectrum width increasing and the central Fresnel number fixed, and it increases monotonously with the central Fresnel number decreasing and the normalized spectrum width fixed. Besides the central Fresnel number and the normalized spectrum width, the shape of spectral intensity of the pulse affects the focal shift too.     

Numerical simulation for parameter optimization of silicon purification by electron beam melting

In this paper a mathematical model is developed to investigate the removal of volatile impurities in molten silicon by electron beam melting (EBM) with a high efficiency and low energy consumption. The temperature distribution of molten silicon is obtained using the commercial software FLUENT. Based on the temperature distribution, the vaporization behaviors of phosphorus and silicon are investigated by Langmiur's vaporization theory. The results show that the evaporation rate of silicon during EBM increases exponentially with the increase of beam power, while, it decreases with the increase of scanning radius. The optimal parameters are discussed from the aspect of efficiency and energy saving. The energy consumption decreases with the decrease of scanning radius and with the increase of the beam power. The optimum values are consider to be with a scanning radius of 0.0339 m and a beam power of 23.4 kW for 0.5 kg silicon when phosphorus is removed from 1.44 × 10⁻² to 1 × 10⁻⁵ (wt.%).     

Propagation of Gaussian-Schell beam in turbulent atmosphere of three-layer altitude model

We propose a method that is used to derive the moment radius of intensity distribution in a turbulent atmosphere. From this study, we have found that the second moment radius is affected only by the first-order expansion coefficient of the wave structure function. If our attention is directed to a higher moment radius, a higher order approximation of the expansion needs to be used. As an example, the propagation of a Gaussian-Schell beam in a slant path has been studied based on the turbulent atmosphere of a three-layer model. The variation of some beam properties, such as the relative waist width, angular spread, and kurtosis parameter with the initial waist width, wavelength, and zenith angle, has been analyzed and discussed in detail. The study shows that there is little difference between the three-layer model and the Kolmogorov model in studying uplink propagation, and the difference is large for downlink propagation. The intensity profile of the Gaussian beam in turbulence does not keep a Gaussian shape unless the beam spreading due to turbulence is very large or very small.     

Encircled energy for systems with truncated-Gaussian apertures of different Fresnel numbers. II. Maximizing beam energy concentration on a target

In Part I of this study [J. Opt. Soc. Am. A24, 2023 (2007)] the Q(2n) functions of E. Wolf and the Y(n) functions of H. H. Hopkins have been generalized for evaluating the fraction of the total energy in systems with focused truncated Gaussian beams by apertures of different Fresnel numbers and different ratios of aperture radius to beam radius. The generalized special functions provide a mathematical basis for a rigorous study of maximizing beam energy concentration on a target. This subject is addressed under two subtitles: (1) active focusing of a Gaussian beam onto a distant target and (2) optimizing photodetection in a focused field.     

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.     

Self-induced Temperature Profile and Inhomogeneity Effect on Second Harmonic Generation Using Focused Laser Beam

The behaviour of optical second harmonic due to crystal inhomogeneity and self-induced thermal effect has been considered for a focused laser beam. Temperature profile created due to a fundamental laser beam along the crystal length shows an increase in temperature band width for various values of focusing parameter. Normalized second harmonic power in inhomogeneous crystals increases up to an optimum value of focusing parameter. Utility of focusing is limited due to formation of filament in crystal for higher values of focusing parameter.     

Spatial distribution of copper vapour from a two-dimensional source using a strip electron beam at aspect ratio greater than 3

We present results on the spatial distribution of copper vapour as a function of temperature, from a 2D evaporating source generated using 130 mm strip electron beam at aspect ratio >3. At this aspect ratio vapour flow is expected to appear approximately as a point source flow. The 2D evaporating source during these studies can be described in terms of inverse Knudsen number (1/K_n) that is proportional to source temperature, ranging from 0.75 to 6.67. These experimental results could be fitted with accuracy of ±5% using a spatial distribution function with different beaming coefficients along the width and the length of a 2D source. It is observed that the beaming exponent along the width of a 2D source saturates at about 2, which is marginally higher than that observed for the aspect ratio in the range of 1 to 2 for the similar range of 1/K_n, whereas, the beaming exponent along the length direction of a 2D source was observed to increase up to 6.34, which is substantially higher than that observed at the aspect ratio in the range of 1-2 for the similar range of 1/K_n. These results clearly indicate that, for given evaporating source conditions, the widthwise atomic collisions, collimation of atomic beam and beaming exponent along the width remains constant. At the same time lengthwise collisions, atomic beam collimation and hence beaming coefficient do not freeze and the wedge-shaped atomic beam does not run out of collisions in the lengthwise direction even at aspect ratio >3. Thus, the atomic vapour from a 2D source does not attain the free molecular regime even at radial distance in excess of 390 mm above the source.     

Efficient analytic model to optimum design laser resonator and optical coupling system of diode-end-pumped solid-state lasers: influence of gain medium length and pump beam M2 factor

A comprehensive analytical model for optimization longitudinal pumping of ideal four-level lasers is presented for accurate analysis by removing limiting assumptions on active length and pump-beam radius in the gain medium. By taking into account the circular-symmetric Gaussian pump beam including the M2 factor, an analytical formula for the root mean square of the pump beam in the active medium is developed to relate properties of the gain medium and pump beam to the requirement on efficient optimum design. Under the condition of minimum root mean square of pump-beam radius inside the active medium, the key parameters of the optimum optical coupling system have been analytically derived. Using these parameters, optimum mode size and maximum output efficiency are derived as a function of the gain medium length, absorption coefficient, pump-beam M2 factor, and input power. Dependence of the obtained parameters on the gain medium length, absorption coefficient, pump-beam M2 factor, and input power has been investigated. The results of this theory are found to be more comprehensive than the previous theoretical investigations. The present model provides a straightforward procedure to design the optimum laser resonator and the coupling optics for maximizing the output.     

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.     

用于近场光刻的表面等离子体透镜的优化设计和加工

表面等离子体透镜(PL)具有优异的光聚束效应,能够形成突破衍射极限的近场光斑,具有广泛的应用前景.为了获得较小的近场光斑,需要选用较短波长的激光入射.选用355 nm径向偏振光作为入射条件,使用COMSOL多物理场耦合仿真软件优化了同心圆环沟槽型PL的结构参数.结果显示,当圆环沟槽半径与槽间距都与表面等离子激元(SPPs)波的波长相等,且增加同心圆环槽数时,SPPs波在PL中心能形成相长干涉,可以获得较大的光增强效应;随着金属膜厚和槽宽的增加,中心处光强先增大后减小,存在最优值.使用聚焦离子束(FIB)加工制备了所设计的PL结构,加工结果具有较好的尺寸精度,但沟槽截面存在一定的锥度.进一步的仿真结果表明,沟槽横截面的小锥度对PL的聚束效应和光增强效应影响较小.