Analysis of beam quality for the laser beams after spectral beam combining

The beam quality of the laser beams after spectral beam combining (SBC) has been analyzed in this paper. Based on the propagation model of the spectral beam combining system, the expression for the output field of an individual beam passing through the spectral beam combining system with lens aberration has been given and the intensity distribution of the combined beam has been studied by the principle of incoherent superposition. Consequently, according to the intensity second-order moments method, the M²-factor of the combined beam has been calculated and the effect of lens aberration on the characteristics of the combined beam has been analyzed quantitatively. It can be shown that the SBC system can improve the beam quality of laser array significantly, and the M²-factor of the combined beam passing through the ideal spectral beam combining system is almost the same as that of an individual beam. For the spectral beam combining system with lens aberration, the spherical aberration has greater effect on the off-axis beam than on the on-axis beam, and the beam quality of combined beam degrades with increase in lens aberration.     

Interaction of a high-order Bessel beam with a submerged spherical ultrasound contrast agent shell - Scattering theory

Background and objective

Acoustic scattering properties of ultrasound contrast agents are useful in extending existing or developing new techniques for biomedical imaging applications. A useful first step in this direction is to investigate the acoustic scattering of a new class of acoustic beams, known as helicoidal high-order Bessel beams, to improve the understanding of their scattering characteristics by an ultrasound contrast agent, which at present is very limited.

Method

The transverse acoustic scattering of a commercially available albuminoidal ultrasound contrast agent shell filled with air or a denser gas such as perfluoropropane and placed in a helicoidal Bessel beam of any order is examined numerically. The shell is assumed to possess an outer radius a = 3.5 microns and a thickness of ∼105 nm. Moduli of the total and resonance transverse acoustic scattering form functions are numerically evaluated in the bandwidth 0 < ka? 3, which corresponds to a frequency bandwidth of 0-205 MHz that covers a wide range of applications for imaging with contrast agents. Particular attention is paid to the shell’s material, the content of its interior hollow region and the fluid surrounding its exterior. The contrast agent shell is assumed to be immersed in an ideal compressible fluid so the viscous corrections are not considered. Analytical equations are derived and numerical calculations of the total and resonance form functions are performed with particular emphasis on the effect of varying the half-cone angle, the order of the helicoidal Bessel beam as well as the fluid that fills the interior hollow space.

Results and conclusion

It is shown that shell wave resonance modes can be excited on an encapsulated micro-bubble. The forward and backscattering vanish for a helicoidal high-order Bessel beam. Additionally, the fluid filling the inner core affects the shell’s response significantly. Moreover, there is no monopole contribution to the axial scattering of a helicoidal Bessel beam of order m ? 1 so that the dynamics of contrast agents would be significantly altered. The main finding of the present theory is the suppression or enhancement for a particular resonance that may be used to advantage in imaging with ultrasound contrast agents for clinical applications.     

Gegenbauer expansion to model the incident wave-field of a high-order Bessel vortex beam in spherical coordinates

The aim of this short communication is to report that Gegenbauer’s (partial-wave) expansion, that may be used (under some specific conditions) to represent the incident field of an acoustical (or optical) high-order Bessel beam (HOBB) in spherical coordinates, anticipates earlier expressions for undistorted waves. The incident wave-field is written in terms of the spherical Bessel function of the first kind, the gamma function as well as the Gegenbauer or ultraspherical functions given in terms of the associated Legendre functions when the order m of the HOBB is an integer number. Expressions for high-order and zero-order Bessel beams as well as for plane progressive waves reported in prior works can be deduced from Gegenbauer’s partial-wave expansion by appropriate choice of the beams’ parameters. Hence the value of this note becomes historical. In addition, Gegenbauer’s expansion in spherical coordinates may be used to advantage to model the wave-field of a fractional HOBB at the origin (i.e. z = 0).     

Complex geometrical optics of Kerr type nonlinear media

The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. Ordinary differential equations for the beam amplitude and for complex curvature of the wave front are derived, which describe the evolution of axially symmetric GB in a Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in a medium of Kerr type including a nonlinear graded-index fiber. The range of applicability of the PCGO theory is discussed as well which is helpful for avoiding nonphysical solutions.     

Electron beam evaporated LaF3 thin films prepared by different temperatures and deposition rates

LaF₃ thin films were prepared by electron beam evaporation with different temperatures and deposition rates. Microstructure properties including crystalline structure and surface roughness were investigated by X-ray diffraction (XRD) and optical profilograph. X-ray photoelectron spectroscopy (XPS) was employed to study the chemical composition of the films. Optical properties (transmittance and refractive index) and laser induce damage threshold (LIDT) at 355 nm of the films were also characterized. The effects of deposition rate and substrate temperature on microstructure, optical properties and LIDT of LaF₃ thin films were discussed, respectively.     

In vitro investigation of anodization and CaP deposited titanium surface using MG63 osteoblast-like cells

The aim of the present study was to investigate surface characteristics in four different titanium surfaces (AN: anodized at 270 V; AN-CaP: anodic oxidation and CaP deposited; SLA: sandblasted and acid etched; MA: machined) and to evaluate biological behaviors such as cell adhesion, cell proliferation, cytoskeletal organization, and osteogenic protein expression of MG63 osteoblast-like cells at the early stage. Surface analysis was performed using scanning electron microscopy, thin-film X-ray diffractometry, and a confocal laser scanning microscope. In order to evaluate cellular responses, MG63 osteoblast-like cells were used. The cell viability was evaluated by MTT assay. Immunofluorescent analyses of actin, type I collagen, osteonectin and osteocalcin were performed. The anodized and CaP deposited specimen showed homogeneously distributed CaP particles around micropores and exhibited anatase type oxides, titanium, and HA crystalline structures. This experiment suggests that CaP particles on the anodic oxidation surface affect cellular attachment and spreading. When designing an in vitro biological study for CaP coated titanium, it must be taken into account that preincubation in medium prior to cell seeding and the cell culture medium may affect the CaP coatings. All these observations illustrate the importance of the experimental conditions and the physicochemical parameters of the CaP coating.It is considered that further evaluations such as long-term in vitro cellular assays and in vivo experiments should be necessary to figure out the effect of CaP deposition to biological responses.     

The existence of periodic solutions for nonlinear beam equations on by a para‐differential method

This paper focuses on the construction of periodic solutions of nonlinear beam equations on the d‐dimensional tori. For a large set of frequencies, we demonstrate that an equivalent form of the nonlinear equations can be obtained by a para‐differential conjugation. Given the nonresonant conditions on each finite dimensional subspaces, it is shown that the periodic solutions can be constructed for the block diagonal equation by a classical iteration scheme.     

埃尔米特梁单元的分块对角与高阶质量矩阵

埃尔米特梁单元常用的集中质量矩阵,是由挠度自由度对应的一致质量矩阵元素通过行求和或节点积分构造。然而,数值结果表明该集中质量矩阵在求解包含自由端的梁振动问题时,会出现频率精度掉阶现象。本文首先从保障质量矩阵最优收敛性的数值积分精度出发,分别针对三次和五次梁单元,发展了质量矩阵的梯度增强节点积分方案。利用梯度增强节点积分方案,可以得到具有分块对角形式的单元质量矩阵,而其组装的整体质量矩阵除边界节点外仍然呈现对角形式。对于两种单元,其分块对角质量矩阵分别具有4阶最优精度和6阶次优精度。再者,将标准一致质量矩阵和具有同阶精度的梯度增强节点积分质量矩阵进行优化组合,建立了具有超收敛特性的高阶质量矩阵。最后,通过数值算例系统验证了三次和五次单元的分块对角与高阶质量矩阵的频率计算精度。     

梁方程时间依赖全局吸引子的存在性

研究了梁方程时间依赖吸引子的存在性,在非线性项f满足临界增长条件时,基于时间依赖全局吸引子的存在性定理,应用先验估计和算子分解方法验证了系数参数与时间t有关时,梁方程对应的过程族{U(t,τ)}的渐近紧性,从而得到梁方程时间依赖全局吸引子的存在性及正则性.     

Site control of InAs quantum dot nucleation by ex situ electron-beam lithographic patterning of GaAs substrates

Conventional electron-beam lithographic patterning of GaAs substrates followed by reactive-ion etching of small holes has been successfully used to control the nucleation of InAs dots. We have observed >50% single dot occupancy for holes wide and deep and show that the dot occupancy and dot size can be varied by changing the size of the holes. Luminescence from an array of these site-controlled dots has been demonstrated. Thus this use of substrate patterning is a viable technique to controllably place single dots at pre-determined positions in devices.