Scattering of laser pulses (plane wave and focused gaussian beam) by spheres

The scattering of laser pulses (in the femtosecond-picosecond range) by large spheres is investigated. We call a sphere large when its diameter is larger than the length associated with the pulse duration, allowing one to observe the temporal separation of scattering modes including surface waves.     

Two-photon-excitation spatial distribution for crossed focused gaussian beams

The spatial distribution of two-photon excitation created by crossed focused Gaussian beams is shown. The effective volume calculation for the two-photon interaction of crossed Gaussian beams is presented. The dimensions of cubic and parallelepiped volumes, in which half of the two-photon interaction is localized, are determined. The memory densities of two-photon three-dimensional memory for crossed focused beams and one focused beam are compared.     

Fiber-diameter measurement by occlusion of a gaussian beam

The amount of light occluded by a fiber as it passes through alaser beam can be used as the basis for fiber-diametermeasurement. This technique is analyzed with a two-dimensionalrigorous model. The occlusion seen for dielectric fibers as afunction of their diameter is highly oscillatory owing to interferencebetween the light transmitted by the fiber and the rest of thediffracted field. Scalar diffraction theory is shown to be adequatein modeling this effect. The oscillation sets a limit to theaccuracy of simple diameter measurement systems and is confirmedexperimentally for glass fibers. However, wool fibers are found tobe better treated as an absorbing material. The effect of beampolarization is investigated and found to be negligible for dielectricfibers but significant for metal fibers of small diameter.     

Restoration of the intensity profile of a focused laser spot by means of combining optical correlation with a numerical method

A method is presented by which intensity profile of a focused light spot is reconstructed from the correlation pattern between itself and a pinhole, which is obtained by moving the focused spot with the aid of an acousto-optic deflector (AOD). The pattern was formulated into a matrix equation by assuming that it was circular symmetric and was approximated by a number of linear functions. The results were numerically given by solving the matrix equation with a modified least-squares method and were assessed for the degree of focus, influence of signal fluctuations, and degradation of the spot resulting from heat generation within the AOD.     

Effects of gaussian beam size on diffraction measurement errors

A numerical simulation has been performed for the diffraction of a gaussian beam at a wire in the Fraunhofer approximation. The wire is symmetrically disposed with respect to the beam axis in the calculations on the shifts in the diffraction minima, while an unsymmetrical position has been used in calculating the diffraction pattern, which is characterized by change in the minima and maxima. Conditions are evaluated under which one can use the homogeneous-beam approximation in diffraction measurements. Translated from Izmeritel'naya Tekhnika, No. 11, pp. 30–32, November, 1997.     

Analytical far-field divergence angle of a truncated gaussian beam

Approximate, but accurate, analytical expressions for the far-field divergence angle of a Gaussian beam normally incident on a circular aperture are derived. A first equation is obtained based on the concept of Gaussian transform, in which the Bessel function present in the far-field diffraction integral is approximated by a Gaussian function. Refining this approach yields another simple, practical closed-form formula with such a level of accuracy that we propose that it can be used as an exact reference. All approximations hold for any combination of Gaussian beam width and aperture radius.     

Diffraction of a gaussian beam around a strip mask

A theoretical treatment is given for the diffraction of a Gaussianbeam around an opaque strip mask. Such situations arise frequentlyin the diffraction of laser beams around wires and fibers. Scalarderivations are given for the Fraunhofer and Fresnel regions with bothdevelopments, leading to similar forms of rapidly convergent series forthe field at an observation plane. Predictions show good agreementwith measurements on the diffraction patterns from wires.     

Axial irradiance of a focused beam

The principal maximum of axial irradiance of a focused beam with a low Fresnel number does not lie at its focal point; instead it lies at a point that is closer to the focusing pupil. It has been shown by the numerical example of a weakly truncated Gaussian beam that its value increases and its location moves closer to the pupil when spherical aberration is introduced into the beam. Such an increase has been referred to as "beyond the conventional diffraction limit." Similarly, an increase in the value and a shift in the location of the principal maximum of axial irradiance of a uniform beam toward the pupil by the introduction of some spherical aberration has been characterized as an unexpected result. We explain why and how such a result comes about and that it neither invalidates any diffraction limit nor is it unexpected. We illustrate this for uniform as well as Gaussian beams of various truncation ratios. Both focused and collimated beams aberrated by spherical aberration or astigmatism are considered.     

Direct focusing modifications of elliptical gaussian beam by non-circular apertures

Abstract

For focusing the elliptical Gaussian beam directly, the effects of a non-circular aperture on the focusing properties are studied. The focusing properties for different shapes of apertures, which include a circle, an ellipse and a rectangle, are calculated and compared. Moreover, for different elliptical Gaussian beams, an empirical aperture selection rule that can be used to circularize the focusing spot is proposed. The energy transmission ratios are also considered in this paper.     

Orientation of biological cells using plane-polarized gaussian beam optical tweezers

Abstract

Optical tweezers are widely used for the manipulation of cells and their internal structures. However, the degree of manipulation possible is limited by poor control over the orientation of the trapped cells. We show that it is possible to controllably align or rotate disc-shaped cells—chloroplasts of Spinacia oleracea—in a plane-polarized Gaussian beam trap, using optical torques resulting predominantly from circular polarization induced in the transmitted beam by the non-spherical shape of the cells.     

Scattering of a spheroidal particle illuminated by a gaussian beam

An approach to expanding a Gaussian beam in terms of the spheroidal wave functions in spheroidal coordinates is presented. The beam-shape coefficients of the Gaussian beam in spheroidal coordinates can be computed conveniently by use of the known expression for beam-shape coefficients, g(n), in spherical coordinates. The unknown expansion coefficients of scattered and internal electromagnetic fields are determined by a system of equations derived from the boundary conditions for continuity of the tangential components of the electric and magnetic vectors across the surface of the spheroid. A solution to the problem of scattering of a Gaussian beam by a homogeneous prolate (or oblate) spheroidal particle is obtained. The numerical values of the expansion coefficients and the scattered intensity distribution for incidence of an on-axis Gaussian beam are given.     

Focal shift of focused truncated Lorentz-Gauss beam

Based on the Collins diffraction integral formula and the complex Gaussian expansion of the aperture function, an analytical expression for a Lorentz-Gauss beam focused by an optical system with a thin lens and a circular aperture has been derived. The focal shift of the focused truncated Lorentz-Gauss beam is investigated with numerical examples, and the dependence of the focal shift on the different parameters of the focused truncated Lorentz-Gauss beam is discussed in detail. This research is useful to the applications of highly divergent laser beams.     

Stress intensity factors in spot welds

This paper looks at stress intensity factors of cracks in resistance spot welded joints. Stress intensity factors have been used in the past to predict fatigue crack propagation life of resistance spot welds. However, the stress intensity factors from all previous work was based on assumed initial notch cracks at the nugget, parallel to the sheets. Physical evidence shows, however, that fatigue cracks in spot welds propagate through the thickness of the sheets rather than through the nugget. In this work, stress intensity factors of assumed notch cracks and through thickness cracks in tensile shear (TS) and modified coach peel (MCP) specimens were determined by the finite element method. The finite element results from the assumed notch cracks were compared with the results in the literature and were found to be in agreement with the results from Zhang’s equations [Int. J. Fract. 88 (1997) 167]. The stress intensity factors of assumed notch cracks were found to be different from those of through thickness cracks. To date, no analytic equations for stress intensity factors of through thickness cracks in spot welds have been published. In the current work, simple equations are proposed to estimate the K_I and K_II values of through thickness cracks in TS and MCP specimens.     

Stress intensity factors in spot welds

This paper looks at stress intensity factors of cracks in resistance spot welded joints. Stress intensity factors have been used in the past to predict fatigue crack propagation life of resistance spot welds. However, the stress intensity factors from all previous work was based on assumed initial notch cracks at the nugget, parallel to the sheets. Physical evidence shows, however, that fatigue cracks in spot welds propagate through the thickness of the sheets rather than through the nugget. In this work, stress intensity factors of assumed notch cracks and through thickness cracks in tensile shear (TS) and modified coach peel (MCP) specimens were determined by the finite element method. The finite element results from the assumed notch cracks were compared with the results in the literature and were found to be in agreement with the results from Zhang’s equations [Int. J. Fract. 88 (1997) 167]. The stress intensity factors of assumed notch cracks were found to be different from those of through thickness cracks. To date, no analytic equations for stress intensity factors of through thickness cracks in spot welds have been published. In the current work, simple equations are proposed to estimate the K_I and K_II values of through thickness cracks in TS and MCP specimens.     

Dynamically shifting the focal spot with tunable pupil filters

Abstract

It is popularly believed that when the focal spot is shifted far away from the optical axis of optical system with the pupil filter, it will be significantly aberrated. Therefore, the pupil filter is usually only used to adjust the distribution of the focal spot at the optical axis of optical system. In this paper, the special combination of the phase pupil filter shifting the focal spot and the high-pass filter eliminating the aberration of the focal spot is designed so that the focal spot can be shifted dynamically at the focal plane. By utilizing the Debye vector diffractive theory, the shifting behaviours of the focal spot are investigated in detail. The proof-of-principle experiment demonstrates the validation of the method for dynamically controlling the position of focal spot. This work is helpful to realize dynamically shifting the focal spot with the pupil filter and may find valuable applications in particle trapping, microscopes, optical engineering, and so on.     

高强度聚焦超声换能器的新型设计

采用高强度聚焦超声（HIFU）治疗局部肿瘤，如何增强对病变区域的辐照效果，而尽量减少对健康区域的辐照损伤是一个很重要的问题。文章基于目前常用的凹球面自聚焦换能器，提出了解决上述问题的方案，设计了新型的换能器，对其工作方式及声场特性进行了研究。结果表明：采用多换能器轮流发射的方式进行治疗是一种行之有效的解决方案。     

Average spreading of a radial gaussian beam array in non-Kolmogorov turbulence

The analytical expression for the rms beam width of the radial gaussian beam array propagating in non-Kolmogorov turbulence is derived, where the coherent combination is considered. The influences of the beam number, the generalized exponent, and the ring radius on the rms beam width are investigated. The results indicate that the rms beam width depends greatly on the generalized exponent and the beam number. Further, an optimum ring radius, which leads to a minimum beam width, is proved to exist within a certain traveling distance and the optimum ring radius increases when the beam number increases.     

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.