高斯光束经过负球差透镜的聚焦

本文讨论高斯光束经过负球差透镜的聚焦，得到了聚焦光场轴上点的光强分布的表示式，并对其进行数值计算。数值计算结果表明，在负球差的情况下，得到光强的最大点位置（最佳聚焦点）相对于无球差情况，往透镜方向移动，并且，最佳聚焦点的光强较无球差时大，当Ｎｗ＝１，Ｎａ＝５，ｋＳ１＝－０．２时，得到的最佳聚焦点的光强是无球差时的１．３４倍。本文还讨论了透镜的菲涅尔数对聚焦光场分布的影响。结果表明，当透镜的菲涅尔数小于１时，球差对高斯光束的聚焦的影响可以忽略。     

Spot size and radial intensity distribution of focused Gaussian beams in spherical and non-spherical aberration lenses

We discussed the radial intensity distribution in the presence of spherical aberrations (SA) for cases in which the incident field is a focused Gaussian spot. A numerical solution of a two dimensional integral diffraction (paraxial ray) equation for a relatively large SA is developed by using the well-known trapezoidal rule for integration. The mesh size was chosen so that convergence of the integration is insured to one part in 10⁻⁸ at successive steps. The spot size and the radial intensity distribution in both SA free lens and lens exhibiting SA are calculated. A relation that determines the spot size at the geometrical focus in aberrated case is developed.     

Effect of spherical aberration on scintillations of Gaussian beams in atmospheric turbulence

The effect of spherical aberration on scintillations of Gaussian beams in weak, moderate and strong turbulence is studied using numerical simulation method. It is found that the effect of the negative spherical aberration on the on-axis scintillation index is quite different from that of the positive spherical aberration. In weak turbulence, the positive spherical aberration results in a decrease of the on-axis scintillation index on propagation, but the negative spherical aberration results in an increase of the on-axis scintillation index when the propagation distance is not large. In particular, in weak turbulence the negative spherical aberration may cause peaks of the on-axis scintillation index, and the peaks disappear in moderate and strong turbulence, which is explained in physics. The strong turbulence leads to less discrepancy among scintillations of Gaussian beams with and without spherical aberration.     

Singularities and spectral changes of Gaussian beams focused by a lens with spherical aberration

We address the effect of the truncation parameter and spherical aberration (SA) on the singularity transformation and spectral behavior of the polychromatic Gaussian beams focused by an aperture lens with SA in detail. The numerical simulation results, based on the derived equations of the intensity and the spectral density, are given. It is found that the axial singularities vanished with the change of the truncated parameter. The intensity and drastic spectral change fade away with an annihilation process of the phase singularities, and the drastic spectral change does not disappear immediately at the moment the phase singularity annihilates. The singularities in the focal region will redistribute with the increment of SA coefficient, some singularities will vanish, some will spilt into two new singularities, and other off-axial singularities will appear and split into two new singularities as well. When SA coefficient changed, we can find that the axial singularities disappear as well with the decreasing value of truncation parameter. These new splitted singularities due to the change of SA coefficient will converge into one singularity again and disappear gradually.     

The intensity distribution of hollow Gaussian beams focused by a lens with spherical aberration

We developed an expression that describes the hollow Gaussian beams (HGBs) passing through a spherically aberrated lens by using the Collins formula. The radial intensity distribution in both spherical aberration SA free lens, lens that exhibits relatively large in both positive spherical aberration PSA, and negative spherical aberration NSA is calculated. Numerical calculations are made and the results show that the PSA and NSA have a strong influence on the intensity distribution especially at the focus. The study showed remarkable results for which there is no hollow Gaussian beam at a large NSA along the optical axis at the focus. In addition, we found that the DSS, and w_r of focused hollow Gaussian beams in the focal region depend not only on the beam radius, and beam order; but also on the spherical aberration.     

The effect of spherical aberration on the phase singularities of focused dark-hollow Gaussian beams

The phase singularities of focused dark-hollow Gaussian beams in the presence of spherical aberration are studied. It is shown that the evolution behavior of phase singularities of focused dark-hollow Gaussian beams in the focal region depends not only on the truncation parameter and beam order, but also on the spherical aberration. The spherical aberration leads to an asymmetric spatial distribution of singularities outside the focal plane and to a shift of singularities near the focal plane. The reorganization process of singularities and spatial distribution of singularities are additionally dependent on the sign of the spherical aberration. The results are illustrated by numerical examples.     

Tsallis, Rényi and nonextensive Gaussian entropy derived from the respective multinomial coefficients

We explore the generalization of the ordinary multinomial coefficient, based on the deformed q-multiplication and q-division. Aim of this study is to construct the appropriate multinomial coefficients, from which one can obtain the Tsallis, Rényi and nonextensive Gaussian entropy, respectively. We show that for all three above entropies there are two possible ways to define the generalized multinomial coefficient. Its consequence is discussed.     

Focusing of a vortex carrying beam with Gaussian background by a lens in the presence of spherical aberration and defocusing

Diffraction pattern formed by a lens for a vortex containing truncated beam with Gaussian background, and in the presence of spherical aberration and defocusing has been studied by Fresnel–Kirchhoff diffraction integral. For the study, two different values of topological charge are selected. Compensation of aberration in the presence of appropriate value of defocusing is investigated. Presence of spherical aberration results in an increase in the size of the dark core of the diffraction pattern. Results are also presented for the encircled energy. Some results are also presented for the influence of truncation parameter of the beam, on the point spread function at different observation planes.     

Application of the matrizant method to calculate the third-order aberration coefficients for a sector magnetic field including fringing-field effects

The matrizant method is used to study the nonlinear dynamics of charged particles in magnetic sector analyzers. The calculations of matrizants (transfer matrices) allow for both fringing-field effects due to the stray field and higher harmonics of the sector magnetic field (up to the third order). For the rectangular distribution of the field components along the optical axis, analytical expressions for the aberration coefficients (including dispersion ones) are derived up to the third order. In the simulation of real fields with a nonzero stray-field width, the smooth distribution of the field components is employed. The aberration coefficients for this distribution were calculated by means of a conservative numerical method.     

The effect of impedance on interaural azimuth cues derived from a spherical head model

Recent implementations of binaural synthesis have combined high-frequency pinna diffraction data with low-frequency acoustic models of the head and torso. This combination ensures that the salient cues required for directional localization in the horizontal plane are consistent with psychophysical expectations, regardless of the accuracy or match of the high-frequency cues, or the fidelity of experimental low-frequency information. This paper investigates the effect of a nonrigid boundary condition on the surface pressure and the resulting interaural cues used for horizontal localization. These are derived from an analytical single sphere diffraction model assuming a locally reacting and uniformly distributed impedance boundary condition. Decreasing the magnitude of a purely resistive surface impedance results in an overall decrease in the sphere surface pressure level, particularly in the posterior region. This produces nontrivial increases in both the interaural level and time difference, especially for sound source directions near the interaural axis. When the surface impedance contains a reactive component the interaural cues exhibit further changes. The basic impedance characteristics of human hair and their incorporation into the sphere diffraction model are also discussed.     

高斯波束对双层粒子的辐射俘获力

从广义米理论出发，将入射高斯波束用矢量球谐函数展开.根据对电磁场动量的讨论，得出了高斯波束对多层球形粒子的辐射俘获力的表示式，并就单高斯波束对在轴双层有吸收粒子受到的辐射俘获力进行了数值模拟，讨论了束腰半径、吸收系数、内外层相对厚度对俘获情况的影响. 关键词： 辐射俘获力 多层球形粒子 光镊 高斯波束     

光束控制系统热效应与球差对激光光束质量的影响

采用Strehl比、桶中功率、β参数和束宽描述远场光束质量，研究了光束控制系统热效应和球差对远场激光光束质量的影响.用四维仿真程序作了详细计算，给出了数值计算结果并进行了物理分析.研究表明，传输通道的热效应和正球差会使远场光强分布扩展，可聚焦能力下降，光束质量变差.有意义的是，当激光发射功率达到一定值时，合适选取负球差会在几何焦面得到比无球差时更高的峰值光强和更好的可聚焦能力.但在以前的工作中，由于焦移，类似的结论是在实际焦面上得出的.非线性热晕的存在是其物理原因，对此用数值计算例子作了说明. 关键词： 高功率激光 热效应 光束控制系统 球差     

The effect of spherical aberration on temperature distribution inside glass by irradiation of a high repetition rate femtosecond pulse laser

In this paper, we study the effect of spherical aberrations on the light intensity and the temperature distribution in the focal region in a 250-kHz femtosecond laser irradiated Ag⁺-doped borosilicate glass. When a focused beam goes through an interface between air and glass, spherical aberration will result in the separation of the focal point and then cause a clear change of the light intensity distribution along the incident direction. That phenomenon will further influence the longitudinal cross-section temperature distribution in glass. Here we use Ag nanoparticle formation as a marker for establishing temperature distribution and we find that the formation of nanoparticle shows a strong dependence on the temperature field and the detailed precipitation process is also discussed.     

The effect of tilt aberration and astigmatism of turbulent atmosphere on the intensity distribution of a vortex carrying Gaussian beam

The effect of tilt and astigmatism aberration of the turbulent atmosphere on the intensity distribution of a focused vortex carrying Gaussian beam was investigated based on the extended Fresnel-Kirchhoff diffraction integral and the quadratic approximation of phase structure function. Our results have shown that the intensity distribution on the focal plane in the effect of tilt aberration changes with the turbulent strength, the propagation distance and the topological charge of the initial beam. The propagation distance is larger, the focal spot size will be larger, and the central dip will be less deep. It is also noticed that the intensity distribution of a beam with single topological charge is affected more by tilt aberration in comparison to the beam with double topological charge. The effect of astigmatism on the intensity distribution is quite less than that of tilt aberration. For focused beam propagation in atmosphere, the effect of the tilt aberration on the intensity distribution of optical vortex beam is the main effect of total turbulent aberration.     

Effect of a magnetic impurity on the optical properties of a spherical ZnSe quantum dot

We consider the electron and hole states in a semiconductor ZnSe spherical quantum dot, in the center of which a magnetic impurity atom of manganese is located. In calculations the quantum dot is approximated by a spherical rectangular well with a finite depth. Within the framework of perturbation theory, the effect of exchange spin interaction of an electron and a hole with a magnetic impurity on the band structure of the system is considered. The optical spectrum of the system for different polarizations of the incident light is studied also.