On-axis Gaussian beam scattering by an eccentrically coated conducting cylinder

Based on the generalized Lorenz–Mie theory (GLMT) framework, an exact analytic solution to electromagnetic scattering by an eccentrically coated conducting cylinder is constructed, for oblique incidence of an on-axis Gaussian beam described by a localized beam model. The solution is found by the classical separation of variables technique and the translational addition theorem. For a tightly focused Gaussian beam propagating perpendicularly to the cylinder axis, numerical results of the normalized differential scattering cross section are presented, and the scattering characteristics are discussed concisely.     

Scintillation index of elliptical Gaussian beam in turbulent atmosphere

A tensor method is used to formulate the on-axis scintillation index for an elliptical Gaussian beam (EGB; astigmatic Gaussian beam) propagating in a weak turbulent atmosphere. Variations of the on-axis scintillation of an EGB are studied. It is interesting to find that the scintillation index of an EGB can be smaller than that of a circular Gaussian beam in a weakly turbulent atmosphere under certain conditions and is closely related to the ratio of the beam waist size along the long axis to that along the short axis of the EGB, the wavelength, and the structure constant of the turbulent atmosphere.     

Temperature elevation generated by a focused Gaussian ultrasonic beam at a tissue-bone interface

When a focused Gaussian ultrasonic beam in soft tissue normally impinges on the boundary of a contiguous bone, reflection and transmission occur. Taking account of the reflection, the steady-state temperature elevation along the beam axis for this case was calculated. The effect of perfusion is also included.     

Fourth order correction to a Gaussian beam focused with a parabolic index lens

We formulate the fourth order correction to a paraxial Gaussian beam propagated along the axis of symmetry of a parabolic index lens. First we examine the evolution of a complex-source-point spherical wave (equivalent paraxially to a Gaussian beam) through the lens in a two-dimensional xz plane. Taking into account the terms of up to fourth order in aperture variables, we find a ray-optical solution to the exit beam that is represented in terms of aberration function. We also analyze the effect of the lens aberration exerted on the degradation in the quality of a Gaussian beam. The fourth order-corrected wave function derived here may be used to evaluate the quality of a Gaussian beam focused with a parabolic index lens. Further it may be applied to the case of an orthogonal system in which the index variations are different in the xz and yz planes.     

Tight focusing effect of annular obstructed incident beam in the focal region of high NA lens

Focusing properties of the azimuthally polarized axisymmetric Bessel-modulated Gaussian beam with Quadratic Bessel Gaussian (QBG beam) and annular aperture are investigated theoretically by vector diffraction theory. Simulation results show that the intensity distribution in focal region of the azimuthally polarized axisymmetric QBG beam can be shifted along optical axis considerably by changing parameter (C). On introducing annular aperture (δ), focal pattern at the focus extends along optical axis. In this paper, we have shown the generation of focal hole and focal shifting in the axial direction of incident beam propagating through aligned optical system which is suitable for application such as optical manipulation and optical trapping.     

Scattering of gaussian beam by a ferrite cylinder

The scattering of a Gaussian beam by a ferrite cylinder is analyzed using two methods. The spatial pictures in the amplitude of the total Gaussian beam near the cylinder resulting from the two methods are both clarified and compared. The scattering by a ferrite cylinder coating a dielectric sleeve is also presented.     

Aberrations of a slightly inclined Gaussian beam in a symmetric optical system

We discuss the Seidel-type aberrations which degrade the quality of the Gaussian beam, while the beam axis is slightly inclined to the axis of an optical system. First we examine the evolution of a complex-source-point spherical wave through multiple spherical boundaries. Then we find a ray-optical solution for the diffracted beam that can be represented as a function of Seidel-type aberrations. We also formulate the characteristic parameters of the aberrated beam. If the beam axis is placed at the yz plane, the x component of beam quality factor is degraded by both spherical aberration and field curvature, and the difference in the x and y components of beam quality factor is caused by linear coma, linear astigmatism, and distortion. The fourth order theory of propagation of the Gaussian beam presented here may be applied to determine the parameters of a slightly inclined Gaussian in a symmetric optical system.     

椭圆高斯光束在强非局域非线性介质中的传输特性

研究了傍轴椭圆高斯光束在强非局域非线性介质中的传输特性，得到了其各参量的演化方程 及其精确解析解.通过对束宽演化方程及其精确解析解的进一步分析，发现傍轴椭圆高斯光 束在强非局域非线性介质中传输时，两横向方向束宽作周期性变化.不管初始功率为多大， 光束都将周期性的由椭圆高斯光束演化为圆对称高斯光束，再由圆对称高斯光束演化为椭圆 高斯光束；并且在演化的过程中，椭圆的半长轴和半短轴会作周期性交替变化.另外，在一 定初始功率下，傍轴椭圆高斯光束可以保持某一横向方向的束宽不变，得到光孤子. 关键词： 强非局域非线性介质 非局域非线性薛定谔方程 椭圆高斯光束 参量演化方程 空间孤子     

Scattering of shaped beam by a conducting infinite cylinder with dielectric coating

Based on the generalized Lorenz–Mie theory (GLMT), which provides the general framework and expansion of the incident shaped beam in terms of cylindrical vector wave functions, an analytic solution to the electromagnetic scattering by coated infinite cylinders is constructed for arbitrary incidence of a shaped beam. As an example, for a tightly focused Gaussian beam propagating perpendicularly to the cylinder axis, the scattering characteristics that obviously demonstrate the three-dimensional nature are described in detail, and numerical results of the normalized differential scattering cross section are evaluated.     

圆柱体的空间圆锥光反射、折射与衍射

用准直或会聚激光束倾斜照射圆柱体时,其反射光、透射光(柱体透明时)、衍射光(柱体较细时)的叠加将形成以光束入射点为顶点的空间圆锥形光面(空间光锥),并且在垂直于柱体轴线方向的观察平面上投影成一圆形光环.空间光锥的形成与所选圆柱体材料及其粗细无关,只要其表面具有一定反射能力即可.空间光锥的锥角等于入射光束主光轴与圆柱体轴线夹角的2倍,与圆柱体和照射光束的直径大小及光波长无关.给出了对光纤及不同直径大小的玻璃和金属圆柱体的实验观察结果,并利用矢量图解法对其进行了详细地理论分析.进而得出,通常所谓单丝衍射图样,实际上是细丝的衍射和其表面的反射光场的叠加图样,对于透明细丝,还包括其透射光场的贡献.圆柱体的这种空间圆锥光反射和衍射原理有可能用于光束定位、成形、表面检测以及三维面形测量等 关键词： 圆柱体 空间光锥 投影光环     

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.     

Investigation in the far field characteristics of TM polarized Gaussian beam from the vectorial structure

Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical TE and TM terms of TM polarized Gaussian beam, the rigorous solution of Maxwell's equations for a confocal resonator, have been presented in the far field. Then in terms of the vectorial structure, TM polarized Gaussian beam is compared with Gaussian TEM₀₀ mode. The TE term is located at the y-axis, and the TM term the x-axis. At the non-paraxial case, the whole beam spot is elliptical, and the long axis is located at the y-axis. Moreover, the whole beam spot of TM polarized Gaussian beam is smaller than that of Gaussian TEM₀₀ mode. At the paraxial case, the whole beam spot is circular, and TM polarized Gaussian beam reduces to be Gaussian TEM₀₀ mode.     

Theory of electromagnetic wave propagation in a longitudinally periodic cylinder

Thinking of photonic crystals, we investigate the theory of electromagnetic wave propagation in a perfectly conducting semi-cylinder endowed with a periodic permittivity along its axis while its circular base is illuminated by an harmonic Bessel beam, symmetric around the cylinder axis. We prove that the Floquet-Bessel expansions of electromagnetic fields whose Floquet parts are solutions of a Mathieu equation. is a suitable tool to handle this kind of problems.     

Propagation of higher order Bessel–Gaussian beams in turbulence

The propagation characteristics of higher order Bessel–Gaussian beams travelling in turbulent atmosphere are investigated. Using extended Huygens–Fresnel principle, I formulated receiver plane intensity and solved it down to a double integral stage. Source beam plots are made illustrating the variation of intensity against order and width parameter. From the examination of receiver intensity graphs, it is seen that Bessel–Gaussian beam are converted into modified Bessel–Gaussian beams at intermediate propagation ranges eventually ending up as Gaussian profiles. The impacts of order and turbulence levels on beam profile are analysed. Focusing effects and beam size change along the propagation axis are studied. PACS 41.85.Ew; 42.68.Bz     

Effect of high magnetic fields on the conductivity of a quantum cylinder under Stark ladder conditions

The conductivity of a quantum cylinder with a parabolic lateral confinement potential and a superstructure is studied under conditions where uniform static quantizing electric and magnetic fields are applied along the cylinder axis. The charge carriers are assumed to be scattered by optical phonons. The dependence of the current density along the superlattice axis on the dc magnetic field is obtained. It is shown that, under certain conditions, the so-called Stark-hybrid-phonon resonance appears due to the hybridization of the electronic energy spectrum. In turn, this gives rise to a sharply nonmonotonic magnetic-field dependence of the current density.     

Study on the response characteristics of adaptive focusing system for flying optics

The ABCD law of parameter q for fundamental-mode Gaussian beam is deduced in this paper. The result shows that the changes of focal length and focal depth are not related to the orders of the Gaussian beam modes when focus lens moves along optical axis in a large range, indicating that the ABCD law of parameter q can be used for any order modes. A laser focusing setup is designed, and the response characteristics of oil pressure system therein are also studied.     

Optical Doppler shift with structured light

When a light beam with a transverse spatially varying phase is considered for optical remote sensing, in addition to the usual longitudinal Doppler frequency shift of the returned signal induced by the motion of the scatter along the beam axis, a new transversal Doppler shift appears associated to the motion of the scatterer in the plane perpendicular to the beam axis. We discuss here how this new effect can be used to enhance the current capabilities of optical measurement systems, adding the capacity to detect more complex movements of scatters.     

Energy flux of a Gaussian beam in microwave band beyond the paraxial approximation

Through the analytic method beyond the paraxial approximation, the energy flux for the general fields of a Gaussian laser beam in microwave band (∼10⁸–10¹⁰ Hz) with different diffraction angles and longitudinal positions are derived. The results indicate a Gaussian beam (GB) has a certain number of transverse energy flux, and it would be enhanced with larger diffraction angle. In the range of beyond paraxial approximation, the transverse flux plays an important role in energy distribution, so that it cannot be ignored when the GB is highly focused. Meanwhile both transverse and longitudinal energy decay along the propagation direction, and the proportion of transverse energy far from beam axis is much more than the counterpart in paraxial area. The transverse energy as mainly characteristic of GB will be much useful for the interactions between electromagnetic field and other field.     

Radiation forces of a dielectric medium plate induced by a Gaussian beam

Based on the angular spectrum method, we investigate the radiation forces on a finite-size dielectric medium plate induced by a Gaussian beam. The formulas for the radiation force along longitudinal and transverse direction are derived, and numerically calculation is performed. It is shown that for the finite-size dielectric medium plate, the radiation forces exerted by the Gaussian beam is dependent upon the angle and position of a single ray striking on the plate and the intensity of light. Our numerical results indicate that if we choose the appropriate parameters there will be enough transverse forces to overcome the gravity force, making the plate move upwards.     

高斯束谐振系统对引力波频率和方向的选择效应

高斯束谐振系统为早期宇宙遗留的随机高频引力波的探测开启了一个非常重要的窗口.计算结果表明，当入射引力波频率和高斯束不同时，高斯束谐振系统产生的一阶扰动光子流没有观测效应；当入射引力波的传播方向与高斯束对称轴的正方向不同时，高斯束谐振系统产生的一阶扰动光子流将降低几个数量级，即高斯束谐振系统只对沿某一特定方向传播的高频遗迹引力波产生有效的响应.因此，高斯束谐振系统对高频遗迹引力波的频率和传播方向具有良好的选择效应. 关键词： 高斯束谐振系统 高频遗迹引力波 一阶扰动光子流 频率选择效应 方向选择效应