Reflection and transmission of Laguerre Gaussian beam from uniaxial anisotropic multilayered media

Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian(LG) beam from uniaxial anisotropic multilayered media are studied. The reflected and transmitted beam fields of an LG beam are derived. In the case where the principal coordinates of the uniaxial anisotropic media coincide with the global coordinates, the reflected and transmitted beam intensities from a uniaxial anisotropic slab and three-layered media are numerically simulated. It is shown that the reflected intensity components of the incident beam, especially the TM polarized incident beam, are smaller than the transmitted intensity components. The distortion of the reflected intensity component is more evident than that of the transmitted intensity component. The distortion of intensity distribution is greatly affected by the dielectric tensor and the thickness of anisotropic media. We finally extend the application of the method to general anisotropic multilayered media.     

附加球面相位引致Airy光束在单轴晶体传输时的两次镜像演化

利用单轴晶体光束传输理论,求得了具有附加球面相位Airy光束在单轴晶体中的传输公式.数值模拟计算结果表明,线偏振附加球面相位Airy光束在晶体中传输时仍为线偏振,但不是传输不变的.粗略地讲,具有附加球面相位的Airy光束在晶体中传输时,近场是传输不变的;而在由晶体寻常与非寻常折射率和球面半径共同确定的两个特定传输距离处,传输光束转换成了取向不同的Gaussian-Airy光束,且高斯依赖的束宽度敏感地与截断因子相关;而当光束依次穿过此两位置时光斑花样先后相对于两横向轴平面做镜像演化,且镜像演化顺序也与晶体寻常和非寻常折射率相对大小密切相关,其总的效果是远场强度花样能恢复原样但花样取向产生了关于对过横平面二、四象限平分平面的镜像演化.这些结果表明,通过恰当选择晶体材料(即折射率)和附加球面相位的半径R,可以调控光束花样的形状、取向及表征各向异性材料的相关性质.     

Comparison of three kinds of polarized Bessel vortex beams propagating through uniaxial anisotropic media

A comparison of differently polarized Bessel vortex beams propagating through a uniaxial anisotropic slab is discussed in terms of the vector wave function expansions.The magnitude profiles of electric field components, the transformation of polarization modes, and the distributions of orbital angular momentum(OAM) states of the reflected and transmitted beams for different incident angles are numerically simulated.The results indicate that the magnitude profiles of electric field components for different polarization modes are distinct from each other and have a great dependence on the incident angle,thus the transformation of polarization modes which reflects the change of energy can be affected largely.As compared to the x and circular polarization incidences, the reflected and transmitted beams for the radial polarization incidence suffer the fewest transformation of polarization modes, showing a better energy invariance.The distributions of OAM states of the reflected and transmitted beams for different polarization modes are diverse as well, and the derived OAM states of the transmitted beam for radial polarization present a focusing effect, concentrating on the state between two predominant OAM states.     

The optical Airy transform and its application in generating and controlling the Airy beam

We propose an optical Airy transform in this paper, and obtain the analytical expressions for the Airy transform of fundamental Gaussian beams and finite energy Airy beams. The setup for performing the optical Airy transform is presented. The Airy transform for Gaussian beams and finite energy Airy beams are theoretically calculated and analyzed. Our results show that the Airy beam can be conveniently generated and controlled through the optical Airy transform of the Gaussian beam. The optical Airy transform also can be used to directly modulate the beam parameters of the incident Airy beam, and it can transform the incident Airy beam into the Gaussian beam.     

Spin Hall effect of light in one-dimensional photonic crystal

We established a general propagating model to investigate the spin Hall effect of light in one-dimensional photonic crystal. A polarized (spin dependent) Gaussian beam which was incident obliquely through one-dimensional photonic crystal was demonstrated. Having decomposed a polarized Gaussian beam into different plane wave components charactering individual wave vectors, we revealed the transmission coefficient and reflection coefficient of each plane wave which propagates through the one-dimensional photonic crystal. It enabled us to obtain exact solution to the electric field of transmitted and reflected beams, and the analytical formula of light intensity, accordingly. A method based upon the partial differentials with the intensity distribution of the transmitted and reflected Gaussian beams was presented to determine the transverse and longitude shifts explicitly. Spin dependent shifts in one-dimensional photonic crystal provide alternative evidence for the spin Hall effect of light.     

Interference simulation in a cold collisionless moving magnetized plasma slab and (free surface of plasma slab)

Abstract

The pattern of intensity due to the interference in a cold collisionless magnetized moving plasma slab is investigated. Theoretically, it is assumed the mentioned layer has been located as a thin layer in an etalon Fabry–Perot interferometer surrounded by vacuum. The direction of external magnetic field is normal to the plasma surface and the plasma slab moves parallel with external constant magnetic field. By taking into account the relativistic considerations, the functions of transmitted intensity are presented coincident with the Airy function form in laboratory and plasma slab frames, respectively. The effects of plasma frequency, cyclotron frequency, thickness of plasma slab, and velocity of the plasma slab on band width, finesse factor, and visibility are simulated. Finally with the assumption that there are two wavelengths near together in incident electromagnetic beam the power resolution for this configuration are analyzed. All studies mentioned above have been done for S-polarized and P-polarized electromagnetic beams separately.     

High-efficiency frequency-modulation non-redundant scanning of a light beam in a half space

It is shown that a large fraction of the energy of the impinging light beam on a parallel plate grating can be injected into only one transmitted order, which is not the zeroth transmitted order, when the incident angle of the beam and the refractive indices of the lossless dielectric bounding media satisfy the condition of total reflection. This signififies that non-redundant scanning of the radiation transmitted through the grafting can be obtained by varying the frequency of the incident radiation with little of the incident energy being scattered into the reflected orders.     

Frustrated Total Internal Reflection: Resonant and Negative Goos–Hänchen Shifts in Microwave Regime

It is well-known that the variations of Goos–Hänchen shifts (GHSs) are closely associated with the energy flux provided by evanescent states in the case of total internal reflection. However, when the frustrated total internal reflection (FTIR) is realized with double-prism system operated in the microwave frequency, we observe that the GHSs for the reflected beam show periodic, resembling the phenomenon for transmitted beams reported in the literatures, versus either the operating frequency or the air layer thickness, which is different from the variation of the corresponding reflected energy. Moreover, in another FTIR based system fabricated by a composite absorptive material slab with a two-dimensional top layer of frequency selective surface (FSS), the GHSs for reflected beam are discovered as not only resonant but also negative with the incidence of transverse electric that is TE polarized, just as predicted theoretically in the literatures.     

Transformation of a Gaussian light beam reflected in the vicinity of the Brewster angle

Variations in the profile and shift of a Gaussian light beam upon reflection from a plane interface between a transparent dielectric and a medium with a complex refractive index are studied. The beam is assumed to be incident at angles close to the Brewster’s angle, where the effects of transformation of the beam profile are most substantial. Based on numerical analysis, the reflected beam profiles are obtained for different properties of the media, parameters of the incident beam, and positions of the plane of observation.     

棱镜-薄膜耦合结构中光束Goos-H(a)nchen位移的增强

棱镜-薄膜耦合结构是单侧镀电介质膜的双棱镜结构中的一种,在光信号传输方面具有十分重要的作用.利用稳态相位法分析了这种结构中反射和透射光束的Goos-Hanchen位移,研究结果表明,反射和透射光束的Goos-Hanchen位移随薄膜厚度或入射角的增大除出现共振峰外,还存在反射光束的Goos-Hanchen位移共振峰为负值的新现象.在共振点处透射和反射光束的正向或负向位移量最大可达百余波长.这一结构中薄膜和入射角.对光束Goos-Hanchen位移的调制在设计新型光位移调制和光传感器件中具有潜在的应用.     

Arbitrary laser beam propagation in free space

The propagation of arbitrary laser beams in free space is examined. For this purpose, starting with an incident field of arbitrary field distribution, the intensity at the receiver plane is formulated via Huygens Fresnel diffraction integral. Arbitrary source field profile is produced by decomposing the source into incremental areas (pixels). The received field through the propagation in free space is found by superposing the contributions from all source incremental areas. The proposed method enables us to evaluate the received intensity originating from any type of source field. Using the arbitrary beam excitation, intensity of various laser beams such as cos-Gaussian, cosh-Gaussian, general type beams are checked to be consistent with the already existing results in literature, and the received intensity distributions are obtained for some original arbitrary beam field profiles. Our received intensity formulation for the arbitrary source field profiles presented in this paper can find application in optics communication links, reflection from rough surfaces, optical cryptography and optical imaging systems.     

Intense femtosecond shaped laser beams for writing extended structures inside transparent dielectrics

We review recent results on the propagation and self-focusing of intense femtosecond laser pulses with shaped beam profiles in transparent dielectric media. At sufficiently high optical power, beam shaping seeds into the transverse modulation instability and results in the deterministic placement of intense laser filaments within the beam profile. Resulting spatial filament distributions may be utilized for writing complex extended structures inside transparent dielectrics. Specific examples of beam shapes we will discuss are Bessel beams, optical vortices, Bessel beams of higher order, and Airy beams.     

拉盖尔-高斯光束在界面反射和折射的质心偏移特性研究

在圆柱坐标系中研究了傍轴线偏振拉盖尔-高斯光束在两种各向同性介质界面反射和折射后光强质心的偏移. 基于菲涅耳近似和泰勒级数展开,分别得到了部分反射和全反射两种情形下,质心的横向偏移和纵向偏移与光束拓扑荷的解析关系式. 研究表明,部分反射时,反射和折射光束的横向偏移的大小与光束的拓扑荷成正比,方向由拓扑荷的符号决定;而纵向偏移仅仅大小与光束的拓扑荷有关. 全反射时,反射光束质心偏移不受拓扑荷影响. 通过数值模拟验证了解析结果的正确性,并得到了解析公式的适用条件. 拉盖尔-高斯光束的质心偏移特性可应用于测量光 关键词： 拉盖尔-高斯光束 横向偏移 纵向偏移 拓扑荷     

多艾里光束合成自聚焦光束的实验实现

多光束合成和单光束聚焦一直是提高激光束功率和功率密度的两个重要方法. 结合艾里光束在自由空间中沿弯曲路径传播的特性, 从数值模拟和实验两个方面, 研究了利用多个一维艾里光束合成自由空间自聚焦光束的方法, 并对所得到的模拟和实验结果进行了对比. 采用分步束传播法, 分别模拟了由四个和八个一维艾里光束合成的自聚焦光束在自由空间中的传播过程, 给出了自聚焦光束在传播过程中横向和纵向的光强分布和变化趋势. 采用计算全息和空间光调制器技术实验, 实现了多个一维艾里光束合成的自聚焦光束. 实验中分别测量了四个和八个一维艾里光束合成的自聚焦光束的横向光强分布. 实验结果和理论结果符合得较好. 另外, 为了进一步增大自聚焦光束的功率, 可以增加参与合成的一维艾里光束的数量. 同时, 自聚焦光束的焦距可以通过调整各个一维艾里光束的相对位置进行调节.     

The fractional Fourier transform of Airy beams using Lohmann and quadratic optical systems

Based on the generalized Huygens–Fresnel integral, the analytical expressions for Airy beams through three types of fractional Fourier transform (FRFT) optical systems (Lohmann I, Lohmann II and quadratic graded-index systems) are derived. Using the two analytical expressions, the propagation properties of Airy beams for the three types of FRFT optical systems are discussed in detail with numerical examples. Results indicate that the intensity of Airy beams periodically changes and remains form-invariant with the changing of fractional order p for the three types of FRFT optical systems.     

Reflection of a focused light beam in a medium with Kerr nonlinearity. I. Estimates in the paraxial-beam approximation

The reflection intensity in a nonlinear dielectric layer is calculated in the approximation of paraxial incident and reflected light beams. It is shown that reflection is mainly determined by discontinuities of the refractive-index on the boundaries. Unlike reflection by a linear dielectric layer, reflection by a nonlinear layer occurs with a three-time decrease in the effective reflection area and the corresponding broadening of the angular spectrum. The intensity of the reflected wave is comparable to that of an incident wave with nearly critical beam power.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 7, pp. 867–875, July, 1996.This work was supported by the International Science Foundation and the Russian Federation Government (projects MR1000 and MR1300).     

无衍射特殊光束的产生与三维表征

无衍射光束(如贝塞尔光束、艾里光束)因具有无衍射、自愈合的特性, 在很多领域都有广泛的应用. 本文提出使用纯相位型空间光调制器对光场的复振幅进行调控, 从而可以产生多种复杂模式的无衍射光束, 如强度可独立调控的多个零阶贝塞尔光束, 两个高阶贝塞尔光束干涉生成的花瓣状无衍射光束, 具有多个主瓣的加速光束等特殊的无衍射光束. 通过在待测焦场附近放置一个平面反射镜, 使其沿光轴快速扫描光场, 并由数字相机同步拍摄反射回来的一系列二维光场强度分布信息, 可实现对无衍射光束三维光场强度分布的快速测量和表征. 本实验方法和技术可以快速产生各种复杂的特殊光场并获得其精确的三维可视化重建效果, 在光学显微、光学俘获、光学微加工等领域有潜在的应用价值.     

Propagation of confluent hypergeometric beam through uniaxial crystals orthogonal to the optical axis

Based on the theory of paraxial electromagnetic beams in anisotropic medium, propagation properties of a linearly polarized confluent hypergeometric (HyG) beam through uniaxial crystals orthogonal to the optical axis are investigated. Analytical expressions are derived for the resultant optical field components. Effects of separate beam parameters together with the ratio of refractive indices of crystals on transversal intensity distributions are revealed by numerical calculations, respectively. It is shown that the beam profile finally converts into an elliptical shape due to influences of anisotropic crystals. Moreover, it is also indicated that through suitable selection of parameters, types of the optical vortices of resultant field would change from a central dark spot to a slight dark ring or an axial shadow during the propagation. These numerical results may provide alternative advantages to the trapping of tiny particles by utilizing HyG beams in practical experiments.     

平面电磁波在任意方向运动的介质-介质界面上的反射和透射

研究平面电磁波从一种介质入射到另一种以任意方向运动的介质时,在介质界面上发生的反射和透射现象,从Maxwell方程组、运动界面的边值关系和运动介质的本构关系出发,得到了反射波和透射波电磁场矢量与入射波电磁场矢量的关系的表达式、反射和透射系数,讨论了反射波、透射波与入射波之间的能量关系,电磁波对运动介质作用力的性质,并得出一些新的结论． 关键词：     

Giant bistable lateral shift owing to surface-plasmon excitation in Kretschmann configuration with a Kerr nonlinear dielectric

We investigate the reflection of a TM-polarized light beam from a Kretschmann configuration with a Kerr nonlinear dielectric. It is found that there exists a hysteretic response between the lateral shift of the reflected beam and the intensity of the incident beam. In contrast to the lower switch threshold, the higher switch threshold of optical bistability is more sensitive to the variations of the angle of incidence and the thickness of metal film. It is also found that the peak value of the lateral shift is strongly dependent on the thickness of metal film.