Direct measurement of group dispersion of optical components using white-light spectral interferometry

We present a simple white-light spectral interferometric technique employing a low-resolution spectrometer for a direct measurement of the group dispersion of optical components over a wide wavelength range. The technique utilizes an unbalanced Mach-Zehnder interferometer with a component under test inserted in one arm and the other arm with adjustable path length. We record a series of spectral interferograms to measure the equalization wavelength as a function of the path length difference. We measure the absolute group refractive index as a function of wavelength for a quartz crystal of known thickness and the relative one for optical fiber. In the latter case we use a microscope objective in front and a lens behind the fiber and subtract their group dispersion, which is measured by a technique of tandem interferometry including also a Michelson interferometer.     

The Klein-Gordon and the Dirac Oscillators in a Noncommutative Space

We study the Dirac and the Klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics of a particle in a commutative space and in a constant magnetic field. The Dirac oscillator in a noncommutative space has a similar equation to the equation of motion for a relativistic fermion in a commutative space and in a magnetic field, however a new exotic term appears, which implies that a charged fermion in a noncommutative space has an electric dipole moment.     

The Dynamics of Pendulums on Surfaces of Constant Curvature

We define the notion of a pendulum on a surface of constant curvature and study the motion of a mass at a fixed distance from a pivot. We consider some special cases: first a pivot that moves with constant speed along a geodesic, and then a pivot that undergoes acceleration along a fixed geodesic.      

光阑对平面光波傍轴性的影响

 根据单色光傍轴度的定义,分别研究了圆形光阑和方形光阑对平面光波傍轴性的影响。推导出平面光波经圆形光阑和方形光阑衍射后其傍轴度的解析表达式。平面光波经圆形光阑或方形光阑衍射后,其傍轴性下降,傍轴度小于1,傍轴度下降量取决于光阑尺寸与入射平面光波波长的比值。数值计算结果表明：随光阑尺寸与入射平面光波波长的比值从零开始增大,平面衍射光波的傍轴度从零开始快速增大而后趋于一饱和值,但光阑的形状不影响平面衍射光波的傍轴性。     

Localized States of an Excess Electron in an Ionic Cluster

A theory of an electron affinity for an ionic cluster is proposed both in a quasiclassical approach and with quantization of a polarization electric field in a nanoparticle. A critical size of the cluster regarding in formation of an electron's autolocalized state, dependencies of energy and radius of a polaron on a cluster's size are obtained by a variational method. It has been found that binding energy of the electron in the cluster depends on a cluster's radius but a radius of electron's auto-localization does not depend on the cluster's radius and it equals to the polaron radius in a corresponding infinity crystal. A bound state of the electron in a cluster is possible only if the cluster's radius is more than the polaron radius.     

氮化铝薄膜中的二次谐波产生

利用X射线衍射技术对用直流反应磁控溅射技术沉积在蓝宝石基底(100)晶面上的氮化铝(AIN)薄膜进行了晶体结构分析,对X射线衍射图样的分析结果表明：用该法沉积在蓝宝石基底(100)晶面上的AIN薄膜为单晶膜;利用脉宽为10ns、重复频率10Hz、最大平均功率为20W、单脉冲的最大能量为2J的Nd：YAG脉冲激光器对其进行了二次谐波产生的实验研究,对实验结果进行分析表明：沉积在蓝宝石基底(100)晶面上的AIN薄膜能在一个很宽的入射角度范围存在有效二次谐波的输出;且输出的二次谐波功率相对于AIN薄膜的表面法线成对称分布,这表明该AIN薄膜的表面法线方向即为AIN的光轴方向。     

Wrinkling of a bilayer resting on a soft substrate under in-plane compression

The wrinkling problem of a bilayer film resting on a soft substrate under in-plane compression is investigated via theoretical analysis and numerical simulations. Such a system may undergo two different wrinkling modes, namely surface wrinkling of the top single layer on a composite substrate or bilayer wrinkling on a homogeneous substrate, depending on the geometric and material parameters. In the present paper, a theoretical solution is first derived for the former case, while a solution available in the literature is applied for the latter. The solution derived here can degenerate both to the classical solution for a stiff layer resting on a semi-infinite soft substrate and that for a stiff layer lying on a compliant substrate of finite thickness. A series of finite element simulations are performed to demonstrate the accuracy of the theoretical solution. In addition, it is found that, at a given compressive strain, a certain change in the elastic modulus of the intermediate layer may lead to a dramatic surface pattern transformation between the two wrinkling modes, indicating a novel approach to realise surface pattern switching.     

Spectral resolution in a Rickart comgroup

A comgroup is a compressible group with the general comparability property. A comgroupwith the Rickart projection property is called a Rickart comgroup. We show that each element of a Rickart comgroup has a rational spectral resolution and a nonempty closed and bounded (real) spectrum. The rational spectral resolution and the spectrum are shown to have many of the properties of the spectral resolution and spectrum of a self-adjoint operator on a Hilbert space. Examples of Rickart comgroups include the additive group of self-adjoint elements in a von Neumann algebra and the Mundici group of a Heyting MV algebra.     

Spectral-domain intermodal interference under general measurement conditions

Spectral-domain intermodal interference is analysed theoretically at the output of a few-mode optical fibre alone and at the output of the optical fibre in a tandem configuration with a Michelson interferometer. The theoretical analysis is performed under general measurement conditions when a light source of a given spectral bandwidth and a spectrometer of a given spectral bandpass are considered and when first- and second-order intermodal dispersion effects in the optical fibre are taken into account. Thus, the effect of a variable spectral bandpass of a low-resolution spectrometer on the spectral fringe visibility functions for a two-mode optical fibre of known intermodal dispersion is specified.     

Spectral singularities of a complex spherical barrier potential and their optical realization

The mathematical notion of a spectral singularity admits a physical interpretation as a zero-width resonance. It finds an optical realization as a certain type of lasing effect that occurs at the threshold gain. We explore spectral singularities of a complex spherical barrier potential and study their realization as transverse spherical electromagnetic waves emitted by a gain medium with a spherical geometry. In particular, for a typical dye laser material, we obtain a lower bound on the size of the gain medium for the occurrence of this kind of spectral singularities.     

2D photonic crystal complete band gap search using a cyclic cellular automaton refination

We present a refination method based on a cyclic cellular automaton (CCA) that simulates a crystallization-like process, aided with a heuristic evolutionary method called differential evolution (DE) used to perform an ordered search of full photonic band gaps (FPBGs) in a 2D photonic crystal (PC). The solution is proposed as a combinatorial optimization of the elements in a binary array. These elements represent the existence or absence of a dielectric material surrounded by air, thus representing a general geometry whose search space is defined by the number of elements in such array. A block-iterative frequency-domain method was used to compute the FPBGs on a PC, when present. DE has proved to be useful in combinatorial problems and we also present an implementation feature that takes advantage of the periodic nature of PCs to enhance the convergence of this algorithm. Finally, we used this methodology to find a PC structure with a 19% bandgap-to-midgap ratio without requiring previous information of suboptimal configurations and we made a statistical study of how it is affected by disorder in the borders of the structure compared with a previous work that uses a genetic algorithm.     

Lyapunov function as potential function： A dynamical equivalence

For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization: a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.     

Unidirectional Single-Mode 532-nm Nd:YAG Laser Using Intracavity Frequency Doubling in Nonplanar Ring Geometry

Intracavity frequency doubling of a single-mode Nd:YAG laser using a nonplanar ring cavity is demonstrated. The nonplanar ring cavity consists of a Brewster-angled Nd: YAG crystal placed in a magnetic field, a KTP crystal, and two spherical mirrors. In this design the Nd:YAG crystal acts as both a nonreciprocal polarization rotator and a partial polarizer, and the nonplanar portion of the ring cavity, which is formed by a relative twist angle between the Brewster-angled end surfaces of the crystal, serves as a reciprocal polarization rotator. Eigenpolarization theory for the cavity configuration is presented and a suitable value of the relative twist angle for unidirectional operation is estimated. A single-mode output power of 22 mW at 532 nm is obtained with a 1.2-W diode laser at 809 nm and a laser linewidth of less than 100 kHz is inferred from a beat note frequency spectrum between two identical laser systems.     

A Hyperboloid Single Lens Focusing on a Spherical Image Surface up to Very High Angles of Incidence

Optical properties of a single hyperboloid lens cut by a lathe were investigated. The lens has a characteristic of focusing the object image to a spherical surface up to an angle of incidence close to 90 degrees. After analyzing the optical properties including spot diagrams in a plane vertical to the principal ray on the surface, the lens was found to be very effective in viewing an object over a very wide angle and is therefore thought to be especially suitable for many fields of application where image and information is transmitted over a very wide field at a time. Practically it is possible to apply this lens as a sensor of robot’s eye with a total field angle of almost 180 degrees.     

Electromagnetically induced transparency and light slowdown for Λ-like systems with a structured continuum

Electric susceptibility of a laser-dressed atomic medium is calculated for a model Λ-like system including two lower states and a continuum structured by a presence of an autoionizing state or a continuum with a laser-induced structure. Depending on the strength of a control field, it is possible to obtain a significant reduction of the light velocity in a narrow frequency window in the conditions of a small absorption. It is shown that increasing the values of the asymmetry parameters leads to an increase of the values of both real and imaginary parts of the medium susceptibility and to an increase of the width of the transparency window, compared with the case of a flat continuum. A smooth transition is shown between the case of a flat continuum and that of a discrete state serving as the upper state of a Λ system.     

污染气体扫描成像红外被动遥测技术研究

傅里叶变换红外光谱技术可实现大气中污染气体的远程被动遥测。而污染气团的位置和分布,对于有害气体泄露情况下泄露位置勘查和污染扩散态势的评估来说是至关重要的。据此设计了一套红外被动成像遥测系统,系统由傅里叶变换光谱仪、数据采集处理软件、扫描系统、可见光成像系统和计算机组成。以六氟化硫为示踪气体,开展了遥测验证实验。通过非线性最小二乘算法结合辐射传输计算反演获得了目标气体的柱浓度,并用伪彩色图显示其分布情况,最后以可见光图像叠加伪彩色柱浓度分布图的形式显示结果。实验分析表明,该系统具有高探测灵敏度,并以可视化和定量的方式显示污染的空间分布情况。     

Photonic mm-Wave Generation Using a Double Passband Fiber Bragg Grating Filter

We report a simplified version of a mm-wave generator employing the sideband filtering technique which uses a single optical sideband filter. Instead of using a Mach-Zehnder-like fiber network to select a pair of sidebands, we employ a single Fabry-Perot fiber Bragg grating with a pair of passbands separated by the mm-wave frequency. Using a single filter eliminated the need for polarization control and pathlength matching that was required by the former interferometer-like arrangement. We describe a 30 GHz generator design and present its mm-wave signal spectrum showing an instrument-limited linewidth of ~20 Hz. The generation of such an extremely narrow signal spectrum from a laser with a 1 MHz linewidth demonstrates the remarkable laser frequency noise cancellation property of the sideband filtering technique.     

Optimal Force Mismatch for Fluctuation-Activated Transition in a System of Two Coupled Bistable Oscillators

We study the fluctuation-activated transition process in a system of two coupled forced bistable oscillators with a mismatch σ in the force constants. As the coupling strength μ is increased, the transition pathway undergoes four stages changes from a two-step process with two candidate pathways to a mixture of a two-step pathway and a one-step pathway to a one-step process with also two candidate pathways and then to a one-step process with a single pathway.Interestingly, we find that the total transition rate depends nonmonotonically on σ in the weak coupling: a maximal rate appears in an intermediate magnitude of σ. Moreover, the rate also exhibits an unexpected maximum as a function ofμ. The results are in an excellent agreement with our numerical simulations by forward flux sampling.     

Tunneling and transport problems for a quantum mechanical Brownian particle

The Kanai model of a quantum mechanical Brownian particle is used to examine the effect of interactions between particles and their environment. Random forces cause the thermalization of the particle. Reflection of a particle from a step barrier is analyzed. The problem of tunneling of the Brownian particle through a rectangular barrier is solved. Finally, a solution for a Brownian particle in a box is presented.