A comparison of spatial discretization schemes for differential solution methods of the radiative transfer equation

A comparison of discretization schemes required to evaluate the radiation intensity at the cell faces of a control volume in differential solution methods of the radiative transfer equation is presented. Several schemes developed using the normalized variable diagram and the total variation diminishing formalisms are compared along with essentially non-oscillatory schemes and genuinely multidimensional schemes. The calculations were carried out using the discrete ordinates method, but the analysis is equally valid for the finite-volume method. It is shown that the S schemes of the genuinely multidimensional family perform quite well, particularly in problems with discontinuous radiation intensity fields. However, they are time consuming, and so they do not always become more attractive regarding the trade-off between accuracy and computational requirements, in comparison with other high-order schemes that, although being less accurate, are also more economical.     

A comparison of optically and electronically controlled optical switches

Electronically and optically controlled optical switches are compared with respect to switch energy requirements. Only switches based on optical phase change are treated, since these have the largest flexibility. Further, only switches that preserve input wavelength at the output are considered, due to cascadeability requirements. It is argued that as long as ‘all-optical’ switches need electronically controlled switches for information transfer to the optical signals controlling the all-optical switch, this will compromise any other advantages that the all-optical switch and the corresponding systems might have. A further application for all-optical switches, which currently are orders of magnitude faster than electronically controlled ones, would be in banks of electronically controlled slower all-optical switches which are all-optically multiplexed to drive all-optical switches to data rates not currently achievable by electronically controlled switches. It is argued that such systems will be complex, requiring sophisticated electronic synchronization and being inferior to corresponding wavelength division multiplexing systems. Power dissipation and switch energy are analyzed for two different physical mechanisms for controllably changing the refractive index in the all-optical and electronically controlled optical switches: Pockels and Kerr effects as well as the plasma or free carrier effect and the relative merits of electronically and optically controlled optical switches using these are discussed. It is shown that, in the former case, (Pockels and Kerr effects) using representative data, electronically controlled switches are generally more power efficient than the all-optical counterparts.     

Mixed phase and absorption thin gratings diffraction

The coupled wave theory of Raman and Nath diffraction is extended to the case of thin anisotropic holographic media with grating vector parallel to the medium boundaries. Solutions for the wave amplitudes, diffraction efficiencies, and angular mismatch sensitivities are given in transmission geometries for the case of mixed dielectric and absorption modulations. For an apparent distinction, the results are given only for dielectric modulation. The main difference of the new results, with respect to the expressions valid for isotropic media, arises due to the walk-off between the wave-front and energy propagation directions. The difference is particularly important in materials with large birefringence, such as organic crystals, ordered polymers, and liquid crystalline cells.     

Solutions of the thin phase grating diffraction equation

An integral solution and a Bessel function solution of the thin phase grating difference-differential equation that describes diffraction by a thin arbitrarily-shaped periodic grating are presented and discussed.     

The thin lens equation for optical parametric image conversion

It is shown that the image upconverter can operate with point source pump-beams as well as the commonly used planar pump source. The major effect of the pump beam divergence is not to degrade the resolution but is to change the transverse and longitudinal magnification of the image. We demonstrate by a paraxial ray-tracing analysis that these changes in image dimensions and location obey relations quite similar to thin-lens formulae.     

原子结构中求解Hartree-Fock方程的几种方法及其比较

主要介绍了原子结构理论中Hartree- Fock方程的几种近似求解方法,并对这几种方法的优缺点进行比较,总结出各种方法的适用范围.     

Comparative study of optical analysis methods for thin films

Three popular optical analysis methods (the transfer-matrix method, the Tinkham formula, and Beer's law) have been used for analyzing the optical spectra of thin films. While the transfer-matrix method is an accurate method, the Tinkham formula and Beer's law are approximate methods. Here we investigated the three methods using measured transmittance spectra of insulating transition-metal dichalcogenide (TMD) thin films on a quartz substrate. Three different semiconducting 2H-TMD systems (MoS₂, MoSe₂, and MoTe₂) were measured and analyzed. The optical conductivities obtained from the measured transmittance spectra using the transfer-matrix method and Tinkham formula and the absorption coefficients obtained using the transfer-matrix method and Beer's law were compared. The comparisons show some discrepancies. The reasons for the discrepancies between the results obtained via the two different methods were examined and the application limitations of the Tinkham formula and Beer's law were discussed.     

利用光学方法测量薄膜厚度的研究

介绍了测量固体薄膜厚度的光学方法。分析了这些方法的光学原理,对所使用的光源、测量范围、测量精度、实现的难度以及方法所适用的场合等多种因素进行了比较分析,结果表明:对于厚度在10～100μm范围的固体薄膜而言,激光干涉法是一种简单、易于实现且测量精度较高的方法。     

Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings

The complete spatiotemporal characterization of the diffracted field of ultrashort pulses after passing through circularly symmetric binary phase diffraction gratings is carried out. The complex field is registered at different planes behind the gratings with an ultrashort-pulse measurement technique called SEA TADPOLE. Numerical simulations based on scalar diffraction theory are compared with the measurements.     

用错位相位光栅产生的可调光学双阱

提出了用相位型错位光栅产生光学双阱的新方案.用平面光波(或TEM₀₀模式高斯光波)照射、正透镜聚焦,在透镜焦平面上产生的适用于冷原子或冷分子囚禁的多对可调光学双阱.计算和推导了双阱的光强分布、强度梯度以及光阱的几何参数与光学系统参数间的解析关系,研究了双阱到单阱三种不同的演化过程.同时还计算了光学双阱囚禁冷原子的光学偶极势和光子散射速率.研究发现,该方案不仅简单可行、操作方便,而且在原子物理、原子光学、分子光学和量子光学领域中有着广阔的应用前景. 关键词： 原子光学 相位光栅 光学双阱 冷原子囚禁     

High speed optical path routing by using four-wave mixing and a wavelength router with fiber gratings and optical circulators

A novel all-optical-path-routing technique is described, which employs four-wave mixing in a dispersion-shifted fiber and a wavelength router with fiber gratings and optical circulators. The signal wavelength is converted to a specified channel by four-wave mixing, and is finally selected with the wavelength router. It offers good potential for enabling the number of output ports of a wavelength router to be extended as it provides a very sharp spectral edge and a low insertion loss.     

A search for the simplest chaotic partial differential equation

A numerical search for the simplest chaotic partial differential equation (PDE) suggests that the Kuramoto-Sivashinsky equation is the simplest chaotic PDE with a quadratic or cubic nonlinearity and periodic boundary conditions. We define the simplicity of an equation, enumerate all autonomous equations with a single quadratic or cubic nonlinearity that are simpler than the Kuramoto-Sivashinsky equation, and then test those equations for chaos, but none appear to be chaotic. However, the search finds several chaotic, ill-posed PDEs; the simplest of these, in the discrete approximation of finitely many, coupled ordinary differential equations (ODEs), is a strikingly simple, chaotic, circulant ODE system.     

衍射光栅位相拼接的计算分析

从光学远场衍射的原理出发 ,研究了两块具有完全相同参数的衍射光栅间相互拼接时不同的位相与谱线强度变化的特性关系 ,建立了相应的数学模型 ,并利用计算机进行了模拟计算。计算的结果表明 :拼接出的光栅比其中单一一块光栅在增加了光强的同时也提高了分辨率 ,为通过采用拼接方法来获取大面积光栅提供了理论依据。     

光学元件波前畸变对驱动器光路设计的影响

高功率激光驱动器光路设计要考虑像传递、鬼像规避和杂散光管理等多项优化措施.基于衍射光学传播理论,从输出负载能力提升的角度研究大口径光学元件波前特性对驱动器光路设计参数优化的影响.研究表明,驱动器末级光路的排布间隔如果控制在6 m以上,将非常有助于提高激光驱动器的输出负载能力.一般情况下,波前峰谷值达到0.34λ的单块大口径光学元件能使高功率激光的近场光束质量最大下降约10%,达到1.36λ后最大下降约21%;波前分布特性不同的多片大口径光学元件的波前相消叠加有利于降低中频波前部分对装置负载能力的影响,但是,大口径光学元件的非线性效应会加重中频波前对装置输出负载能力的影响;在限定大口径元件损伤阈值20J/cm~2的前提下,光路排布紧凑的激光驱动器末级输入激光通量控制在16.8J/cm~2之下不易损伤光学元件.相对宽松的光路设计可以进一步提高末级输出激光的平均通量水平,非常有利于激光驱动器装置输出负载能力的提升.     

光场空间相干性的测量方法及比较

本文归纳了基于分波前干涉原理的具有代表性的干涉测量方法——杨氏双孔干涉法、逆波前杨氏干涉法和非冗余孔径阵列干涉测量法,以及基于分振幅干涉原理的干涉测量方法——自参考干涉测量法;介绍了各种测量方法的工作原理、实验配置;比较了4种测量方法的优缺点,并给出每种方法的最佳应用领域。本文结论可为根据对空间相干性测量的不同要求,选择合适的测量方法提供初步参考。     

Superradiant emission dynamics of an optically thin material sample in a short-decay-time optical cavity

We report observations of optical superradiant emission and the atomic evolution it drives under conditions closely approximating those originally envisioned in the classic work of Dicke [Phys. Rev. 93, 99 (1954)]. Our experiment involves an optically thin solid sample in a short-lifetime optical cavity whose homogeneous coherence is cryogenically stabilized. Pulsed coherent excitation initiates superradiant emission which subsequently drives the sample to higher or lower states of coherence. Suppression of dephasing via cryogenics and propagation effects through use of an optically thin sample and cavity provides one of the clearest and cleanest examples of Dicke superradiance yet reported.     

On the comparison of semi-analytical methods for the stability analysis of delay differential equations

This paper provides the first comparison of the semi-discretization, spectral element, and Legendre collocation methods. Each method is a technique for solving delay differential equations (DDEs) as well as determining regions of stability in the DDE parameter space. We present the necessary concepts, assumptions, and equations required to implement each method. To compare the relative performance between the methods, the convergence rate and computational time for each method is compared in three numerical studies consisting of a ship stability example, the delayed damped Mathieu equation, and a helicopter rotor control problem. For each study, we present one or more stability diagrams in the parameter space and one or more convergence plots. The spectral element method is demonstrated to have the quickest convergence rate while the Legendre collocation method requires the least computational time. The semi-discretization method on the other hand has both the slowest convergence rate and requires the most computational time.     

Investigations on the wavelength dependence of optically induced long-period Bragg gratings

We numerically analyze the conversion of transverse modes with optically induced long-period Bragg gratings. These gratings are generated by a recently developed technique which uses a writing beam guided within the fiber to introduce a transient grating via the optical Kerr effect. We demonstrate several settings for conversion between different transverse modes, including conversion over a broad spectral range of up to 60?nm. The tunability of the grating parameters could promote novel applications.