Optimal design of a multilayer diffractive optical element for dual wavebands

A method for optimal design of a multilayer diffractive optical element (MLDOE) for dual-wide-waveband optical systems is presented with consideration of polychromatic integral diffraction efficiency (PIDE) and the weight factors of PIDE for each waveband. The design process and simulation of a MLDOE in mid-wave and long-wave IR are described, and the comparison of diffraction efficiency of the MLDOEs for different design wavelength pairs determined by different methods is given. This method can make the design process more rational and more reasonable and can give a better design result than that with the conventional design method.     

Optimization and analysis of multi-layer diffractive optical elements in visible waveband

An optimization for diffraction efficiency of the multi-layer diffractive optical elements (MLDOEs) is presented, then the construction process of optimization program is introduced in detail. A new optimization initial point is proposed, which contributes to analyze the relationship between the optimal relief heights and the base materials. Through the optimization examples, diffraction efficiency higher than 99.7% from F line (486.1327 nm) to C line (656.2725 nm) of visible waveband can be achieved, and the polychromatic integral diffraction efficiency (PIDE) over the entire waveband is 99.94%. Moreover, this paper compares and analyzes optimization results of different glass pairs, and the relationship between the optimal relief heights pairs and base materials pairs is obtained.     

含有双层衍射光学元件的中波/长波消热差光学系统的设计

建立了工作在一定入射角度范围内的多层衍射光学元件的复合带宽积分平均衍射效率的分析模型。基于衍射光学元件所具有的独特的消色差和消热差性质,设计了一个含有双层衍射光学元件的工作在(3.7~4.8) μm和(7.7~9.5) μm红外双波段光学系统。光学系统的焦距为200 mm,F#为2。采用像元数为320×256、间距为30 μm的制冷型探测器。该系统在空间频率17 lp/mm时,中、长波红外MTF分别高于0.66和0.54;最大RMS半径小于11.702 μm;波前像差小于0.191 7λ;最大离焦量小于焦深;在-55℃~71℃范围内实现了无热化设计。入射到衍射面上的角度为0°~5.19°,该双层衍射光学元件在中波和长波波段的复合带宽积分平均衍射效率分别为99.81%和97.36%。含有双层衍射光学元件的红外双波段光学系统结构简单,像质优良,可以广泛应用于军事探测系统中。     

A generalized 2D FDTD model for photonic crystal fibers with frequency dependent media

A generalized model based on the two-dimensional finite-difference time-domain (2D FDTD) method for photonic crystal fibers (PCF) with frequency dependent media is presented. The Maxwell’s curl equations are formulated using flux density and the magnetic field. Auxiliary differential equations are used with complex-conjugate pole-residue pairs which incorporate the material dispersion of the dispersive media. The model is demonstrated to be a unified approach for arbitrary dispersive materials; therefore, it definitely reduces implementation cost when dealing with different frequency-dependent materials.     

Modelling and Numerical Valuation of Power Derivatives in Energy Markets

In this work we investigate the pricing of swing options in a model where the underlying asset follows a jump diffusion process. We focus on the derivation of the partial integro-differential equation (PIDE) which will be applied to swing contracts and construct a novel pay-off function from a tree-based pay-off matrix that can be used as initial condition in the PIDE formulation. For valuing swing type derivatives we develop a theta implicit-explicit finite difference scheme to discretize the PIDE using a Gaussian quadrature method for the integral part. Based on known results for the classical theta-method the existence and uniqueness of solution to the new implicit-explicit finite difference method is proven. Various numerical examples illustrate the usability of the proposed method and allow us to analyse the sensitivity of swing options with respect to model parameters. In particular, the effects of number of exercise rights, jump intensities and dividend yields will be investigated in depth.     

The investigation of three layers diffraction optical element with wide field of view and high diffraction efficiency

In this paper, a novel three layers diffraction optical element (TLDOE) composed of the optical materials with different indices and dispersion in each layer has been designed and investigated, the principle of selecting optical materials is discussed as well. The diffraction efficiency of the TLDOE at each wavelength in designed band is larger than 90% and the field of view (FOV) can even reach 110°, which can effectively improve energy utilization ratio and image quality of the hybrid refractive–diffractive optical system.     

Observations of dispersion cancellation of entangled photon pairs

An experimental study of the dispersion cancellation occurring in frequency-entangled photon pairs is presented. The approach uses time-resolved up-conversion of the pairs, which has temporal resolution at the femtosecond level, and group-delay dispersion sensitivity of ≈ 20 fs2 under experimental conditions. The cancellation is demonstrated with dispersion stronger than ± 10(3) fs2 in the signal (-) and idler (+) modes.     

Study of angular responses of mixed amplitude--phase holographic gratings: shifted Borrmann effect

We present theoretical results for angular responses of transmitted and diffracted beams in mixed amplitude-phase holographic gratings. Experimental results for gratings recorded in photographic emulsions and developed without a bleaching bath, with diffraction efficiencies of >20% , are also presented. The model shows an angular shift between minimum transmittance and maximum diffraction efficiency when both index modulation and absorption coefficient modulation are present. Also, the Borrmann effect was found outside the Bragg angle. This method can be extended to a study of the mechanism of image formation in materials such as bacteriorhodopsin and azo-dye-doped polymers that exhibit both types of modulations (index and absorption).     

温度涨落和波长偏离对衍射透镜性能的影响

根据菲涅耳衍射透镜的特点,阐明了温度色散和波长色散的概念,并建立了相应的数学表达式,给出了衍射效率与温度和波长的关系式,在此基础上做了较为全面系统的理论和数值分析,评估了温度场发生变化以及使用波长和设计波长发生偏离对衍射透镜性能的影响程度.结果表明:波长偏离对衍射透镜性能的影响要比温度涨落明显得多,其中,波长色散具有非线性特征.     

Nonsinusoidal absorption gratings in photographic materials

The diffraction efficiencies of pure absorption gratings are investigated in photographic materials using a coupled multiwave analysis with a realistic photographic film model. It is, for example, shown that the maximum efficiency of the order +1 of non-sinosoidal absorption gratings is almost independent of the generally used regime indicator Q′. Examples of diffraction characteristics for thin absorption gratings are included.     

利用各向同性半导体晶体差频产生可调谐THz辐射的理论研究

理论研究了利用剩余射线带色散补偿相位匹配原理，在Ⅲ-Ⅴ族和Ⅱ-Ⅳ族光学各向同性的半导体非线性晶体中差频产生可调谐THz波的可行性问题.根据这些半导体材料的色散特性，并以近简并点双共振KTP-OPO的可调谐相干双波长输出作为差频抽运源，对它们的相位匹配能力、差频增益特性、品质因数以及差频过程中的相干长度进行了理论分析和计算，确定了ZnTe晶体是在共线相位匹配情况下较为理想的THz波差频晶体，而InP晶体则更适合用于非共线相位匹配情况. 关键词： 非线性光学 THz辐射 差频 各向同性半导体晶体     

Revised interpretations of the available x-ray data for B-DNA

Comparisons are made between calculations based on the double-helix and side-by-side models of DNA and data taken from the available x-ray diffraction measurements of the B form of DNA. The SBS model invoked here is an improvement on the one which was published earlier. In our estimation the fibre diffraction patterns do not significantly favour either model. However, the DH model is incompatible with the on-axis form of the cylindrically-averaged Patterson function, whereas the SBS model is compatible (this result is relatively insensitive to appreciable modifications to the SBS structure)—the crucial question is whether the quality of the data is sufficient to make this finding significant. It is shown that the maximum expected effect on the fibre pattern, of exchanging A-T base pairs for G-C base pairs, is less than the probable experimental error.     

衍射光栅的第二类角色散及其特性分析

在由矢量衍射理论得到的锥面衍射情形下的广义光栅方程基础上，给出了对应于衍射极角的衍射光栅第一类角色散公式和对应于衍射方位角的衍射光栅第二类角色散公式，并通过理论和数值分析导出了第二类角色散发生突变的条件及相应的数学表达式. 关键词： 衍射光栅 锥面衍射 第一类角色散 第二类角色散     

Modeling of pulsed finite-amplitude focused sound beams in time domain.

A time-domain numerical model is presented for simulating the finite-amplitude focused acoustic pulse propagation in a dissipative and nonlinear medium with a symmetrical source geometry. In this method, the main effects responsible in finite-amplitude wave propagation, i.e., diffraction, nonlinearity, and absorption, are taken into account. These effects are treated independently using the method of fractional steps with a second-order operator-splitting algorithm. In this method, the acoustic beam propagates, plane-by-plane, from the surface of a highly focused radiator up to its focus. The results of calculations in an ideal (linear and nondissipative) medium show the validity of the model for simulating the effect of diffraction in highly focused pulse propagation. For real media, very good agreement was obtained in the shape of the theoretical and experimental pressure-time waveforms. A discrepancy in the amplitudes was observed with a maximum of around 20%, which can be explained by existing sources of error in our measurements and on the assumptions inherent in our theoretical model. The model has certain advantages over other time-domain methods previously reported in that it: (1) allows for arbitrary absorption and dispersion, and (2) makes use of full diffraction formulation. The latter point is particularly important for studying intense sources with high focusing gains.     

Modelling Laser-Based Table-Top THz Sources: Optical Rectification,Propagation and Electro-Optic Sampling

A model describing the generation of THz pulses by optical rectification and the detection of THz pulses by electro-optic sampling is presented. The model is comprehensive and mostly analytical: physical phenomena such as dispersion, group velocity mismatch, multiple reflections and diffraction are represented by one dimensional transfer functions. The model is compared with experimental results and shows good agreement with experiments. It is shown that including diffraction is crucial for retrieving the details of the THz spectrum.     

An accurate method to calculate the negative dispersion generated by prism pairs

Based on the principle of diffraction for light transport in prisms, we figured the physical image for light beams passing through a pair of prisms. The mechanism to induce negative dispersion was analyzed and the numerical expression of optical path length was provided. From a series of mathematical equations, we calculate the quantity of negative dispersion, such as the second- and third-order dispersion, induced by prism pairs. Compared with the expressions of Fork et al. (Opt. Lett. 9(5) (1984) 150), our equations can lead to accurate results and reasonably elucidate the implication of dispersion.     

The small‐angle and wide‐angle X‐ray scattering set‐up at beamline BL9 of DELTA

The multi‐purpose experimental endstation of beamline BL9 at the Dortmund Electron Accelerator (DELTA) is dedicated to diffraction experiments in grazing‐incidence geometry, reflectivity and powder diffraction measurements. Moreover, fluorescence analysis and inelastic X‐ray scattering experiments can be performed. Recently, a new set‐up for small‐angle and wide‐angle X‐ray scattering utilizing detection by means of an image‐plate scanner was installed and is described in detail here. First small‐angle X‐ray scattering experiments on aqueous solutions of lysozyme with different cosolvents and of staphylococcal nuclease are discussed. The application of the set‐up for texture analysis is emphasized and a study of the crystallographic texture of natural bio‐nanocomposites, using lobster and crab cuticles as model materials, is presented.     

基于双光栅成像的RGB模型色彩还原效果的研究

基于双光栅衍射成像的实验方案,利用双光栅的色散和汇合光谱效应特性,用电脑摄像头拍摄作为物体的RGB模型,得到了RGB颜色模型的像。利用Photo shop软件将RGB颜色模型和得到的像进行颜色通道分离,再进行数据化分析处理,探究双光栅的RGB色彩模型色彩还原情况以及不同光栅组合对RGB颜色模型的色彩还原效果的影响。     

Single mode optical fiber characterisation by the LP11 mode radiation pattern

We describe a method for determining the V-value from the far-field radiation pattern of dual mode optical fibers (this method is an extension of the work by Gambling et al. for the LP₁₁ modes). The method involves measurements of the maximum radiation angle and the angle of the first minimum. Curves are presented which can be used with dual mode fibers, determining the core diameter, the refractive index difference between core and cladding, as well as the V-value in the single mode regime for longer wavelength operation with the help of dispersion curves of the dopant materials.     

Lagrangian Dispersion in Gaussian Self-Similar Velocity Ensembles

We analyze the Lagrangian flow in a family of simple Gaussian scale-invariant velocity ensembles that exhibit both spatial roughness and temporal correlations. We argue that the behavior of the Lagrangian dispersion of pairs of fluid particles in such models is determined by the scale dependence of the ratio between the correlation time of velocity differences and the eddy turnover time. For a non-trivial scale dependence, the asymptotic regimes of the dispersion at small and large scales are described by the models with either rapidly decorrelating or frozen velocities. In contrast to the decorrelated case, known as the Kraichnan model and exhibiting Lagrangian flows with deterministic or stochastic trajectories, fast separating or trapped together, the frozen model is poorly understood. We examine the pair dispersion behavior in its simplest, one-dimensional version, reinforcing analytic arguments by numerical analysis. The collected information about the pair dispersion statistics in the limiting models allows to partially predict the extent of different phases of the Lagrangian flow in the model with time-correlated velocities.