Transmission matrices and lumped parameter models for continuous systems

The use of transmission matrices and lumped parameter models for describing continuous systems is the subject of this study. Non-uniform continuous systems which play important roles in practical vibration problems, e.g., torsional oscillations in bars, transverse bending vibrations of beams, etc., are of primary importance.

A new approach for deriving closed form transmission matrices is applied to several classes of non-uniform continuous segments of one dimensional and beam systems. A power series expansion method is presented for determining approximate transmission matrices of any order for segments of non-uniform systems whose solutions cannot be found in closed form. This direct series method is shown to give results comparable to those of the improved lumped parameter models for one dimensional systems.

Four types of lumped parameter models are evaluated on the basis of the uniform continuous one dimensional system by comparing the behavior of the frequency root errors. The lumped parameter models which are based upon a close fit to the low frequency approximation of the exact transmission matrix, at the segment level, are shown to be superior. On this basis an improved lumped parameter model is recommended for approximating non-uniform segments. This new model is compared to a uniform segment approximation and error curves are presented for systems whose areas very quadratically and linearly. The effect of varying segment lengths is investigated for one dimensional systems and results indicate very little improvement in comparison to the use of equal length segments. For purposes of completeness, a brief summary of various lumped parameter models and other techniques which have previously been used to approximate the uniform Bernoulli-Euler beam is a given.

FDTD analysis of Talbot effect of a high density grating

Talbot effect of a grating with different flaws is analyzed with the finite-difference time-domain (FDTD) method. The FDTD method can show the exact near-field distribution of different flaws in a high-density grating, which is impossible to obtain with the conventional Fourier transform method. The numerical results indicate that if a grating is perfect, its Talbot imaging should also be perfect; if the grating is distorted, its Talbot imaging would also be distorted. Furthermore, we can evaluate high density gratings by detecting the near-field distribution.

Optical generaton of millimeter-wave pulses using a fiber Bragg grating in a fiber-optics system

A scheme is proposed to transform an optical pulse into a millimeter-wave frequency modulation pulse by using a weak fiber Bragg grating (FBG) in a fiber-optics system. The Fourier transformation method is used to obtain the required spectrum response function of the FBG for the Gaussian pulse, soliton pulse, and Lorenz shape pulse. On the condition of the first-order Born approximation of the weak fiber grating, the relation of the refractive index distribution and the spectrum response function of the FBG satisfies the Fourier transformation, and the corresponding refractive index distribution forms are obtained for single-frequency modulation and linear-frequency modulation millimeter-wave pulse generation. The performances of the designed fiber gratings are also studied by a numerical simulation method for a supershort pulse transmission. (c) 2007 Optical Society of America.

频谱泄漏对正弦相位调制干涉测量精度的影响何

在正弦相位调制(SPM)干涉仪中,若调制频率或者采样频率发生变化将使干涉信号出现频谱泄漏,减小了谐波分量的幅值,在测量结果中引入了误差。对频谱泄漏的产生及其对测量精度的影响进行了理论分析,获得了频谱泄漏引入测量误差的计算方法。实验测得频率漂移量在-0.3～0.3 Hz内,得到的频谱泄漏引入的误差为0.3～7.9 nm,当超出这个范围时,频谱泄漏误差将迅速增长。实验结果与模拟分析结果一致。

新型板条激光器的离轴混合腔模场计算

报道了一种新型双板条离轴混合腔激光器。这种激光器结构通过改变传统的冷却方式和采用特殊的谐振腔设计，将使从第一块介质板条高温一侧出射的激光对称地进入另一块板条的低温一侧，从而可对由于温度分布不均匀造成的波面畸变进行一定程度的自校正，减少热效应的影响，可望提高激光器的输出功率和光束质量。利用快速傅里叶变换（FFT）对这种激光器的近场、远场以及相位等模场特性进行了数值计算。分析了波面畸变对输出光束质量的影响，并与常规双板条激光器进行了比较，结果表明这种新型双板条离轴混合腔激光器可以实现一定程度的波面畸变自补偿，

Mode properties of off-axis one-sided hybrid resonator for novel high average power dual-slab laser

A novel dual-slab laser with off-axis one-sided hybrid resonator is presented. The mode properties of the hybrid resonator are calculated using a fast Fourier transform method (FFT). The influence of wavefront distoration on the output beam quality is considered. Results indicate that the novel dual-slab laser is better than the normal dual-slab laser with off-axis one-sided hybrid resonator.

Optimization of near-field optical field of multi-layer dielectric gratings for pulse compressor

Multi-layer dielectric (MLD) gratings for pulse compressors in high-energy laser systems should provide high diffraction efficiency as well as high laser induced damage thresholds (LIDT). Nonuniform optical near-field distribution is one of the important factors to limit their damage resistant capabilities. Electric field distributions in the gratings and multi-layer film region are analyzed by using Fourier modal method. Optimization of peak electric field in the gratings ridge is performed with a merit function, including both diffraction efficiency and electric field enhancement when the top layer material is HfO2 and SiO2, respectively. A set of optimized gratings parameters is obtained for each structure, which reduce the peak electric field within the gratings ridge to being respective 1.39 and 1.84 times the value of incident light respectively. Finally, we also discuss the effects of gratings refractive index, gratings sidewall angle and incident angle on peak electric field in the gratings ridge. (c) 2006 Elsevier B.V. All rights reserved.

多层介质膜脉冲压缩光栅近场光学特性分析

利用傅里叶模式理论分析了TE波自准直角入射的使用条件下，多层介质膜光栅的光栅区和多层膜区电场分布的特点．分别讨论了HfO2和SiO2为顶层光栅材料时，光栅结构参数对光栅脊峰值电场的影响，结果表明，对于不同膜厚的顶层材料，存在一个最佳膜厚度，使光栅脊峰值电场最小，并且当膜厚增大时，设计大高宽比的光栅可以降低该电场峰值．最后，在大角度条件下使用多层膜光栅也可以降低光栅脊处的峰值电场．

Design of high-efficiency diffraction gratings based on total internal reflection for pulse compressor

We present designs of high-efficiency compression grating based on total internal reflection (TIR) for picosecond pulse laser at 1053 nm. The setup is devised by directly etching gratings into the bottom side of a prism so that light can successfully enter (or exit) the compression grating. Dependence of the -1 order diffraction efficiencies on the constructive parameters is analyzed for TE- and TM-polarized incident light at Littrow angle by using Fourier modal method in order to obtain optimal grating structure. The electric field enhancement within the high-efficiency TIR gratings is regarded as another criterion to optimize the structure of the TIR gratings. With the criterion of high diffraction efficiency, low electric field enhancement and sufficient manufacturing latitude, TIR compression gratings with optimized constructive parameters are obtained for TE- and TM-polarized incident light, respectively. The grating for TE-polarized light exhibits diffraction efficiencies higher than 0.95 within 23 nm bandwidth and relatively low square of electric field enhancement ratio of 5.7. Regardless of the internal electric field enhancement, the grating for TM-polarized light provides diffraction efficiencies higher than 0.95 within 42 nm bandwidth. With compact structure, such TIR compression gratings made solely of fused silica should be of great interest for application to chirped pulse amplification (CPA) systems. (c) 2007 Elsevier B.V. All rights reserved.

全内反射式衍射光栅近场光学特性

利用傅里叶模式理论分析了具有高衍射效率的全内反射式衍射光栅在TE和TM偏振态下的近场光分布特点，讨论了光栅结构参数以及入射角度对光栅内电场增强的影响。结果表明：全内反射光栅内部电场分布对偏振态较敏感，光栅槽深和占宽比对电场增强影响较小，光栅内的峰值电场随光栅周期增大而增大，并且峰值电场随着入射角度的增大而减小。在应用于高功率激光时，降低光栅内部的电场增强可以有效降低损伤风险。

反射型导模共振滤波器设计

导模共振滤波器由于其高峰值反射率,低旁带反射,窄带以及带宽可控等优良特性引起了人们极大的关注,采用亚波长光栅的导模共振效应可以实现传统基于高低折射率介质的多层膜滤波器所无法实现的特殊功能,在弱调制模式下,其共振带宽可以被压缩到零点几纳米,但是由于介质表面和空气层的菲涅耳反射,使得偏离或者远离共振区时的反射率偏高,根据等效介质理论,亚波长光栅在远离共振区可以被看为均匀的薄膜,本文通过对导模共振光栅进行单层、双层以及三层抗反射设计,有效的降低了导模共振光栅的旁带反射率,从而在可见光波段获得了性能优良的共振滤波器.

可见光波段双层浮雕型导模共振滤波器设计与分析

基于傅里叶模式理论分析了双层浮雕型导模共振光栅的共振效应,分别讨论了光栅的槽深、剩余厚度、周期以及填充系数对峰值反射率、带宽、旁带反射率的影响.数据计算表明,欠刻蚀情形的误差宽容度远远优于过刻蚀情形,两者在光栅槽深相对误差小于15%的范围内,都能保证共振峰的衍射效率高于99.5%,在相同的误差范围内,共振峰线宽的相对误差将分别达到7%和60%,因此厚度误差集中反映在对共振线宽的改变上.另外,光栅周期和填充系数的变化将明显改变共振峰中心波长和线宽.

Electric field distribution in resonant reflection filters under normal incidence

Electric field distributions inside resonant reflection filters constructed using planar periodic waveguides are investigated in this paper. The electric fields may be intensified by resonance effects. Although the resonant reflection peaks can be quite narrow using weakly modulated planar periodic waveguides, the strong electric field enhancement limits their use in high-power laser systems. Strongly modulated waveguides may be used to reduce the electric field enhancement and a cover layer may be used to narrow the bandwidth at the same time. Desired results (i.e. almost no electric field enhancement together with narrow bandwidth) can be realized using this simple structure.

Ultra-narrow bandwidth resonant reflection grating filters using the second diffracted orders

In this paper, we design resonant reflection grating filters employing the second diffracted orders as the leaky modes, then analyze the bandwidth of the reflection peak and the electric field distributions inside the wavegude under resonance. The numeric calculation confirms that ultra-narrow resonant reflection peaks can be observed in these structures. At the same time, strong electric field enhancement appears under resonance. It provides a new approach to diversify the resonant reflection filters and may open a new way to the realization of ultra-narrow bandwidth filters. (C) 2008 Elsevier B.V. All rights reserved.

Periodic autoregressive moving average models for the analysis of streamflow [abstract]

EXTRACT (SEE PDF FOR FULL ABSTRACT): Streamflow values show definite seasonal patterns in their month-to-month correlation structure. The structure also seems to vary as a function of the type of stream (coastal versus mountain or humid versus arid region). The standard autoregressive moving average (ARMA) time series model is incapable of reproducing this correlation structure. ... A periodic ARMA time series model is one in which an ARMA model is fitted to each month or season but the parameters of the model are constrained to be periodic according to a Fourier series. This constraint greatly reduces the number of parameters but still leaves the flexibility for matching the seasonally varying correlograms.