Wavelength-scanning interferometry of a transparent parallel plate with refractive-index dispersion

Testing for flatness of an optical parallel plate in a Fizeau interferometer suffers from problems caused by multiple-beam interference noise. Each internal-reflection component can be separated from the signal by its modulation frequency in a wavelength-scanned interferometer; however, the frequency depends on the thickness and the refractive-index dispersion of the test plate and on the nonlinearity of the scanning source. With a new 19-sample wavelength-scanning algorithm we demonstrate the elimination of the reflection noise, the effect of the dispersion up to the second order of the reflectance of the test plate, and as the nonlinearity of the source. The algorithm permits large tolerance in the air-gap distance, thus making it somewhat independent of the thickness of the test plate. The minimum residual reflection noise with this algorithm for testing a glass plate is approximately lambda/600. Experimental results show that the front surface of the test plate was measured within 1 nm rms of its true shape over a 230-mm-diameter aperture.     

Stochastic dark solitons for a higher-order nonlinear Schrödinger equation in the optical fiber

In this paper, a stochastic higher-order nonlinear Schrödinger equation, which describes the wave propagation in the optical fiber with stochastic dispersion and nonlinearity, is investigated analytically. Via the symbolic computation and white noise functional approach, the stochastic dark one- and two-soliton solutions are obtained, and effects of the Gaussian white noise on the stochastic dark one and two solitons are discussed. For the stochastic dark one soliton, velocity and phase change randomly because of the Gaussian white noise, but the energy, shape and amplitude keep unchanged during the soliton propagation. For the stochastic dark two solitons, effect of the Gaussian white noise leads to the inversion of the velocity directions, while the velocities have the same varying trend so that the interaction appears that the stochastic dark two solitons keep parallel.     

High-accuracy thickness measurement of a transparent plate with the heterodyne central fringe identification technique

In a modified Twyman-Green interferometer, the optical path variation is measured with the heterodyne central fringe identification technique, as the light beam is focused by a displaced microscopic objective on the front/rear surface of the test transparent plate. The optical path length variation is then measured similarly after the test plate is removed. The geometrical thickness of the test plate can be calculated under the consideration of dispersion effect. This method has a wide measurable range and a high accuracy in the measurable range.     

Determination of lamb wave dispersion data in lossy anisotropic plates using time domain finite element analysis. Part I: theory and experimental verification

A theoretical and experimental approach for extraction of guided wave dispersion data in plate structures is described. Finite element modeling is used to calculate the surface displacement data (in-plane and out-of-plane) when the plate is subject to either symmetrical or antisymmetrical impulsive force stimulation at one or both of the parallel faces. Fourier transformation of the resultant space-time displacement histories is then employed to obtain phase velocity as a function of frequency. Experimental verification in the case of antisymmetrical stimulation is provided by means of a high-power Q-switched laser source that is used to excite guided waves in the plate. The subsequent out-of-plane displacement data were then obtained by means of a scanning laser vibrometer, and good agreement between theory and experiment is demonstrated. Examples of dispersion data are provided for aluminum, and excellent correlation between the data sets and conventional Rayleigh-Lamb theory for plate structures was obtained. This was then extended to lossy polymeric plates, in addition to both unpolarized and polarized piezoelectric ceramic plates, again with good agreement between the finite element modeling and optical experiments. The last set of results prepares the way for a detailed investigation of the nonhomogeneous piezoelectric composite waveguides described in a companion paper (Part II).     

Interferometry for the evaluation of the dynamical optical and mechanical properties of transparent materials

A theory is developed which leads to an interferometric method for determining the dynamic ratio, Poisson's ratio to the modulus of elasticity, and the dynamic stress-optical coefficients of transparent plates, both during the same set of tests and without attaching mechanical or electrical sensors on the surface of the specimen.

The method requires a monochromatic light source, that is, a parallel beam is directed perpendicularly to the vicinity of a crack tip which exists in the plate specimen under investigation. The rays impinging on the crack tip are transmitted through the plate and reflected by the two parallel surfaces of the plate. At the same time, because of the variation of the optical path (index of refraction and thickness of the plate) in the said area, the rays are refracted in such a way as to form two caustic surfaces, one by the transmitted and one by the reflected rays. These two caustic surfaces, when intercepted with two opaque screens, provide two strongly illuminated curves of a general epicycloid shape called caustics.

The size of the caustics is directly related to the applied load, the material properties and the distance specimen-screen. Their ratio, however, as it is taken at equally distant screens, depends only on the optical and mechanical properties of the material in question.

In addition, an interferogram consisting of fringes, as formed from rays reflected by the two surfaces of the plate, is obtained. The fringe number depends on the wavelength of the light source and the optical path. When the plate specimen is loaded, the optical path changes. This results in a change of the fringe number and consequently to a displacement of fringes with respect to a reference point as they are observed on an opaque screen.

The ratio of the two caustics, taken during a static test, and the number of displaced fringes per applied load, taken during a dynamic test, provide enough information for the determination of the aformentioned mechanical and optical parameters.

Experiments conducted according to the method developed on acrylic plates and for a tensile impulse of total time duration of 600 μsec produced a reduced by 23.5% ratio of Poisson's ratio to modulus of elasticity from the static value and a reduced by 21% stress-optical coefficient from the static value.     

Influences of the thickness, misalignment, and dispersion of the Savart polariscope on the optical path difference and spectral resolution in the polarization interference imaging spectrometer

After reviewing the spectrum-dividing principle of the Savart polariscope (SP) in the polarization interference imaging spectrometer (PIIS) that we developed, we analyze the influences of the thickness, misalignment, and dispersion of the SP on the optical path difference (OPD). The theoretical expression of the OPD for the misalignment of the SP optical axis is deduced, and the OPD is analyzed when the incident plane is parallel, at 45°, or orthogonal to the principal section of the left plate of the SP. The selective thickness of the single Savart plate is analyzed when it is placed at the ideal and misalignment positions. The influence of dispersion of the SP on the OPD is analyzed when the misalignment error is ±1'. The relationships between the OPD and wavelength are simulated and validated with experiments. This work can provide theoretical and practical guidance for the design, calibration, modulation, innovation, experiment, and engineering of the PIIS.     

Dispersion of linearly polarized light propagating in a thin birefringent plate

We analyze theoretically the dispersion of linearly polarized light propagating in a uniaxial anisotropic medium where multibeam interference is present. Explicit expressions of the group-delay dispersion for transmitting waves are derived for the simplest situation, and the effect of dispersion on pulse broadening is analyzed for a few selected cases. Our results reveal that at normal incidence and in the situation where the optic axis is parallel to the surface of birefringent plate (in the x-y plane), the dispersion of the refracted wave decreases with the extent of birefringence. In particular, the dispersion for the electric field parallel to the polarization direction of the incident light changes with the rotation angle between the optic axis and the polarization direction of the incident field, whereas the dispersion for the refracted field whose direction is vertical to the polarization of incident light is independent of this angle. For oblique incidence, dispersion varies substantially for different incident angles. In the situation where the optic axis is in the x-z plane at either normal or oblique incidence, the dispersion increases in a periodically oscillating manner as a function of the relative thickness of the birefringent plate.     

SH导波在钢板缺陷检测中的传播特性

水平剪切(Shear Horizontal,SH)导波在传播的过程中有对称模式和反对称模式,其相速度和群速度主要取决于试件的厚度和频率之积(频厚积)。利用COMSOL有限元分析软件,建立了钢板缺陷的3-D模型,仿真分析了SH0导波在钢板中的传播特性。仿真结果表明SH波在传播过程中很少发生波束方向的改变,无频散和模式转换,信噪比高。利用电磁超声方法激励SH波,对钢板中的裂纹和焊缝缺陷进行了实验,验证了仿真结果的正确性及可行性,为超声导波在板材缺陷检测中的应用提供基础。     

Dispersion relations and modes of wave propagation in inclusion-reinforced composite plates

This paper is intended to examine the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness on the dispersion relations and modes of wave propagation in inclusion-reinforced composite plates. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Mori–Tanaka mean-field theory is used to predict the effective elastic moduli of the composite plate explicitly. The effective elastic moduli are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior. The resulting moduli are then used to determine the dispersion relations and the modal patterns of Lamb waves using the dynamic stiffness matrix method. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions are symmetrical or antisymmetric about the midplane of the plate. Classifying the wave type in an anisotropic plate is not as simple as that in an isotropic plate, and has not received proper attention in the literature. The wave types and orders are identified by analyzing the dispersion curves and inspecting the calculated modal patterns, and the results indicate that the Lamb waves in an orthotropic composite plate can also be classified as either symmetric or antisymmetric waves. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns. Propagation speed is generally increased with the aspect ratio, e.g., using longer fibers generally results in a higher propagation speed.     

A new method for estimating the aperture uncertainty of A/Dconverters

Aperture uncertainty measurements are strongly influenced by quantization, converter nonlinearity and test setup noise. The proposed method solves the difficulties arising from quantization, and nonlinearity. The method estimates the noise distribution function by fine adjustment of the input signal offset. The contribution of jitter-induced voltage noise is separated from additive noise in two different ways. Finally, the aperture uncertainty, assumed independent of the frequency, is estimated by varying the signal frequency. Experimental results obtained on 8 and 10 bit converters are discussed     

Surface plasmon-assisted optical bistability in the quantum dot-metal nanoparticle hybrid system

We theoretically investigated optical bistability (OB) of a coupled excition–plasmon hybrid system in a unidirectional ring cavity. It is found that the threshold and the region of OB can be tuned by adjusting the center–center distance between the quantum dot and metal nanoparticle (MNP), the Rabi frequency of the control field and the radius of the MNP. Due to the significantly enhanced optical nonlinearity by the surface plasmon effect, the threshold of OB can be decreased greatly when the probe field is parallel to the major axis of the hybrid system. The enhanced OB may have promising applications in optical switching and optical storage.     

Chemical etching of berlinite in sulphuric acid solutions

The aim of this work is to chemically etch AT wafers of berlinite AIPO₄ in sulphuric acid solutions in order to reach a thickness previously chosen (manufacturing of high frequency plate resonators). The kinetics of etching is studied: the decrease of thickness is followed by frequency measurement. The influence of temperature and acid concentration is measured and the evolution of surface texture is checked both by roughness measurements, resonance frequency and scanning electron microscopy methods.     

基于有限元边界元方法的薄板声辐射分析

分析了薄板结构的声辐射功率与其厚度及其激振频率的关系,从理论上指出了激振频与厚度对薄板结构声辐射的影响,分析当激励频率与结构的固有频率十分接近时,薄板的声辐射特性,同时分析了方形结构与条形结构声辐射的差异,从而为薄板结构的在工程中的低噪声设计提供参考。     

Comparison of Shearography to Scanning Laser Vibrometry as Methods for Local Stiffness Identification of Beams

Local stiffness of Euler–Bernoulli beams can be identified by dividing the bending moment of a deformed beam by the local curvature. Curvature and moment distributions can be derived from the modal shape of a beam vibrating at resonance. In this article, the modal shape of test beams is measured by both scanning laser vibrometry (SLV) and shearography. Shearography is an interferometric optical method that produces full‐field displacement gradients of the inspected surface. Curvature can be obtained by two steps of derivation of the modal amplitude (in the case of SLV) or one step of derivation of the modal shape slope (in the case of shearography). Three specially prepared aluminium beams with a known stiffness distribution are used for the validation of both techniques. The uncertainty of the identified stiffness distributions with both techniques is compared and related to their signal‐to‐noise ratios. A strength and weakness overview at the end of the article reveals that the shearography is the technique that shows the most advantages.     

Combined optical solitons with parabolic law nonlinearity and spatio-temporal dispersion

In this work, combined optical solitons are constructed in a weakly nonlocal nonlinear medium. The spatio-temporal dispersion (STD), parabolic law nonlinearity, detuning, nonlinear dispersion as well as inter-modal dispersion are taken into account. The integration tool that is applied is the complex envelope function ansatz. The influences of different parameters on dynamical behavior of combined optical solitons are discussed. The results are useful in describing the propagation of combined optical solitons with STD and parabolic law nonlinearity.     

Discontinuous surface measurement by wavelength-tuning interferometry with the excess fraction method correcting scanning nonlinearity

Wavelength-tuning interferometry can measure surface shapes with discontinuous steps using a unit of synthetic wavelength that is usually larger than the step height. However, measurement resolution decreases for large step heights since the synthetic wavelength becomes much larger than the source wavelength. The excess fraction method with a piezoelectric transducer phase shifting is applied to two-dimensional surface shape measurements. Systematic errors caused by nonlinearity in source frequency scanning are fully corrected by a correlation analysis between the observed and calculated interference fringes. Experiment results demonstrate that the determination of absolute interference order gives the profile of a surface with a step height of 1?mm with an accuracy of 12?nm.     

窄条控制件对旋转振荡板尾流的控制

两个小窄条对称地放于两侧,对宽厚比B/H=3的旋转振荡平板的尾流旋涡脱落进行抑制.板在平行于来流位置附近绕对称轴作旋转振荡,振幅为10°.窄条长边与板的旋转轴平行,窄条表面与来流方向垂直,窄条宽度与板的厚度之比b/H=1/3.控制参数为窄条位置.尾流流动显示图片和尾流脉动速度谱结果表明,当窄条位于有效区域内时,板两侧的涡脱落得到有效抑制.有效区尺度随着无量纲频率的增大而增大,随着雷诺数的增大而减小.     

Selective IR absorption in molecular nanofilms

We have formulated a microscopic theory of optical properties of ultrathin molecular films (nanofilms), i.e. quasi 2D systems parallel to XY planes bounded by two surfaces. Exposure of nanofilms to the external electromagnetic fields has result in creation of excitons - but different than bulk ones. Harmonic exciton states were calculated using the method of two-time, retarded, temperature dependent Green’s functions. It has been shown that two types of optical excitations can occur: bulk and surface exciton states. Exciton energy dispersion law shows discrete behavior with non-zero values. Analysis of the dielectric properties of these crystalline systems for low exciton concentration shows that the permittivity strongly depends on boundary parameters and the thickness of the film. In addition, permittivity shows very narrow and discrete dependence of external electromagnetic field frequency, which is a consequence of both resonance and quantum size effects. Influences of boundary conditions on optical characteristics (through analyses of dynamical absorption coefficient) of these nanostructures were specially and in details explored.     

Scanning white-light interferometer for measurement of the thickness of a transparent oil film on water

The thickness of a transparent layer of oil upon the surface of water is measured as the distance between the surface of oil film and the interface of the oil with the water. Two experimental results have demonstrated that the interface can reflect a white-light beam well enough to form an interferogram, even if the light is subjected to oil-film dispersion. When a beam of white light is incident vertically onto the oil-film surface, a scanning white-light interferometer in the Michelson configuration is employed to locate two serial reflections, surface reflection and interface reflection. The thickness of the transparent oil film on water is calculated based on the separation of these two interferograms. A limitation thickness, approximately 250 microm with 1.25 microm resolution, is achieved under the condition that there is 50 nW of optical power incident onto the oil-film surface with a wavelength centered at 1310 nm.     

阻尼板材在高架轨道箱梁结构噪声控制中的应用研究

为探讨高架桥梁结构噪声的控制措施,以京沪高铁32 m无砟轨道箱梁结构为原型,设计制作1/10的模型试验系统。通过将TD09型高性能阻尼板材分别敷设于箱梁翼缘板、腹板等位置,进行多工况的桥梁结构噪声降噪的模型试验研究。结果表明:高架轨道箱梁结构噪声峰值频段为200~1000 Hz,敷设阻尼板材在峰值频段内具有一定的降噪效果。阻尼板材对桥梁结构降噪效果与阻尼板材的敷设位置有关,其在桥梁结构噪声控制中有一定的应用价值。在峰值频率500 Hz处,翼缘板敷设阻尼板材对翼缘板下侧降噪效果最好,降噪约为1.6 dB(A);腹板敷设阻尼板对底板处的降噪效果最好,降噪可达3.8 dB(A);腹板及翼缘板同时敷设阻尼板材也对底板处的降噪效果最好,降噪可达3 dB(A)。