Effects of a modified spectral model on the spatial coherence of a laser beam

The influence of a modified (bump) spectrum of refractive index fluctuations on the spatial coherence of an optical wave is studied here and compared with that based on a von Karman spectrum. Analytical expressions are derived for the mutual coherence function (MCF) and wave structure function (WSF) of a lowest-order Gaussian beam wave from which the beam spot size and degree of coherence are deduced. The qualitative behaviour of beam spreading and coherence length is basically the same for both spectral models. Also, when the radius of the Fresnel zone and initial beam radius are of comparable size, the presence of a spectral bump appears to have minimal effect on spatial coherence for all beams. However, the choice of spectral model is important for certain ranges of parameters. In particular, the implied spatial coherence length for a collimated beam based on the modified spectrum is significantly smaller than that based on the von Karman spectrum whenever the Fresnel zone is either much larger or much smaller than the initial beam radius, whereas for a focused beam the predicted coherence length based on the modified spectrum is slightly larger when the Fresnel zone size is much smaller than the initial beam radius.     

Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Numerical,analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

Abstract

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Double pass wave structure function in weak to strong optical turbulence

The authors have recently published one-way horizontal path wave structure function expressions for plane, spherical, and Gaussian-beam waves. Those results are based on a modification of the Rytov approximation method and, by comparison with experimental data, are believed to be valid under all irradiance fluctuation conditions. In this paper, the earlier results are extended to the double pass case in which the received wave is reflected from a smooth target. The point target case is considered for incident plane, spherical, and Gaussian-beam waves. The finite target case is considered for an incident spherical wave with reflection from a plane mirror or a retroreflector. Comparisons are made between the results derived here, the standard Rytov approximation results, and the asymptotic results given by Banakh for conditions of strong irradiance fluctuations.     

Double pass wave structure function in weak to strong optical turbulence

The authors have recently published one-way horizontal path wave structure function expressions for plane, spherical, and Gaussian-beam waves. Those results are based on a modification of the Rytov approximation method and, by comparison with experimental data, are believed to be valid under all irradiance fluctuation conditions. In this paper, the earlier results are extended to the double pass case in which the received wave is reflected from a smooth target. The point target case is considered for incident plane, spherical, and Gaussian-beam waves. The finite target case is considered for an incident spherical wave with reflection from a plane mirror or a retroreflector. Comparisons are made between the results derived here, the standard Rytov approximation results, and the asymptotic results given by Banakh for conditions of strong irradiance fluctuations.     

湍流大气中光波闪烁的圆环孔径平均因子

利用弱起伏条件下球面波在大气湍流中传输的光强起伏(闪烁)理论和圆环孔径滤波函数,获得了圆环孔径平均因子的精确表达式。将圆环孔径平均因子关于一个无量纲参量(孔径半径与菲涅耳尺度的比值)拟合成2阶多项式,再找出多项式系数与孔径内外径之比的函数关系,获得了圆环孔径平均因子关于该参量和孔径内外径之比的函数关系式。通过误差分析确定了拟合关系式的适用范围,在此范围内,拟合式与精确式的相对误差小于25%。分别用Tatarskii谱和修正Hill谱分析了湍流内尺度对圆环孔径平均因子的影响,结果显示:在其他条件不变的情况下,内尺度越大,孔径平均效应相对越小。     

Monostatic lidar in weak-to-strong turbulence

Abstract

A heuristic scintillation model previously developed for weak-to-strong irradiance fluctuations of a spherical wave is extended in this paper to the case of a monostatic lidar configuration. As in the previous model, we account for the loss of spatial coherence as the optical wave propagates through atmospheric turbulence by eliminating the effects of certain turbulent scale sizes that exist between the scale size of the spatial coherence radius of the beam and that of the scattering disc. These mid-range scale-size effects are eliminated through the formal introduction of spatial scale frequency filters that continually adjust spatial cut-off frequencies as the optical wave propagates. In addition, we also account for correlations that exist in the incident wave to the target and the echo wave from the target arising from double-pass propagation through the same random inhomogeneities of the atmosphere. We separately consider the case of a point target and a diffuse target, concentrating on both the enhanced backscatter effect in the mean irradiance and the increase in scintillation in a monostatic channel. Under weak and strong irradiance fluctuations our asymptotic expressions are in agreement with previously published asymptotic results.     

Backscattering from different objects in turbulent media

Abstract

The connection between diffraction characteristics of the scatterer and distribution of average backscattered intensity of a spherical wave is considered. In experiments with an ‘infinite’ plane mirror it is shown that the distribution of average backscattered intensity coincides with the correlation function of the intensity fluctuation of a virtual point source located at the mirror and observed from the real source plane. Non-monotonic dependence (with a minimum at the Fresnel number of scattered mirror?1) between the enhancement factor and the size of reflected mirror is observed in experiments.     

On-axis irradiance distribution of axicons illuminated by spherical wave

The focusing properties of an axicon illuminated by spherical wave are investigated. We define the Fresnel number of the focusing axicon impinged on by spherical wave. The on-axis irradiance distribution versus Fresnel number is studied. It is shown that, similar with the plane wave, focal squeeze, which is defined as deviations for the position of the maximum irradiance, also appears in low Fresnel number. Besides, the on-axis irradiance will be smoothed for appropriate curvature radius of the divergent spherical wave; meanwhile, when the convergent spherical wave is incident on the axicon, the on-axis irradiance varies more seriously.     

AN OPEN RESONATOR FOR PHYSICAL STUDIES

The excitation efficency of the TEM_01q oscillation of an two-mirror hemispherical open resonator (OR) is studied. The resonator is excited by the TE₀₁ wave of a circular waveguide joined in the middle of the OR plane mirror. Given the waveguide optimum size, the TEM_01q mode excitation efficiency reaches 78%. Analysis of the resonant system spectrum in the 4-mm wave region shows that this waveguide-OR system offers a single mode resonance curve across almost a 10-GHz tuning range. The TEM₀₁₁₀ mode field distribution with and without the circular waveguide in the middle of the OR plane mirror is available due to the small scatterer method. It is shown that the considered open system is suitable for measuring electromagnetic characteristics of high-loss substances and metamaterials in the short-wave end of the millimeter (mm) region as well as in the submillimeter (submm) wave region.     

Scintillation of a laser beam propagation through non-Kolmogorov strong turbulence

Atmospheric turbulence causes strong irradiance fluctuations of propagating optical wave under the severe weather conditions in long-distance free space optical communication. In this paper, the scintillation index for a Gaussian beam wave propagation through non-Kolmogorov turbulent atmosphere is derived in strong fluctuation regime, using non-Kolmogorov spectrum with a generalized power law exponent and the extended Rytov theory with a modified spatial filter function. The analytic expressions are obtained and then used to analyze the effect of power law, refractive-index structure parameter, propagation distance, phase radius of curvature, beam width and wavelength on scintillation index of Gaussian beam under the strong atmospheric turbulence. It shows that, with the increasing of structure parameter or propagation distance, scintillation index increases sharply up to the peak point and then decreases gradually toward unity at rates depending on power law. And there exist optimal value of radius of curvature and beam width for minimizing the value of scintillation index and long wavelength for mitigating the effect of non-Kolmogorov strong turbulence on link performance.     

基于多级微反射镜的时空联合调制傅里叶变换成像光谱仪:原理及数据处理

介绍了一种基于多级阶梯微反射镜的时空联合调制傅里叶变换成像光谱仪的原理及数据处理方法.仪器利用一块多级阶梯微反射镜取代传统迈克尔逊干涉仪中的动镜以实现静态干涉,通过摆镜扫描使目标物体成像在不同的子阶梯反射面上从而获得目标物体不同光程差的干涉信息.某一时刻,目标物体经摆镜与前置成像系统后在平面镜与多级阶梯微反射镜上形成两个一次像点,两个一次像点被平面镜和多级阶梯微反射镜反射之后经后置成像系统最终成像在探测器焦平面上.平面镜与多级阶梯微反射镜之间的高度差会使到达探测器的两束光的光程差不同,因此探测器焦平面上可以获得目标物体的二维空间信息及一维干涉信息.根据多级阶梯微反射镜参数及光学系统设计参数计算得到摆镜步进角度为0.095°.利用实验获得的三维数据立方体进行了图像拼接与光谱复原.针对子阶梯反射镜存在宽度差异的问题,提出了一种基于极坐标霍夫变换的图像分割方法.为缓解拼接全景图中的间断线效应,将图像变换到HSI颜色空间并插值拟合其亮度分量后再变换回原空间.对拼接后的干涉图像进行了降维、去直流、寻址、切趾、相位校正、傅里叶变换及光谱分辨率增强等处理,完成了光谱复原工作.复原光谱分辨率为194 cm-1,优于设计指标(250 cm-1).     

Slant path average intensity of finite optical beam propagating in turbulent atmosphere

The average intensity of finite laser beam propagating through turbulent atmosphere is calculated from the extended Huygens Fresnel principle. Formulas are presented for the slant path average intensity from an arbitrarily truncated Gaussian beam. The new expressions are derived from the modified von Karman spectrum for refractive-index fluctuations, quadratic approximation of the structure function,and Gaussian approximation for the product of Gaussian function and Bessel function. It is shown that the form of average intensity is not a Gaussian function but a polynomial of the power of the binomial function, Gaussian function, and the incomplete gamma function. The results also show that the mean irradiance of a finite optical beam propagating in slant path turbulent atmosphere not only depends on the effective beam radius at the transmitting aperture plane, propagation distance, and long-term lateral coherence length of spherical wave, but also on the radius of emit aperture.     

Reflective point-diffraction microscopic interferometer with long-term stability

An on-axis phase-shifting reflective point-diffraction microscopic interferometer for quantitative phase microscopy based on Michelson architecture is proposed.A cube beamsplitter splits the object wave spectrum into two copies within two arms.Reference wave is rebuilt in one arm by low-pass filtering on the object wave frequency spectrum with a pinhole-mask mirror,and interferes with the object wave from the other arm.Polarization phase-shifting is performed and phase imaging on microscale specimens is implemented.The experimental results demonstrate that the proposed scheme has the advantage of long-term stability due to its quasi common-path geometry with full use of laser energy.     

Expressions of the scintillation index for optical waves propagating through weak non-Kolmogorov turbulence based on the generalized atmospheric spectral model

The high frequency “bump” which occurs in the turbulence spectral model just prior to the turbulence cell dissipation is important for the analysis of the irradiance scintillation for optical wave propagating through atmospheric turbulence. In this study, expressions of the irradiance scintillation index are developed from the generalized modified atmospheric spectral model for optical waves propagating through weak non-Kolmogorov turbulence. Compared with the expressions of the irradiance scintillation index derived from the general non-Kolmogorov spectral model, the new expressions can consider the influences of finite turbulence inner and outer scales and the influence of finite diameter aperture receiver. As the irradiance scintillation is caused mainly by the small scale turbulence cells' diffractive effects for weak turbulence, the turbulence outer scale's influence can be ignored. Numerical simulations show that variable inner scale values produce obvious effects on the irradiance scintillation for non-Kolmogorov turbulence.     

High-resolution four-photon intracavity laser spectroscopy with the external phase conjugation mirror

The phase conjugation regime is experimentally implemented in a cell with a liquid (water, ethanol, carbon tetrachloride) at the four-wave mixing of counter-propagating beams of diode lasers. Intracavity enhancement of the conjugate wave and the wave of the coherent anti-Stokes Raman scattering (CARS) arising in the interaction of the conjugate wave and one of the pumping waves in CARS scheme is detected. The latter process occurs in a narrow spectral range when the geometry of the wave vectors of the interacting waves in CARS scheme ensures arrival of the CARS signal at the laser aperture. It is found out that the quality of the four-photon phase conjugate mirror in the given interaction scheme is very sensitive to any perturbations (mechanical, acoustic, thermal, etc.) of the induced grating in the sample, which manifests itself in the distortion of the signal spectrum.     

Effect of interdiffusion on band structure and intersubband absorption coefficient of GaAs/GaAlAs double quantum well

The influence of Ga and Al atoms interdiffusion on the band structure and absorption coefficient of coupled double quantum wells are investigated on the basis of a potential composed of four modified Wood–Saxon potentials. Wave functions of the real potential are expressed as a superposition of the stationary state wave functions of the “basal” potential. It is shown that interdiffusion leads to the smearing of the rectangular profile of the potential and to the disappearance of the barrier between the wells, as a result of which, the degradation of doublet character of the electron energetic spectrum is observed. It is also shown that interdiffusion leads to the significant change in oscillator strength and in the enhancement of the thermal stability of the absorption spectrum of the considered heterostructure.     

复杂传播路径条件下激光光强起伏特性研究

对复杂地形情况下实际湍流大气中的激光强度起伏进行了系统的实验观测,分析了光强起伏统计特征的周日及全年变化规律。结果发现：复杂地形情况下实际湍流大气中的激光光强起伏,不论是概率密度分布还是其功率谱等统计特征均与理论上的偏离很大。     

葡萄糖分子的表面增强拉曼光谱研究

本文以密度泛函理论(density functional theory, 简称DFT)采用B3LYP混合泛函和6-31++G(d, p)基函数组计算的葡萄糖的分子振动光谱为根据, 首次对葡萄糖分子的常规拉曼光谱(NRS)进行了详细的指认, 并对葡萄糖分子的振动模式进行了归属。在以4-巯基吡啶为桥联剂分子修饰的银镜衬底上, 观测到葡萄糖分子的表面增强拉曼散射(SERS), 并对葡萄糖分子在银表面的吸附状态进行了分析。     

Performance of discrete dipole approximation for prediction of amplitude and phase of electromagnetic scattering by particles

Electromagnetic scattering provides useful signatures for nonintrusive particle characterization. Scattered wave which carries characteristic information about particles is identified completely by its intensity, polarization state and phase. Recent developments in measurement techniques have enabled measurement of phase of the scattered wave which is a source of additional information about particles. In the present study, accuracy of discrete dipole approximation (DDA) in predicting amplitude and phase of scattered wave is investigated via publicly available DDSCAT code by Draine and Flatau, which is a well-established tool for DDA and has found wide range of applications in the literature due to its flexibility. DDSCAT routine is modified to enable accurate computation of phase of complex amplitude scattering matrix (ASM) elements as well as their magnitude. DDA method was implemented by using lattice dispersion relation for dipole polarizabilities, generalized prime factor algorithm for fast-Fourier transformation and pre-conditioned bi-conjugate gradient method with stabilization for the solution of the complex linear system of equations. Accuracy of ASM elements predicted by DDA is assessed on single sphere problems with various size parameters and refractive indices by validation against Mie theory solutions. Excellent agreement between predictions and exact solutions proves the reliability of the modified DDSCAT code for prediction of amplitude and phase of scattered electromagnetic wave. Applicability conditions and requirements of the present DDA application to ensure accurate prediction of complete set of scattering parameters are mapped for single spheres, on an extensive domain of size parameters and refractive indices. A correlation is presented to estimate the magnitude and phase errors associated with given size parameter, refractive index and cubic lattice subdivision. Assessment of computational time requirements for different optical constants shows that implementation of DDA with the present specifications is unfeasible for size parameters larger than 4 when Re(m)>2 and Im(m)<0.1 at the same time, due to slow convergence rate.