Circular partially coherent flattened Gaussian beam

An alternative theoretical model called circular partially coherent flattened Gaussian beam (FGB) is developed to describe a circular partially coherent beam with a flat-topped spatial profile. Explicit expression for the propagation factor of a circular partially coherent FGB is derived. We drive the analytical formulae for the cross-spectral density and mean-squared beam width of a circular partially coherent FGB propagating through a paraxial ABCD optical system based on the generalized Collins formula. The intensity, spreading and directionality properties of a circular partially coherent FGB propagating in free space are studied as numerical examples. The propagation properties of a circular partially coherent FGB agree well with those of a partially coherent flat-topped beam reported in the literature. Thus, our model provides an alternative but reliable model for describing a circular partially coherent beam with flat-topped profile.     

平顶高斯光束和超高斯光束传输特性的相似性

 在直角坐标系下对平顶高斯光束和超高斯光束的传输特性的相似性问题作了讨论。研究表明,当有相同的M²因子但束宽不同的平顶高斯光束和超高斯光束通过光阑效应可忽略ABCD光学系统传输时,在广义菲涅尔数F相等处有相似的光强分布。对于有光阑和用球差透镜聚焦的情况,若平顶高斯光束和超高斯光束具有相同的M²因子和束腰宽度,则在相同传输距离处仍可得到相似的光强分布。     

Paraxial propagation of a partially coherent flattened Gaussian beam through apertured ABCD optical systems

By expanding the hard aperture function into a finite sum of complex Gaussian functions, some approximate analytical formulae for the cross-spectral density of a partially coherent flattened Gaussian beam (FGB) propagating through apertured aligned and misaligned ABCD optical systems are derived based on the generalized Collins formula. The results obtained by using the approximate analytical formula are in good agreement with those obtained by using the numerical integral calculation. As a numerical example, the focusing properties (including average irradiance distribution and focal shift) of a partially coherent FGB focused by an apertured thin lens are studied, and it is found that the focusing properties of a partially coherent FGB are closely related to its initial coherence and the aperture width. Our results provide an effective and fast way for studying the paraxial propagation of a partially coherent FGB through apertured ABCD optical systems.     

平顶高斯光束与超高斯光束传输特性的比较研究

对平顶高斯光束与超高斯光束的传输特性作了研究和比较,并给出了典型的数值计算例．所得的主要结论是有相同M²因子和束宽的平顶高斯光束与超高斯光束在通过光学系统时,具有非常相似的包括光强分布和光阑衍射效应在内的传输变换特性． 关键词：     

截断平顶高斯光束M2因子的比较研究

使用熵束宽、渐近分析和环围功率法对截断平顶高斯光束的束腰宽度w、远场发散角θ0和M²因子作了比较研究.结果表明:按不同束宽定义得到的截断平顶高斯光束的w、θ0和M²因子不同,且与截断参量a/w0(a为光阑半宽度,w0为平顶高斯光束初始束腰宽度)有关.随a/w0的增加,三种方法计算得到的w、θ0和M²都分别趋于某常量.     

Algorithms for flattened Gaussian beams passing through apertured and unapertured paraxial ABCD optical systems

The propagation property of flattened Gaussian beams (FGBs) is studied based on the Collins formula, and analytical propagation equations for FGBs with and without an aperture are derived. It is shown that the closed-form expressions for the FGB of order N passing through paraxial ABCD optical systems without an aperture can be written as the combinations of Confluent Hyper-geometric Functions, and that the analytical equations for the FGB of order N passing through apertured paraxial ABCD optical systems may involve Error Functions. The proposed algorithms for the considered beams can save computing time, provide intuitive physical insights, and help to design optical systems. Our results are confirmed and illustrated with numerical examples.     

Bending wave intensity in a thick beam

I.IntroductionMeasurementSofbendingwaveintensityinoneortwodimensi0na1structuresbecomequitepopularandgetavarietyofindustria1app1icati0ns.Theexistingintensitytheory['-']wasderivedbasedontheclassicaIBernou11i-Eu1ertheorywhichisanapproximatetheoryforana-lyzingstructuralvibration.Inthe1ow-frequencylimitwherebendingwavelengthsaremuchlongincomparisonwiththethicknessofthestructurealongwhichtheypr0pagate(i.e.,thinstructurcs),theuse0ftheclassica1theorywi1lresu1tinanegligiblyerro/`].Forshortwave-1ength…     

The measurement of bending wave intensity in a two-dimensional structure

I.IntroductionOfallstructuralwaves,bendingwaveismostimportant.Itiseasilyexcitedandresultsinairbornenoiseradiation'Inpractice,itisnecessarytodeterminetheenergydistributionandpowertransmissionincoupledstructl1res.Bendingwaveenergycanbecalculatedfrombendingwaveaccelerationwhilebendingwavepowertransmissionischaracterizedbybendingwaveintensitywhichisavectorgivillgthemagnitudeanddirection.TheengineeringaPplicationofthevectorpropertyofbendingwaveilltensityisnumerous[1~3]buttheinvestigationinitispre…     

X‐ray third‐order nonlinear plane‐wave Bragg‐case dynamical diffraction effects in a perfect crystal

Two‐wave symmetric Bragg‐case dynamical diffraction of a plane X‐ray wave in a crystal with third‐order nonlinear response to the electric field is considered theoretically. For certain diffraction conditions for a non‐absorbing perfect semi‐infinite crystal in the total reflection region an analytical solution is found. For the width and for the center of the total reflection region expressions on the intensity of the incidence wave are established. It is shown that in the nonlinear case the total reflection region exists below a maximal intensity of the incidence wave. With increasing intensity of the incidence wave the total reflection region's center moves to low angles and the width decreases. Using numerical calculations for an absorbing semi‐infinite crystal, the behavior of the reflected wave as a function of the intensity of the incidence wave and of the deviation parameter from the Bragg condition is analyzed. The results of numerical calculations are compared with the obtained analytical solution.     

A Modified Monte Carlo Model of Speckle Tracking of Shear Wave Induced by Acoustic Radiation Force for Acousto-Optic Elasticity Imaging

A modified Monte Carlo model of speckle tracking of shear wave propagation in scattering media is proposed.The established Monte Carlo model mainly concerns the variations of optical electric field and speckle.The twodimensional intensity distribution and the time evolution of speckles in different probe locations are obtained.The fluctuation of speckle intensity tracks the acoustic-radiation-force shear wave propagation,and especially the reduction of speckle intensity implies attenuation of shear wave.Then,the shear wave velocity is estimated quantitatively on the basis of the time-to-peak algorithm and linear regression processing.The results reveal that a smaller sampling interval yields higher estimation precision and the shear wave velocity is estimated more efficiently by using speckle intensity difference than by using speckle contrast difference according to the estimation error.Hence,the shear wave velocity is estimated to be 2.25 m/s with relatively high accuracy for the estimation error reaches the minimum(0.071).     

磁场对螺旋波等离子体波和能量吸收影响的数值研究

本文考察在径向电子数密度呈抛物形分布的情况下,外加稳恒磁场,射频通过螺旋波天线在等离子体中激发电磁波的传播性质.采用线性扰动波假设,数值求解Maxwell方程组,得到80—800 G(1 G=10-4T)磁场条件下等离子体中径向电、磁场强度及能量沉积密度的分布情形.计算结果表明,磁场增大(80→800G)时,螺旋波受到的阻尼较小,可深入等离子体传播;Trivelpiece-Gould(TG)波受到的阻尼增大,在等离子体-真空边界处衰减增强;整体的能量吸收向边界集中.磁感应强度小于100 G时,TG波可深入主等离子体区传播,等离子体径向能量吸收相对均匀.     

Effects of finite probe intensity on degenerate frequency mixing in saturable amplifiers

Phase conjugation by degenerate frequency mixing (DFM) in saturable amplifiers, including the effects of pump depletion, a non-zero incident probe wave intensity and saturated gain of all waves in the nonlinear medium, is analyzed numerically. Plane wave DFM reflectivities greater than unity are predicted, even in the presence of pump depletion, for sufficiently large amplifier gains. At a given level of incident probe-wave intensity the DFM reflectivity approaches its weak probe-wave value at sufficiently large incident pump intensities, but deviates from these values at lower pump intensities. Conditions are established under which the DFM reflectivity is effectively independent of the incident probe-wave intensity even when the incident pump intensity is smaller than that of the incident probe wave. Under these conditions the system holds the potential for faithful conjugation using pump waves that are considerably weaker than the probe waves being conjugated. The results also predict that under certain conditions, the intensity of the backward-generated wave can be larger than either the incident probe wave or the incident pump wave.     

Characteristics of surface sound pressure and absorption of a finite impedance strip for a grazing incident plane wave

Distributions of sound pressure and intensity on the surface of a flat impedance strip flush-mounted on a rigid baffle are studied for a grazing incident plane wave. The distributions are obtained by superimposing the unperturbed wave (the specularly reflected wave as if the strip is rigid plus the incident wave) with the radiated wave from the surface vibration of the strip excited by the unperturbed pressure. The radiated pressure interferes with the unperturbed pressure and distorts the propagating plane wave. When the plane wave propagates in the baffle-strip-baffle direction, it encounters discontinuities in acoustical impedance at the baffle-strip and strip-baffle interfaces. The radiated pressure is highest around the baffle-strip interface, but decreases toward the strip-baffle interface where the plane wave distortion reduces accordingly. As the unperturbed and radiated waves have different magnitudes and superimpose out of phase, the surface pressure and intensity increase across the strip in the plane wave propagation direction. Therefore, the surface absorption of the strip is nonzero and nonuniform. This paper provides an understanding of the surface pressure and intensity behaviors of a finite impedance strip for a grazing incident plane wave, and of how the distributed intensity determines the sound absorption coefficient of the strip.     

平顶高斯光束的相关概念和对称化变换

 对平顶高斯光束有关的一些重要概念,例如场分布和束宽等作了物理分析。进一步将二维平顶高斯光束推广到三维情况,并且对三维平顶高斯光束的对称化变换,包括在X和Y方向束宽相等和ｚ平面处曲率半径相等,进行了详细的研究。     

关于椭圆偏振光的几点讨论

对椭圆偏振光在直角坐标系中的分解,椭圆偏振光的光强,椭圆偏振光经过偏振片的出射光强,以及椭圆偏振光的"瞬时光强"等几个问题做了讨论.     

Development and transition of spiral wave in the coupled Hindmarsh--Rose neurons in two-dimensional space

The dynamics and the transition of spiral waves in the coupled Hindmarsh--Rose (H--R) neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient D’, is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons (or sites) and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.     

The effect of broadband noise on the human brainstem auditory evoked response. I. Rate and intensity effects

A series of experiments investigated the effects of continuous broadband noise (ipsilateral) on wave V of the click-evoked brainstem auditory evoked response (BAER). In general, a broadband noise masker increases the latency and decreases the amplitude of wave V. Varying both click and noise intensity, it was found that noise levels above about 40 dB SPL increase the latency and decrease the amplitude of wave V, regardless of click intensity. The effects of noise on wave V amplitude appear constant across click intensity, whereas the effects of a constant noise level on wave V latency decrease at higher click intensities. Both masking and adaptation increase wave V latency, but their combined effects are occlusive: rate-induced wave V latency shift decreases in the presence of continuous broadband noise. The clinical and theoretical implications of these findings are discussed.     

Intensity profile of chirped polychromatic laser in an apertured system

Propagation expression of chirped polychromatic laser in an aperture system is deduced in our investigation. Influences of the chirp parameter and the aperture width on the intensity profile of the chirped polychromatic laser are studied and illustrated by numerical calculation. The results showed that intensity of the wave rear presents spreading effect but that of the wave front presents narrowing effect. Namely, the intensity distribution spreads with decreasing the aperture width and increasing the chirp parameter in the wave rear whereas it tends to concentrate with increasing the chirp parameter in the wave front. A physical explanation based on a simplified representation indicated that the influence of the chirp parameter on the intensity was determined not only by its quantity but also by the sign of the local time.     

Analysis of a heat wave induced by laser radiation absorption in an optical fiber on the basis of a 2D nonstationary heat conduction equation

A heat wave resulting from the absorption of laser radiation in the core of an optical fiber is studied using a nonstationary 2D heat conduction equation. The velocity of the wave as a function of the laser intensity is determined, and the threshold intensity generating the heat wave is calculated. At high intensities, the velocity of the wave can be qualitatively described by a well-known formula from combustion theory; i.e., the velocity is shown to be proportional to the square root of the radiation intensity. The analytical threshold laser intensities closely agree with the available experimental data.     

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The characteristic of electromagnetic scattering by plasma cylinder is researched in this paper. Scattered fields of the parallel-polarized wave and vertical-polarized wave by plasma cylinder are calculated and analyzed. The calculated results show that the higher the electron density, is the greater the scattering intensity in the outside of the cylinder and the higher the plasma frequency of collision, is the smaller the scattering intensity in the outside of the column. In addition, the electromagnetic wave polarization and frequency of the incident wave also have a significant impact on the scattering intensity of electromagnetic waves, the vertically polarized wave is more likely to be scattered, and the lower frequency of the incident wave is also easier to scattering. These have certain reference value for designing and studying of the plasma antenna.