Two-photon counting statistics for the superposition of coherent and chaotic fields

Approximate formulae for two-photon counting statistics for the superposition of coherent and chaotic fields are proposed and the exact second factorial moment is calculated. The accuracy of the proposed formulae is demonstrated by comparing the exact and approximate third factorial moments for the chaotic lorentzian field.     

Diffraction of light by adjacent fundamental and second or fourth harmonic ultrasound beams: Comparison of exact and simplified formulae with experiment

Theoretical expressions and their approximate formulae for the intensities of light diffracted by two adjacent ultrasonic beams are discussed and compared with experimental data for the case when the second beam is an even harmonic of the first (fundamental). In the special case of the fundamental and its second or fourth harmonic, relatively simple formulae are found for the first and second diffraction orders describing the variation of light intensity with phase shift and intensity ratio.The approximate formulae describe the experiments satisfactorily only for small values of ζ₁ and α_n. For higher values the exact formulae give better agreement. Only the Raman-Nath region is considered.     

Approximate,non-relativistic scattering phase shifts,bound state energies,and wave function normalization factors for a screened Coulomb potential of the Hulthén type

Non-relativistic scattering phase shifts, bound state energies, and wave function normalization factors for a screened Coulomb potential of the Hulthén type are presented in the form of relatively simple analytic expressions. These formulae have been obtained by a suitable renormalization procedure applied to the quantities derived from an approximate Schrödinger equation which contains the exact Hulthén potential together with an approximate angular momentum term. When the screening exponent vanishes, our formulae reduce to the exact Coulomb expressions. The interrelation between our formulae and Pratt's ‘analytic perturbation theory for screened Coulomb potentials’ is discussed.     

Relativistic scattering phase shifts,bound state energies,and wave function normalization factors for a screened Coulomb potential of the Hulthén type: New,approximate formulae

Relativistic scattering phase shifts, bound state energies, and wave function normalization factors for a screened Coulomb potential of the Hulthén type are presented in the form of relatively simple analytic expressions. These formulae have been obtained by a suitable renormalization procedure applied to the quantities derived from an approximate Dirac equation which contains the exact Hulthén potential together with approximate angular momentum terms. When the screening exponent vanishes, the formulae reduce to the exact Coulomb expressions.     

光谱仪谱线和谱带弯曲现象的精确表述方式

在矢量衍射理论基础上给出了任意倾斜入射下的光栅方程一般形式以及衍射极角和衍射方位角的完整解析表达式,由此首次导出了平面光栅光谱仪谱线和谱带弯曲量的精确计算公式和对应于衍射极角和衍射方位角的两类角色散公式,比较了谱线弯曲精确公式和近似公式的计算结果,进而指出和弥补了近似公式的不足,并数值考察了入射狭缝高度对光谱仪色散能力的影响程度。由于在以上各式的推导过程中未作任何近似,且涉及到了导致谱线和谱带弯曲的所有可能因素,因而它要比以往所用近似公式更为全面和可靠,可作为实际光谱仪器设计、测试、装调和使用的理论依据。     

Efficient and accurate method for radiation transfer problems

An efficient method of analysis, which utilizes trial functions based on Case's eigenvalues, is developed for solving radiation transfer in an absorbing and scattering homogeneous semi-infinite plane-parallel medium subjected to externally incident radiation. Expressions for the forward and backward intensities, reflectivity and total radiation intensity are included. Numerical results are given and compared involving different forms of the externally incident radiation on the boundary surface. It is shown that the solution converges rapidly to the exact results and that lower-order solutions predict values of the physical parameters that are accurate to five figures in all values of the single-scattering albedos in the range 0.1 ≤ ω ≤ 1. The method has been also used to get approximate formulae for calculating Chandrasekhar's characteristic H-functions and their moments.     

Approximate formulae for the overlap integral of two harmonic oscillator wave functions

The use of second-order perturbation theory to derive approximate formulae for the overlap integral of two harmonic oscillator wave functions is discussed, and the results applied to the theory of intensity distributions in vibrational progressions in electronic spectra. For the vibrational progression m←0 an approximate formula is given which, when the vibrational frequencies of the initial and final states differ by less than 10%, reproduces to an accuracy of 1% or less the intensity profile calculated using the exact formulae for the overlap integrals.     

Theory of light fluctuation filtering in the two-photon absorption process by multiple second harmonic generation. II. Quantum description. Possibilities of experimental realization

Two-photon absorption is treated from the point of view of quantum theory in this paper. Both rigorous and approximate solutions are presented. It is shown that the theoretical extreme value of photon antibunching, characterized by the normalized variance of integrated intensity, is ? 1/2, while its practical value in real experiments is about ?1/3 for both coherent and chaotic input radiation. In the case of the chaotic input radiation, fully coherent radiation can be obtained in this process. Possibilities for experimental realization of two-photon absorption by means of multiple second harmonic generation in thin nonlinear plates, with the generated second harmonic radiation filtered out, are discussed and some values of nonlinear plate thickness, number of light transits and mean intensity of input radiation are estimated. From the standpoint of the possibilities of detection of statistical properties of the resulting light, classical light fluctuation filtering seems to be more practical than the quantum counterpart.     

Radiation heat transfer between specularly and diffusely reflecting surfaces

Radiation heat transfer between specularly and diffusely reflecting plane surfaces is exactly analyzed based on radiation intensity without employing the image method. With this analysis, specular reflection can be treated easier than with the image method, leading to possible formulation of the basic equation in defiance of the number of specular reflections. The basic equation is applied to the simple two-dimensional radiation transfer system, from which approximate expressions are made for the surfaces nearly perfectly reflecting diffusely and for those nearly perfectly reflecting specularly. Numerical solutions are obtained of both exact and approximate expressions for systems of parallel plates and adjoint plates. It is confirmed that the approximations are quite acceptable, except for the case with very low emittance. The mean heat fluxes over the plate obtained by approximate solutions agree well with those by exact expressions.     

Scattering length and effective range in closed form for the Coulomb plus Yamaguchi potential

From the known expression for the off-shell T-matrix corresponding to the potential consisting of the sum of the Coulomb potential and the Yamaguchi potential, the physical scattering amplitude can be derived in a satisfactory way. We derive simple exact closed formulae for the scattering length a_cs and the effective range r_cs from this amplitude. These are compared with approximate formulae derived by Harrington. Also a few numerical calculations are reported and compared with results obtained by Harrington and by Ali et al.     

聚合物电光波导传播常数和损耗系数的微扰解

对于聚合物电光波导,依据理想光波导耦合理论的微扰理论,推导传播常数和损耗系数的近似表达式,从而将求解本征值的复杂复数运算简化成简单实数运算。数值计算表明,这些近似解与正确解很好相符。给出的近似公式和特征曲线可供聚合物电光波导及其器件的设计和制备作参考。     

Exact and approximate results of non-extensive quantum statistics

We develop an analytical technique to derive explicit forms of thermodynamical quantities within the asymptotic approach to non-extensive quantum distribution functions. Using it, we find an expression for the number of particles in a boson system which we compare with other approximate scheme (i.e. factorization approach), and with the recently obtained exact result. To do this, we investigate the predictions on Bose-Einstein condensation and the blackbody radiation. We find that both approximation techniques give results similar to (up to ) the exact ones, making them a useful tool for computations. Because of the simplicity of the factorization approach formulae, it appears that this is the easiest way to handle with physical systems which might exhibit slight deviations from extensivity. Received 19 August 1999 and Received in final form 1 November 1999     

Equation of state and correlation function contact values of a hard sphere mixture

Recently, there has been considerable activity in the study of the equation of state and correlation functions of a hard sphere mixture when the concentration of the large spheres is exceedingly small. This system is of considerable interest both as a simple prototype of an asymmetric mixture and as a simple but useful model of a colloidal suspension. We review our ad hoc formulae for the correlation function contact values and discuss the evidence, both pro and con, from exact and nearly exact theorems, computer simulations and experiment. Our conclusion is that our formulae are, on the whole, correct but the large sphere–large sphere correlation function contact value seems to need revision when the concentration of the large spheres is small but not exceedingly small. We propose a modest revision that preserves the seemingly correct aspects of our formula and this is in good agreement with the most recent simulations.     

On the aproximate formulae and the exact method to compute wavefront reflectivity in degenerate four-wave mixing

Wavefront reflectivity in a conventional degenerate four-wave mixing (FWM) configuration can be calculated, using either approximate formulae, or exact numerical methods to solve the nonlinear coupled-wave equations. We have computed the wavefront reflectivity for FWM in a transmission and reflection geometry, respectively, using these two different methods. A comparison between them indicates that these formulae are reasonable approximations when beam coupling, diffraction efficiency and absorption are all low, and especially in the case of transmission geometry.     

Calculation of radiative heat transfer in SF6 arcplasmas

Radiation transport in SF₆ are plasmas have been treated for pressures of 0.101, 0.5, and 1.0 MPa. We have investigated the use of an approximate method of partial characteristics. We have calculated spectral absorptivities for SF₆ plasmas for temperatures from 300 to 35 000 K, and have used these absorptivities to calculate the two functions designated ΔI and ΔSim. These functions are integrals over all radiation frequencies for given line segments with a linear variation of temperature along the line. The ΔI and ΔSim values are functions of the end temperatures and the length of the line, and are used to evaluate radiation transfer from line segments in the plasma where the temperature variation for each line segment is approximated as being linear. The validity of this method of partial characteristics has been demonstrated by comparing exact calculations with the approximate calculations to evaluate radiation intensities, radiation fluxes, and divergence of radiation fluxes for specified temperature profiles. The method of partial characteristics has been applied to one- and three-dimensional calculations of radiative heat transfer in simplified temperature profiles. Agreement up to 10% is obtained with exact calculations, but with a large reduction of computation time     

Digital image watermarking using gyrator transform and chaotic maps

We propose a new method for digital image watermarking using gyrator transform and chaotic maps. Four chaotic maps have been used in the proposed technique. The four chaotic maps that have been used are the logistic map, the tent map, the Kaplan-Yorke map and the Ikeda map. These chaotic maps are used to generate the random phase masks and these random phase masks are known as chaotic random phase masks. A new technique has been proposed to generate the single chaotic random phase mask by using two chaotic maps together with different seed values. The watermark encoding method in the proposed technique is based on the double random phase encoding method. The gyrator transform and two chaotic random phase masks are used to encode the input image. The mean square error, the peak signal-to-noise ratio and the bit error rate have been calculated. Robustness of the proposed technique has been evaluated in terms of the chaotic maps, the number of the chaotic maps used to generate the CRPM, the rotation angle of the gyrator transform and the seed values of the chaotic random phase masks. Optical implementation of the technique has been proposed. The computer simulations are presented to verify the validity of the proposed technique.     

Approximate approach to the quantum statistics of the superposition of coherent and chaotic fields

Formulae recently derived for the integrated intensity distribution, the photon-counting distribution and its factorial moments in the statistics of the superposition of multimode coherent and chaotic fields are analyzed in greater detail and their validity as approximate formulae for light of arbitrary spectrum is investigated. It is shown by explicit calculation of the third factorial moment of the photon-counting distribution for the superposition of a one-mode coherent field with a Gaussian Lorentzian field that the proposed formulae hold with very good accuracy over a wide range of conditions.The authors thank Dr. Z. Braunerová and M T. Kojecký of the Computer Center of Palacký University for their help with calculations.     

紧聚焦激光束作用于电子实现单个阿秒脉冲输出

研究了电子在聚焦的圆偏振高斯激光束中的非线性汤姆孙散射过程，在此基础上提出了实现单个阿秒脉冲输出的新机理.通过计算机模拟，发现利用紧聚焦的激光脉冲可以有效地增大辐射脉冲链的最高峰和次高峰的峰值强度比即信噪比，从而将阿秒脉冲链变为单个阿秒脉冲输出.紧聚焦情形下，随着驱动激光强度的增大，辐射信号的脉宽变短，信噪比变大；同时当减小激光束腰半径时，辐射信号信噪比也能得到有效改善.研究还发现，利用几个光周期的极短激光脉冲与电子的相互作用也能实现单个阿秒脉冲输出. 关键词： 阿秒脉冲 紧聚焦 信噪比     

Model studies on the systematics and interpolation of Franck-Condon factor arrays

A simple harmonic oscillator approximation is used to derive approximate algebraic expressions for low vibrational quantum number Franck-Condon factors for band systems for which molecular data are sparse. These simple expressions involve a transition parameter u which is characteristic of the electronic transition involved. The expressions provide Franck-Condon factors which agree quite well with RKR values when these are available. The formulae are used to explain quantitatively the dependence on u of the systematic properties of Franck-Condon factor arrays and to provide a method for their interpolation. The formulae are also used to describe quantitatively the dependence on u of the gross appearance of molecular band systems in emission and absorption.     

An exact,closed form,solution for the flexural vibration of a thin annular plate having a parabolic thickness variation

An exact, closed form, solution is obtained for the transverse vibrations, with nodal diameters and circles, of a thin annular plate having a parabolic thickness variation. Representative numerical values for the frequency parameter and typical mode shapes are presented for three different combinations of simple boundary conditions. The corresponding exact solution for an aeolotropic annular plate of the same geometry is also presented. Aside from possible design applications, these exact, closed form, data can be used as test cases for assessing the accuracy of various approximate methods of solution. The analysis involves only the powers of the radius and is simpler than that for the constant thickness solution which involves Bessel functions.