Numerical propagation of partially coherent laser beams through optical systems

The propagation of partially coherent beams through optical systems is computed numerically in one transverse dimension. The optical system is divided into different elementary segments, through which the propagation of light can be calculated by appropriate operators, working on the coherence function or the Wigner distribution function respectively. For the necessary changes between these two functions describing the partially coherent beams, the use of the remarkable z-transform seems to be an advantage. With this algorithm the grid and the resolution in the spatial frequency domain can be arbitrarily chosen in contrast to the usual Fourier transform, the influence of phase aberrations on the focusability of Gauss-Schell model beams is discussed as an application example of the numerical model. With the help of this tool, practical beam guiding systems can be simulated for use with multimode laser radiation.     

一维介观结链中电荷孤子的控制

研究了一维介观结链中的电势分布随各岛上门电压和电子数分布的变化关系,并发现在一个岛上加一个门电压会产生一个静电势孤子.通过调节门电压可以较好地控制静电势孤子的形状及其位置,从而达到对电荷孤子的有效控制. 关键词： 电荷孤子 介观结 单电荷隧穿     

Magnetic bubble refraction and quasibreathers in inhomogeneous antiferromagnets

We study the dynamics of magnetic bubble solitons in a two-dimensional isotropic antiferromagnetic spin lattice in the case where the exchange integral J(x, y) is position dependent. In the near-continuum regime, this system is described by the relativistic O(3) sigma model on a space-time with a spatially inhomogeneous metric determined by J. We use the geodesic approximation to describe the low-energy soliton dynamics in this system: the n-soliton motion is approximated by geodesic motion in the moduli space M _n of static n-solitons equipped with the L ² metric γ. We obtain explicit formulas for γ for various natural choices of J(x, y). Based on these, we show that single soliton trajectories are refracted with J⁻¹ being analogous to the refractive index and that this refraction effect allows constructing simple bubble lenses and bubble guides. We consider the case where J has a disk inhomogeneity (with the value J ₊ outside a disk and J ₋ < J ₊ inside) in detail. We argue that for sufficiently large J ₊/J ₋, this type of antiferromagnet supports approximate quasibreathers: two or more coincident bubbles confined within the disk spin internally while their shape oscillates with a generically incommensurate period. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 191–208, July, 2007.     

Solitary wave solutions of nonlinear financial markets :data-modeling-concept-practicing

This paper seeks to solve the difficult nonlinear problem in financial markets on the complex system theory and the nonlinear dynamics principle, with the data-model-concept-practice issue-oriented reconstruction of the phase space by the high frequency trade data. In theory, we have achieved the differentiable manifold geometry configuration, discovered the Yang-Mills functional in financial markets, obtained a meaningful conserved quantity through corresponding space-time non-Abel localization gauge symmetry transformation, and derived the financial solitons, which shows that there is a strict symmetry between manifold fiber bundle and guage field in financial markets. In practical applications of financial markets, we have repeatedly carried out experimental tests in a fluctuant evolvement, directly simulating and validating the existence of solitons by researching the price fluctuations (society phenomena) using the same methods and criterion as in natural science and in actual trade to test the stock Guangzhou Proprietary and the futures Fuel Oil in China. The results demonstrate that the financial solitons discovered indicates that there is a kind of new substance and form of energy existing in financial trade markets, which likely indicates a new science paradigm in the economy and society domains beyond physics.      

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

Refraction of light in media

The roles of the magnetic field and electric field of the light are investigated when the light is refracted in the medium. The model of the electron cloud conductor is presented. Electron cloud in a molecule is treated as a conductor and the Faraday’s Law is applied to this conductor that is in the alternating magnetic field of the light. dB _M/dt of the light gives rise to an alternating induced current on the electron cloud conductor, and the light exchanges energy, i.e. the refractive energy, with the electron cloud conductor. Formulas of refractive index, which is the ratio of light speed in vacuum to that in the medium, are derived with this model. These formulas are tested with several mediums and Langevin’s diamagnetic susceptibility of helium gas, and the results are in good agreement with the measured data. The anisotropy and the nonlinearity of the refractive index are explained with the theory described in this work. Supported by Beijing Science and Technology New Star Program (Grant No. 952870400), the Beijing Municipal Commission of Education and the Excellent Young Teachers Program of Ministry of Education of China     

Comparative Study on Large and Small Signal Theory for Intensity Modulation Response of Semiconductor Lasers Including Higher-Order Dispersion Terms

In this article, the comparison of large signal theory and small signal theory has been done with dispersive propagation of optical signal with IMDD (Intensity Modulation Direct Detection) systems for semiconductor lasers with higher-order dispersion terms. The expressions for an exact large signal theory and small signal theory including higher-order dispersion terms for propagation of an optical wave with sinusoidal amplitude and frequency modulation in a dispersive fiber have been derived. It is observed that small signal theory is more sensitive compared to large signal theory in terms of intensity modulation/direct detection systems. Also, it is reported that for large signal analysis the higher-order effects of dispersion can be ignored, whereas for small signal theory, the higher-order effects can be ignored for lower modulation frequencies only. The variation in the transfer function for various values of modulation indices are greater for small signal analysis than for large signal analysis. Also, as the intensity modulation index is increased, there is a decrease in the value of transfer function. The large signal model approximates the small signal model for lower values of the intensity modulation index.     

Propagation of the kurtosis parameter of Hermite-cosh-Gaussian beams

Starting from the propagation equation of Hermite-cosh-Gaussian (HChG) beams and the intensity moments definition, an analytical expression for the propagation of the kurtosis parameter of unapertured HChG beams passing through paraxial optical ABCD systems is derived and illustrated numerically. Special interesting cases are discussed, in particular, the kurtosis parameter of HChG beams at the waist plane is obtained readily from our general propagation expression.     

A compactness result for Kähler Ricci solitons

In this paper we prove a compactness result for compact Kähler Ricci gradient shrinking solitons. If (Mi,gi) is a sequence of Kähler Ricci solitons of real dimension n?4, whose curvatures have uniformly bounded Ln/2 norms, whose Ricci curvatures are uniformly bounded from below and μ(gi,1/2)?A (where μ is Perelman's functional), there is a subsequence (Mi,gi) converging to a compact orbifold (M_∞,g_∞) with finitely many isolated singularities, where g_∞ is a Kähler Ricci soliton metric in an orbifold sense (satisfies a soliton equation away from singular points and smoothly extends in some gauge to a metric satisfying Kähler Ricci soliton equation in a lifting around singular points).