The propagation of a polarized gaussian beam in a smoothly inhomogeneous isotropic medium

In the frame of the eikonal-based complex geometrical optics, which describes the phase front and cross section of a light beam using the quadratic expansion of a complex-valued eikonal, we investigate the transverse deflections of a polarized Gaussian beam (GB) in a smoothly inhomogeneous isotropic medium, which is called the spin Hall effect of the beam. The linear complex-valued eikonal terms are introduced firstly to describe the polarization-dependent transverse shifts of the beam in the inhomogeneous medium. We find that the polarization-dependent transverse shifts of the beams include two parts: one originates from the coupling between the spin angular momentum and the extrinsic orbital angular momentum due to the curve trajectory of the center of gravity of the polarized GB, and the other from the coupling between the spin angular momentum and the intrinsic orbital angular momentum due to the rotation of the beam with respect to the central ray.     

Eikonal expansion

An eikonal expansion of the potential scattering T matrix is evaluated, without approximation, through third order in the inverse momentum. Based on the results, their correspondence with the WKB approximation and a new statement of the unitarity constraint, we propose a sequence of four approximations to the exact impact parameter (Fourier-Bessel) representation of the scattering matrix. The sequence consists of the Glauber approximation and three systematic corrections to the Glauber approximation. The corrections are analytic functions of the impact parameter for Yukawa and Gaussian potentials; they vanish for a Coulomb potential.The sequence of eikonal amplitudes is convergent at high energy and is clearly established for small momentum transfer. Validity for all momentum transfer is conjectured based on systematic cancellation, explicitly verified through third order in the expansion, of momentum transfer dependence in the eikonal impact parameter representation. Such cancellation is shown to occur in the explicit construction of the eikonal expansion of the second Born amplitude for a Yukawa potential.Numerical tests of the sequence of eikonal amplitudes show systematic increase of the angular range of validity by comparison with partial wave results for continuous potentials; the theory is not convergent for discontinuous potentials.The WKB phase shift formula is shown to produce a systematic connection with eikonal expansion results. From this we deduce a generating function for the eikonal phase corrections of arbitrary order and also conjecture a sum of the eikonal expansion valid in the limit of high energy and arbitrary potential strength.     

Exact quantum mechanical description of the motion of spin-1/2 particles and of spin motion in a uniform magnetic field

The Dirac-Pauli equation is used to obtain the exact equation of spin motion for spin-1/2 particles with an anomalous magnetic moment in a constant and uniform magnetic field. Exact formulas are established for the angular velocity of the revolution of such particles along circular orbits and the rotation of the particle spin with respect to momentum. Finally, a quantum mechanical equation for the motion of the particles in a strong magnetic field is derived. Zh. éksp. Teor. Fiz. 114, 448–457 (August 1998)     

Planckian Scattering from Kerr Black Holes: Eikonal and Beyond

Planckian scattering of particles with angular momenta is studied by describing them as sources of the Kerr metric. In the shock wave formalism, it is found that the angular momenta do not contribute to the scattering amplitude in the eikonal limit. This is confirmed by using the wave equation of the test particle in the Kerr background.     

Optics of oblique meridional and nonmeridional rays of a conicoid

Based on the exact expression for the angular eikonal of an axisymmetric conicoid (a surface formed by revolution of a second-order curve, or conic) the expressions for the Gaussian optics of oblique meridional rays are obtained, which differ from the well-known Gullstrand-Young invariants for a sphere by a set of independent arguments and contain explicitly the parameters of an optical system. The collinear properties of an optical surface with oblique meridional beams are studied. The theory of astigmatism is extended to the case of oblique nonmeridional rays, which makes it possible to construct and analyze in the first approximation the focal surfaces of an actual wide beam of rays. The theory is tested using the example of optimization of an aplanatic lens for the case of an off-axis point of an object. Based on the exact expression for the angular eikonal, definitions of integral aberrations are given. It is proposed to use the method developed in optimization of optical systems.     

Inelastic scattering of electrons from inert gas atoms in the eikonal distorted-wave approximation

The excitation of dipole states in neon and argon by electron impact has been calculated in the eikonal distorted-wave approximation. The total and differential cross-sections, the angular distributions of electrons and photons are in good agreement with experiment.     

Excitation of atomic hydrogen by electron impact in the modified Glauber method with exchange

The 1–2 excitation of atomic hydrogen by electron impact is analyzed with the modified Glauber amplitude proposed recently. Exchange effects are included via the Glauber eikonal exchange formulas [1]. The results are found to be in good agreement with experimental data.     

Multiplicity distributions in the eikonal model

Explicit formulas for the generating function, topological cross sections and multiplicity moments are obtained in the eikonal model with a single Regge trajectory. The existence of Koba-Nielsen-Olesen (KNO) scaling in this model is discussed. It is shown that strict KNO scaling is not valid. However, there exists a limited range of energy where KNO scaling takes place approximately.     

Dual pole eikonal ands-channel singularities

Eikonalization of dual pole amplitudes, such as the Veneziano amplitude, is shown to lead to singularities in the impact parameter plane, which, in the eikonal approximation, may be interpreted as branch points in the direct channel angular momentum plane. This result is discussed in the light of dual absorption models.     

Some first passage and covering times for a time-continuous random walk with a central force

Exact formulas for the mean first passage and covering times for the reflecting and central states are derived for a restricted time-continuous random walk with a central force.     

On the theory of the relativistic cross-sections for stimulated bremsstrahlung on an arbitrary electrostatic potential in the strong electromagnetic field

On the base of relativistic generalized eikonal approximation wave function the multiphoton cross-sections of a Dirac particle bremsstrahlung on an arbitrary electrostatic potential and strong laser radiation field are presented. In the limit of the Born approximation the ultimate analytical formulas for arbitrary polarization of electromagnetic wave have been obtained and numerically analyzed. Received 5 April 2001 / Received in final form 18 March 2002 Published online 28 June 2002     

An ideal optical system with double-sided symmetry

A theory of an ideal optical system possessing double-sided (or planar) symmetry is developed using the projective transformations technique. In terms of the angular eikonal theory in the paraxial approximation, the theory developed is applied to the construction of a multimodular optical system consisting of ideal, at least two-component, optical systems with double-sided symmetry.     

Two-electron transitions in collisions of fast multiply-charged ions with helium-like atoms

Single and double excitation and ionization of a helium-like atom are considered based on the eikonal approximation. Simple analytical formulas are derived for the cross sections of inelastic collision. A comparison with the experiment is conducted. Scientific Research Institute of Applied Physics at Tashkent State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 44–48, February, 2000.     

Correlation effects in small-angle multiple neutron scattering

The dependence of the spectra of small-angle multiple neutron scattering on the volume fraction occupied by scattering grains is considered. The concentration expansion is used to develop scattering theory in the eikonal approximation. The leading term of the expansion reproduces the standard low-concentration theory (Mollier). Some properties of the first correction term are analyzed, and it is shown that the angular distribution narrows with an increase in concentration, in qualitative agreement with the experimental data.     

Hartmann势加新环型势的相对论束缚态解(英文)

在矢势与标势相等的情况下,对Hartmann势加新环型势的Klein-Gordon方程精确求解.给出了归一化的角向和径向波函数,同时获得了能谱方程.     

Atom-surface interaction in inelastic scattering: He/Ag(111)

The amplitude of inelastic He scattering from Rayleigh waves on a Ag(111) surface is calculated in the framework of the distorted wave Born approximation (DWBA) for a two-body exponential potential. Using the potential parameters recently obtained by Bortolani et al. from a quantum mechanical calculation, agreement is obtained with the experimental data. Simple explicit formulas are presented both in the DWBA and in the eikonal approximation. The essential factor in both cases describes an approximate exponential decay of the intensity for increasing parallel momentum transfer.     

Fast sweeping method for the factored eikonal equation

We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss–Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss–Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.     

Light propagation in media with a highly nonlinear response: An analytical study

The problem of light propagation in highly nonlinear media is studied with the help of a recently introduced systematic approach to the analytical solution of equations of nonlinear optics [L.L. Tatarinova, M.E. Garcia, Exact solutions of the eikonal equations describing self-focusing in highly nonlinear geometrical optics, Phys. Rev. A 78 (2008) 021806(R)(1—4)]. Numerous particular cases of media exhibiting high-order nonlinear refractive indices are considered. We obtain analytical expressions for determining the self-focusing position and a new exact expression for calculating the filament intensity. The constructed solutions allowed us to revise a so-called self-focusing scaling law, i.e., the functional dependence of the self-focusing position on the initial light peak intensity. It was demonstrated that this dependence is governed by the form of the nonlinear refractive index and not by the laser beam shape at the boundary.     

An analytical method for the calculation of the aberrations of optical systems

Based on the exact expression for the angular eikonal of a second-order surface, an analytical method for the analysis of the aberrations of an optical system is constructed and the principles for the optimization of such a system are formulated. Examples of the analysis and optimization of a single surface are given. The theoretical method developed is supported by the results of modeling of the caustic and the focal set in the image space of a point of a spherical refracting surface. The method constructed is exact and does not require using programs for tracing rays through the system.     

Extension of the Mott–Gurney Law for a Bilayer Gap

Steady drift states of an electron flow in a planar gap filled with a bilayer dielectric have been considered. Exact mathematical formulas have been derived that describe the distributions of the electrostatic potential and space charge limited electron flow current (extended Mott–Gurney law for a bilayer diode).