Atomic phenomena in bichromatic laser fields

We present a review of work that has been done during the last 10 years on atomic scattering and reaction processes in bichromatic laser fields. Of particular interest will be the case where the field is composed of two components of commensurate frequencies, usually consisting of a fundamental component ω and one of its low harmonics 2ω or 3ω. These two components are in general out of phase by an angle ϕ. The above processes are then investigated as a function of the relative phase ϕ. This procedure was termed the coherent phase control (CPC) of the atomic process considered. The idea was originally born in molecular physics as a possible means to manipulate molecular reactions.     

Neutron diffuse scattering in Fe3O4 due to molecular polarons

The results of a precise re-examination of neutron diffuse scattering above the Verwey transition of Fe₃O₄ are reported. A model to describe the properties of valence fluctuations at the B-site Fe-ions are proposed, which assumes the existance of “molecular polarons”. The experimental results of anisotropic distribution of diffuse scattering seem to give an evidence for the feasibility of the proposed model.     

Second-order time evolution of PN equations for radiation transport

Using polynomials to represent the angular variation of the radiation intensity is usually referred to as the P_N or spherical harmonics method. For infinite order, the representation is an exact solution of the radiation transport solution. For finite N, in some physical situations there are oscillations in the solution that can make the radiation energy density be negative. For small N, the oscillations may be large enough to force the material temperature to numerically have non-physical negative values. The second-order time evolution algorithm presented here allows for more accurate solutions with larger time steps; however, it also can resolve the negativities that first-order time solutions smear out. Therefore, artificial scattering is studied to see how it can be used to decrease the oscillations in low-order solutions and prevent negativities. Small amounts of arbitrary, non-physical scattering can significantly improve the accuracy of the solution to test problems. Flux-limited diffusion solutions can also be improved by including artificial scattering. One- and two-dimensional test results are presented.     

Optical properties of donor electrons in semimagnetic semiconductors

The cross section of the spin-flip Raman scattering and the absorption coefficient of the electric-dipole spin-resonance of donor electrons in Cd_1?x Mn_xSe are calculated. The exchange induced spin-splitting of a donor level is described taking into account three sources of a local magnetization: external magnetic field, thermodynamical fluctuations of magnetization and molecular field of the donor electron (bound magnetic polaron). The theory takes into account the selection rules appropriate for the hexagonal CdMnSe. The role played by fluctuations of composition is considered. It is suggested that a spin-flip line is inhomogeneously broadened by thermodynamical fluctuations of magnetization and additionally, in high fields, by fluctuations of the composition.     

Reduction of stimulated brillouin scattering by the generation of ion acoustic harmonics

Ion wave harmonics generated by the primary ion acoustic wave excited in stimulated Brillouin scattering are shown to introduce heavy nonlinear damping of the process and to considerably reduce the anomalous reflectivity in an underdense plasma (n/n_c<0.5). The generation of ion wave harmonics acts similarly to strong linear damping and provides an alternative explanation to the heavy damping indicated by experiments.     

Well-width dependence of interface roughness scattering in GaAs/Ga1 − xAlxAs quantum wells

Well-width dependence of quantum and transport mobilities of electrons in GaAs/GaAlAs multiple quantum wells is studied for wells with widths ranging between 50 Å and 145 Å Experimental results are obtained from the amplitude analysis of the Shubnikov–de Haas (SdH) oscillations and from conventional Hall measurements at temperatures betweenT = 15 K and 4.2 K. A novel technique is employed to estimate, theoretically, the interface roughness parameters from electron quantum and transport lifetimes. The modelling is carried out for a range of layer fluctuations, width (Δ) and lateral size (Λ), as to obtain the best fit to the experimental results for individual samples. Our results indicate that the interface roughness scattering limits equal both quantum and transport mobilities at low temperatures, and that the nature of scattering by interface roughness (small or large angle) depends not only on the size and the width of the fluctuations but also on the distribution of these fluctuations within the samples. Therefore, unlike the predictions of the existing theoretical models, which assume constant values of Δ and Λ for all well widths, the well-width dependence of interface roughness scattering cannot be verified experimentally.     

Stabilization of stokes pulse energies in the nonlinear regime of stimulated Raman scattering

An experimental study of quantum mechanical pulse energy fluctuations in stimulated Raman scattering from hydrogen is presented. The probability density function P(W) for Stokes pulse energy W is measured for highly transient scattering in both the linear and nonlinear gain regimes. While large pulse energy fluctuations (100%) occur in the linear gain regime, the fluctuations are reduced to about 20% in the nonlinear regime where the laser pulse is depleted significantly. The results are in excellent agreement with the theoretical predictions of Lewenstein.     

Spontaneous emission and elastic scattering of light from quantum-well excitons in a Fabry-Perot microcavity

A theory of spontaneous emission and elastic light scattering by quasi-two-dimensional excitons in a quantum well placed in a Fabry-Perot microcavity is developed. The problem is solved by means of electrodynamic Green’s functions with inclusion of fluctuations of the quantum-well width and cavity wall shape treated as a perturbation. General expressions are found in a zero approximation of perturbation theory (plane interfaces) for the radiative decay rates of quasi-two-dimensional excitons and for their energy shifts in the cavity. The boundary conditions for the electromagnetic field are taken into account through the coefficients of inward light reflection from the cavity walls. Resonance contributions to the scattering cross sections, which differ in the polarizations (p or s) of the incident and scattered waves, are derived in the lowest (Born) approximation in quantum-well width fluctuations. The spectral and angular dependences of elastic light scattering are studied numerically for Gaussian and exponential correlation functions. It is shown that the contribution from quantum-well width fluctuations to light scattering exceeds that due to single interfaces (surfaces) of a heterostructure by two orders of magnitude.     

Microscopic collective dynamics of atoms in the amorphous metallic alloy Ni33Zr67

The structural properties and microscopic collective dynamics of atoms in the amorphous metallic alloy Ni₃₃Zr₆₇ are studied using molecular dynamics simulations with a pair-additive model potential. The calculated equilibrium structural and dynamic characteristics are compared with experimental data on neutron diffraction and inelastic X-ray scattering. Theoretical analysis of the structural relaxation of microscopic density fluctuations for amorphous metallic alloys is performed within the Lee’s recurrent relation approach. The results of theoretical calculations for the intensity of scattering I(k, ω) for the amorphous metallic alloy Ni₃₃Zr₆₇ are in good agreement with the results of computer simulation and experimental inelastic X-ray scattering data. The low-frequency excitations observed in the longitudinal current spectra are related to the vibrational motions of individual atom clusters, which include Ni and Zr atoms.     

Reflectance of two-layer composite porous media with linear-anisotropic scattering

We report an analysis of the hemispherical reflectance of composite slabs made up of two porous layers. To allow realistic modeling of most porous materials, anisotropic scattering is considered. The reflectance is obtained by using the method of spherical harmonics to solve the equation of transfer. Results from the P-11 approximation are presented for a wide range of governing parameters, including the single-scattering albedos and scattering phase-function coefficients for both porous layers. The effects of anisotropic scattering are illustrated.     

Pseudogap-state superconductivity in a “hot-point” model: Gor’kov equations

The specific features of the superconducting state (with s and d pairing) are considered in terms of a pseudogap state caused by short-range order fluctuations of the “dielectric” type, namely, antiferromagnetic (spin density wave) or charge density wave fluctuations, in a model of the Fermi surface with “hot points.” A set of recurrent Gor’kov equations is derived with inclusion of all Feynman diagrams of a perturbation expansion in the interaction between an electron and short-range order fluctuations causing strong scattering near hot points. The influence of nonmagnetic impurities on superconductivity in such a pseudogap state is analyzed. The critical temperature for the superconducting transition is determined, and the effect of the effective pseudogap width, correlation length of short-range-order fluctuations, and impurity scattering frequency on the temperature dependence of the energy gap is investigated.     

Thermal fluctuations in smectic-<Emphasis Type="Italic">A</Emphasis> films on the surface of solid substrates

The static and dynamic characteristics of layer displacement fluctuations in smectic-A films supported on the surface of a solid substrate are calculated with due regard for the profiles of the flexural and tensile (compressive) moduli of smectic layers. The difference in the surfaces bounding the film and the asymmetry of the profiles of the elastic moduli with respect to the central layer of the film are taken into account. The profiles of fluctuations of smectic-layer displacements and the correlations between these fluctuations are determined for the films formed by liquid-crystal compounds that can undergo a bulk smectic-A-nematic phase transition. The dynamic correlation functions derived for these fluctuations are used for calculating the correlations between the intensities of x-ray scattering by a film at different instants of time. It is demonstrated that, in smectic-A films supported on the surface of a solid substrate, unlike free-standing smectic-A films, the effect of temperature on the dynamics of layer displacement fluctuations can be observed in experiments on dynamic x-ray scattering from films that are not very thick (the number of layers N ～ 20) and at considerably smaller recoilmomentum components in the film plane.     

Elliptic PDE formulation and boundary conditions of the spherical harmonics method of arbitrary order for general three-dimensional geometries

The inherent complexity of the radiative transfer equation makes the exact treatment of radiative heat transfer impossible even for idealized situations and simple boundary conditions. Therefore, a wide variety of efficient solution methods have been developed for the RTE. Among these solution methods the spherical harmonics method, the moment method, and the discrete ordinates method provide means to obtain higher-order approximate solutions to the equation of radiative transfer. Although the assembly of the governing equations for the spherical harmonics method requires tedious algebra, their final form promises great accuracy for any given order, since it is a spectral method (rather than finite difference/finite volume in the case of discrete ordinates). In this study, a new methodology outlined in a previous paper on the spherical harmonics method (P_N) is further developed. The new methodology employs successive elimination of spherical harmonic tensors, thus reducing the number of first-order partial differential equations needed to be solved simultaneously by previous P_N approximations (=(N+1)²). The result is a relatively small set (=N(N+1)/2) of second-order, elliptic partial differential equations, which can be solved with standard PDE solution packages. General boundary conditions and supplementary conditions using rotation of spherical harmonics in terms of local coordinates are formulated for the general P_N approximation for arbitrary three-dimensional geometries. Accuracy of the P_N approximation can be further improved by applying the “modified differential approximation” approach first developed for the P₁-approximation. Numerical computations are carried out with the P₃ approximation for several new two-dimensional problems with emitting, absorbing, and scattering media. Results are compared to Monte Carlo solutions and discrete ordinates simulations and a discussion of ray effects and false scattering is provided.     

Solution of the three-dimensional problem of wave diffraction by an ensemble of objects

The pattern equations method is extended to solving three-dimensional problems of wave diffraction by an ensemble of bodies. The method is based on the reduction of the initial problem to a system of N (N is the number of scatterers in the ensemble) integro-operator equations of the second kind for the scattering patterns of scatterers. With the use of the series expansions of the scattering patterns in angular spherical harmonics, the problem is reduced to an algebraic system of equations in the expansion coefficients. An explicit (asymptotic) solution to the problems is obtained in the case when the scattering bodies are separated by sufficiently long distances. It is shown that the method can be used to model the characteristics of wave scattering by complex-shaped bodies.     

N-soliton quantum scattering in the sine-Gordon theory

The quantum treatment of soliton scattering in the sine-Gordon model, using the path integral collective coordinate method is generalized to N solitons. The solitions. The first quantum correction to the phase shift of N-soliton scattering is equal to the zero-point energy of an effective multi-soliton Hamiltonian. The energies of the oscillators of this Hamiltonian are shown to be equal to the stability angles of a complete set of solutions of the Schrödinger equation for small fluctuations around a classical N-soliton. Consequently, calculating the fluctuations and their stability angles by the inverse scattering method, we obtain the energies of the oscillators. The first quantum correction to the phase shift (the O(1) part in a development in powers of γ) is evaluated by summing the stability angles. This result is in agreement with the “exact” scattering amplitude conjectured by Faddeev, Kulish and Korepin.     

A finite element-spherical harmonics radiation transport model for photon migration in turbid media

In this paper, we solve the steady-state form of the Boltzmann transport equation in homogeneous and heterogeneous tissue-like media with a finite element-spherical harmonics (FE-P_N) radiation transport method. We compare FE-transport and diffusion solutions in terms of the ratio of absorption to reduced scattering coefficient, (μ_a/μ_s′) and the anisotropy factor g. Two different scattering phase function formulas are employed to model anisotropic scattering in the slab media with high g-value. Influence of void-like heterogeneities, and of their boundaries with the surrounding medium on the transport of photons are also examined.     

Rotationally inelastic,classical rigid shell scattering

Rotationally inelastic atom-diatom collisions at wide angles and energies large compared to the attractive potential well depth are approximately described by classical scattering of structureless particles and rigid rotor molecules interacting by a rigid potential shell ofC _∞υ symmetry. The double differential cross section for deflection and rotational energy transfer isanalytically related to the geometry of the shell. In continuation of previous work the influence of molecular rotation before collision is considered. It is found: The conspicuous structure of bulge scattering or orientational rainbows in this cross section persists, but is modified by initial rotation. The modifications are angle dependent. The (classical) information of bulge scattering on the anisotropy of the potential is increasingly averaged out by higher initial rotation. In experiments exploiting this new probe to the anisotropy of the repulsive molecular interaction initial rotation should be kept as low as possible.     

Structure of A = 3 nuclear systems using realistic Hamiltonians

The structure of A = 3 low-energy scattering states is described using the hyperspherical harmonics method with realistic Hamiltonian models, consisting of two- and three-nucleon interactions. Both coordinate and momentum space two-nucleon potential models are considered.     

Notes on number density fluctuations and the scattering cross section for electromagnetic waves scattered from a thermal nonequilibrium plasma

The scattering cross section and the Doppler spectrum for electromagnetic waves scattered by the electron density fluctuations of a plasma, where the mean kinetic temperature of the electronsT _e may differ from that of the ionsT _i , has been obtained among others byFejer, Buneman, Renau, Camnitz andFlood, andSalpeter. These authors use different methods of approach to calculate the autocovariance of the electron number-density fluctuations (from the mean) and then obtain the scattering cross section. Because of the differing results, the methods, concepts, and derivations of the scattering cross section are carefully examined in this paper. It is shown that the short-time dynamical considerations incorporated in the formulation of the statistical theory of the electron number-density fluctuations of the plasma as used by several authors (for instanceFejer, Buneman, Salpeter,) leads to results of limited validity. In addition, a fundamental error in calculating the electron density fluctuations leads these latter authors to an incorrect scattering cross section. The theory of scattering of electromagnetic waves from a plasma, where the electrons arenot in thermal equilibrium with the ions but statistical equilibrium exists, is developed in a general way. The covariance of the number-density fluctuations from the mean of the charged species of the plasma and the scattering cross sectionσ(q) are obtained. In particular it is shown that for a wavelength λ much greater than the effective Debye lengthd, the backscattering cross section increases and approaches complete incoherent scattering asT _e /T _i increases. This result is explained by noting that in the case of thermal equilibrium, the predicted value of the back-scattering cross section is smaller than that of the backscattering cross section from completely uncorrelated electron density fluctuations because the electrostatic interaction between the charged particles of the plasma, which is a function ofT _e andT _i , introduces a certain amount of organization in otherwise completely uncorrelated electron density fluctuations. When the mean temperature of the electrons increases relative to that of the ions, the organization introduced in the fluctuations diminishes because of the increasing thermal agitation of the electrons relative to that of the ions, and the backscattering process approaches that of incoherent backscattering (Thomson-type scattering). The spectrum function of incoherent scattering of electromagnetic waves from a nonequilibrium plasma is obtained and some cases of current interest are plotted.     

Second-harmonic pressure generation of a non-diffracting acoustical high-order Bessel vortex beam of fractional type α

Background and motivation

Generalized Bessel vortex beams are regaining interest from the standpoint of acoustic scattering and radiation force theories for applications in particle rotation, mixing and manipulation. Other possible applications may include medical and nondestructive imaging. To manipulate heavy particles in a host medium, a minimum threshold of the incident sound field intensity is required at relatively high wave amplitudes such that nonlinear wave propagation occurs and the generation of harmonics may be detected. Thus, predictions of the harmonics generation become crucial from the standpoint of experimental design, and the present analysis should assist in the development of more complete models related to the (nonlinear) scattering and radiation forces under such circumstances. The purpose of this research is to construct a theoretical model for the second-harmonic pressure generation associated with a category of non-diffracting Bessel vortex beams known as high-order Bessel vortex beams of fractional typeα (HOBVBs-Fα).

Method

The weakly nonlinear wave propagation of a HOBVB-Fα is investigated based on Lighthill’s formalism. Analytical solutions up to the second-order level of approximation are derived and discussed. Closed-form solutions are obtained, which are expressed as a function of first-order quantities available from the classical linear theory. Lateral profiles of the HOBVB-Fα are computed and compared.

Results and conclusion

The results show that the beam’s width reduces and becomes narrower, the side-lobes decrease in magnitude, and the hollow region diameter (or null in magnitude) increases as the order of nonlinearity increases. Furthermore, the nonlinearity of the medium preserves the non-diffracting feature of the beam’s second-harmonic generation within the pre-shock range.