Complex Wave Vector Research Articles

Monte Carlo analysis of the propagation of fusion neutrons in a high enriched uranium system

Monte Carlo methods were used to calculate experimental observables related to the propagation of pulses of fusion neutrons in a compact and highly enriched (90%) subcritical system. These observables are the amplitude and phase of the Fourier transform of the detection rate of a 3He moving detector, they correspond to the propagation of neutron waves excited by a sinusoidal neutron source. The MCNP code was used to model in great details all the heterogeneities of the experimental set up allowing in particular to have a good model of the neutron leakage in the direction perpendicular to the propagation.The very good results of the comparison with the experimental results contrast with previous comparisons with diffusion and transport theory models. The Monte Carlo modeling allows a full analysis of neutron wave experiment in space, time and energy allowing to define asymptotic regions where global complex wave vector exists. We propose to use the extensive literature of neutron wave experiments for further benchmark of MCNP.

Magnetic moment of an electron near a surface with dispersion

Boundary-dependent radiative corrections that modify the magnetic moment of an electron near a dielectric or conducting surface are investigated. Normal-mode quantization of the electromagnetic field and perturbation theory applied to the Dirac equation for a charged particle in a weak magnetic field yield a general formula for the magnetic moment correction in terms of any choice of electromagnetic mode functions. For two particular models, a non-dispersive dielectric and an undamped plasma, it is shown that, by using contour integration techniques over a complex wave vector, this can be simplified to a formula featuring just integrals over TE and TM reflection coefficients of the surface. Analysing the magnetic moment correction for several models of surfaces, we obtain markedly different results from the previously considered simplistic ‘perfect reflector’ model, which is due to the inclusion of physically important features of the surface like evanescent field modes and dispersion in the material. Remarkably, for a general dispersive dielectric surface, the magnetic moment correction of an electron nearby has a peak whose position and height can be tuned by choice of material parameters.

Compression Induced Folding of a Sheet: An Integrable System

The apparently intractable shape of a fold in a compressed elastic film lying on a fluid substrate is found to have an exact solution. Such systems buckle at a nonzero wave vector set by the bending stiffness of the film and the weight of the substrate fluid. Our solution describes the entire progression from a weakly displaced sinusoidal buckling to a single large fold that contacts itself. The pressure decrease is exactly quadratic in the lateral displacement. We identify a complex wave vector whose magnitude remains invariant with compression.

Propagation of electroacoustic axial shear waves in a piezoelectric medium reinforced by continuous fibers

The propagation of electroacoustic axial shear waves in a fiber reinforced piezocomposites is studied in which matrix and fibers consist of piezoelectric transversely isotropic materials with symmetry axes parallel to the fiber axes. The effective medium method self-consistent variant as developed by Sabina and Willis is used to obtain explicit equations for the complex wave vector and it is solved numerically. Its real part determines the effective wave velocity and the imaginary part the attenuation factor. Integral equations expressed via dynamic Green’s function kernels are set up. The central problem of the method is the axial shear electroacoustic wave scattering on one isolated fiber in the medium having the effective piezoelectric properties. It is solved approximately by the Galerkin type method. The obtained expressions for the effective wave velocity and attenuation factor cover not only the long-wave region but the intermediate wave and it is valid for long wavelenghts up to the diameter of the inclusion. Wave velocity and attenuation coefficient coincide with ones obtained earlier in some other way. Some numerical examples are presented for real materials.

Radial distribution functions of non-additive hard sphere mixtures via Percus’ test particleroute

Using fundamental density functional theory we calculate the partial radial distribution functions,gij(r), of a binary non-additive hard sphere mixture using either Percus’ test particle approachor inversion of the analytic structure factor obtained via the Ornstein–Zernike route. Wefind good agreement between the theoretical results and Monte Carlo simulation data forboth positive and moderate negative non-additivities. We investigate the asymptotic,, decay of the gij(r) and show that this agrees with the analytic analysis of the contributions to the partialstructure factors in the plane of complex wavevectors. We find the test particle densityprofiles to be free of unphysical artefacts, contrary to earlier reports.

Superposition of finite-amplitude waves propagating in a principal plane of a deformed Mooney–Rivlin material

Here we consider finite-amplitude wave motions in Mooney–Rivlin elastic materials which are first subjected to a static homogeneous deformation (prestrain). We assume that the time-dependent displacement superimposed on the prestrain is along a principal axis of the prestrain and depends on two spatial variables in the principal plane orthogonal to this axis. Thus all waves considered here are linearly polarized along this axis. After retrieving known results for a single homogeneous plane wave propagating in a principal plane, a superposition of an arbitrary number of sinusoidal homogeneous plane waves is shown to be a solution of the equations of motion. Also, inhomogeneous plane wave solutions with complex wave vector in a principal plane and complex frequency are obtained. Moreover, appropriate superpositions of such inhomogeneous waves are also shown to be solutions. In each case, expressions are obtained for the energy density and energy flux associated with the wave motion.

A feasibility study of the use of bounded beams resembling the shape of evanescent and inhomogeneous waves

Plane waves are solutions of the visco-elastic wave equation. Their wave vector can be real for homogeneous plane waves or complex for inhomogeneous and evanescent plane waves. Although interesting from a theoretical point of view, complex wave vectors normally only emerge naturally when propagation or scattering is studied of sound under the appearance of damping effects. Because of the particular behavior of inhomogeneous and evanescent waves and their estimated efficiency for surface wave generation, bounded beams, experimentally mimicking their infinite counterparts similar to (wide) Gaussian beams imitating infinite harmonic plane waves, are of special interest in this report. The study describes the behavior of bounded inhomogeneous and bounded evanescent waves in terms of amplitude and phase distribution as well as energy flow direction. The outcome is of importance to the applicability of bounded inhomogeneous ultrasonic waves for nondestructive testing.

The properties of a dynamo wave in the case of intense meridional circulation

The solution of a Parker dynamo was constructed for the case of intensive meridional circulation using a method similar to WKB. We show how to build a solution in the transition from the traveling-wave regime to the regime of stationary magnetic field configuration. A solution of the Hamilton-Jacobi equations was discovered for the problem of a dynamo containing a triple point in the complex plane wave vector.

Ray model and ray-wave correspondence in coupled optical microdisks

We introduce a ray model for coupled optical microdisks in which we select coupling-efficient rays among the splitting rays. We investigate the resulting phase-space structure and report island structures arising from the ray coupling between the two microdisks. We find the microdisks's refractive index to influence the phase-space structure and calculate the stability and decay rates of the islands. Turning to ray-wave correspondence, we find many resonances to be directly related to the presence of these islands. We study the relation between the (ray-picture originating) island structures and the (wave-picture originating) spectral properties of resonances, especially the leakiness of the resonances represented as the imaginary part of the complex wave vector.

Cold plasma wave analysis in magneto-rotational fluids

This paper is devoted to investigate the cold plasma wave properties. The analysis has been restricted to the neighborhood of the pair production region of the Kerr magnetosphere. The Fourier analyzed general relativistic magnetohydrodynamical equations are dealt under special circumstances and dispersion relations are obtained. We find the x-component of the complex wave vector numerically. The corresponding components of the propagation vector, attenuation vector, phase and group velocities are shown in graphs. The direction and dispersion of waves are investigated.

Dispersion relation and group velocity for inhomogeneous waves in a hot magnetoplasma with application to an electron-Bernstein-wave propagation experiment in a laboratory plasma

[1] Lewis and Keller (1962) derive the dispersion relation for homogeneous waves propagating in a hot magnetoplasma. Homogeneous waves are ones for which the real and imaginary parts of the wave vector, kr and ki, are parallel. In this paper a generalization to Lewis and Keller is made for inhomogeneous waves, that is, waves for which kr and ki are not parallel. If ki is assumed to be in the same plane as kr and the magnetic field H0 in the Lewis and Keller generalization, comparison can be made with the dispersion relation of Stix (1992); good agreement is found with one exception. This generalization is applied to observations of electrostatic (ES) wave propagation in a laboratory plasma. Bernstein waves propagating perpendicular to H0 are undamped. The dispersion relation for homogeneous waves indicates that severe damping should occur for propagation slightly off perpendicular. Laboratory experiments indicate that severe damping does not occur. The laboratory results can be explained if inhomogeneous waves are considered. Muldrew and Gonfalone (1974) used the dispersion equation for homogeneous waves in a hot magnetoplasma to explain the signal maxima in the pattern when electron-Bernstein waves interfere with the electromagnetic field. Good agreement is obtained when ki is small compared to kr. However, when ki becomes significant, the pattern can no longer be explained. Different approaches to explaining the results using inhomogeneous waves are presented that are superior to the one using homogeneous waves. In one approach, plasma waves with a complex wave vector can propagate without large attenuation, and propagation characteristics can be determined, by choosing the direction of ki to be a free parameter that makes Im{k · vg} = 0, or have a minimum value; k = kr + iki, vg is the complex group velocity ∂ω/∂k and ω is the real angular wave frequency. When this condition is satisfied, good agreement in the signal maxima is obtained with the laboratory experiments if the direction of energy flow in the plasma is taken to be Re{vg}. This method of calculating the interference pattern is compared with the least damped method which calculates the potential of an oscillating point charge in a plasma. Good agreement between the two methods is found if an assumption is made regarding the wave(s) interfering with the ES Bernstein mode.

Wave properties of isothermal magneto-rotational fluids

In this paper, the isothermal plasma-wave properties in the neighborhood of the pair-production region for the Kerr black-hole magnetosphere are discussed. We consider the Fourier-analyzed form of the perturbed general relativistic magnetohydrodynamical equations whose determinant leads to a dispersion relation. For the special scenario, the x-components of the complex wave vectors are calculated numerically. Respective components of the propagation vector, attenuation vector, phase and group velocities are shown in graphs. We have investigated, in particular, the existence of a Veselago medium and wave behavior (modes of waves dispersion).

Surface plasmon Fourier optics

Surface plasmons are usually described as surface waves with either a complex wavevector or a complex frequency. When discussing their merits in terms of field confinment or enhancement of the local density of states, controversies regularly arise as the results depend on the choice of a complex wavevector or a complex frequency. In particular, the shape of the dispersion curves depends on this choice. When discussing diffraction of surface plasmon a scalar approximation is often used. In this work, we derive two equivalent vectorial representations of a surface plasmon field using an expansion over surface waves with either a complex wavevector or a complex frequency. These representations can be used to account for propagation and diffraction of surface waves. They can also be used to discuss the issue of field confinment and local density of states as they have a non-ambiguous relation with the two dispersion relations.

Spin rotation, spin filtering, and spin transfer in directional tunneling through barriers in noncentrosymmetric semiconductors

We discuss possible tunneling phenomena associated with complex wave vectors along directions where the spin degeneracy is lifted in noncentrosymetric semiconductors. We show that the result drastically depends on the direction. In the [110] direction, no solution can be calculated in the usual way assuming that the wave function and its derivative are continuous. A method for obtaining physical solutions is given and consequences are drawn. As a result, there is no spin filtering in such a direction but the spin undergoes a precession through the barrier with the rotation angle being proportional to the barrier thickness. In a direction close to [001] we find a spin-filter effect in close agreement with the model discussed by Perel' et al. [Phys. Rev. B 67, 201304(R) (2003)].

Evanescent states in two-dimensional electron systems with spin-orbit interaction and spin-dependent transmission through a barrier

We find that the total spectrum of electron states in a bounded two-dimensional electron gas with spin-orbit interaction contains two types of evanescent states lying in different energy ranges. The first-type states fill in a gap, which opens in the band of propagating spin-splitted states if tangential momentum is nonzero. They are described by a pure imaginary wave vector. The states of second type lie in the forbidden band. They are described by a complex wave vector. These states give rise to unusual features of the electron transmission through a lateral potential barrier with spin-orbit interaction, such as an oscillatory dependence of the tunneling coefficient on the barrier width and electron energy. However, of most interest is the spin polarization of an unpolarized incident electron flow. Particularly, the transmitted electron current acquires spin polarization even if the distribution function of incident electrons is symmetric with respect to the transverse momentum. The polarization efficiency is an oscillatory function of the barrier width. Spin filtering is most effective if the Fermi energy is close to the barrier height.

Generalized Bloch theorem for complex periodic potentials: A powerful application to quantum transport calculations

Band-theoretic methods with periodically repeated supercells have been a powerful approach for ground-state electronic structure calculations but have not so far been adapted for quantum transport problems with open boundary conditions. Here, we introduce a generalized Bloch theorem for complex periodic potentials and use a transfer-matrix formulation to cast the transmission probability in a scattering problem with open boundary conditions in terms of the complex wave vectors of a periodic system with absorbing layers, allowing a band technique for quantum transport calculations. The accuracy and utility of the method are demonstrated by the model problems of the transmission of an electron over a square barrier and the scattering of a phonon in an inhomogeneous nanowire. Application to the resistance of a twin boundary in nanocrystalline copper yields excellent agreement with recent experimental data.

The complex Bloch bands of a 2D plasmonic crystal displaying isotropic negative refraction

The propagation characteristics of a subwavelength plasmonic crystal are studied based on its complex Bloch band structure. Photonic crystal bands are generated with an alternative 2D Finite Element Method formulation in which the Bloch wave problem is reduced to a quadratic eigenvalue system for the Bloch wavevector amplitude k. This method constitutes an efficient and convenient alternative to nonlinear search methods normally employed in the calculation of photonic bands when dispersive materials are involved. The method yields complex wavevector Bloch modes that determine the wave-scattering characteristics of finite crystals. This is evidenced in a comparison between the band structure of the square-lattice plasmonic crystal and scattering transfer-functions from a corresponding finite crystal slab. We report on a wave interference effect that leads to transmission resonances similar to Fano resonances, as well as on the isotropy of the crystal's negative index band. Our results indicate that effective propagation constants obtained from scattering simulations may not always be directly related to individual crystal Bloch bands.

Quantum electrodynamics near a dielectric half-space

Radiative corrections in systems near imperfectly reflecting boundaries are investigated. As an example, the self-energy of an unbound electron close to a single surface is calculated at one-loop level. The surface is modeled by a nondispersive dielectric half-space of a constant refractive index $n$. In contrast to previous, perfectly reflecting models, the evanescent modes in the optically thinner medium are taken into account and are found to play a physically very important role. The Feynman propagator of the photon field is determined and given in two alternative representations, which include the evanescent modes either as a separate contribution or through analytic continuation and deformation of the integration path for the normal component of the complex wave vector $\mathbf{k}$. The evaluation of the self-energy diagram encounters a number of problems that are specific to the boundary dependence and to the imperfect reflection at the boundary. These problems and methods for their resolution are discussed in depth.

Plane Inhomogeneous Elastic Waves in Transversely Isotropic Media: Explicit Analysis of Different Types of Degeneracy

An intrinsic trait of the plane inhomogeneous waves in elastic media is a particular parametrization duality, stemming from two components characterizing the complex wave vector (bivector) k with respect to the reference frame of orthonormal vectors. Correspondingly, the characteristic condition associated with the equation of motion involves two parameters p and λ, where p is the eigenvalue of the Stroh matrix N (λ) and λ is the eigenvalue of the complex Christoffel matrix λ (p). One of the consequences is a rather elaborate layout of the complex-valued degeneracy types implying repeated p, or λ, or both p and λ. Different types of degeneracy are characterized by dissimilar analytical, algebraic and topological features. The general theory, which has been established for an arbitrary anisotropic medium, is developed in the present paper into an explicit form for a transversely isotropic continuum. By reducing the number of geometrical parameters and enabling factorization of the characteristic polynomial, transverse isotropy fosters explicit resolving of the equations which define different degeneracy types. A particular thrust of the paper is concerned with the algebraic analysis of the conditions, under which the degenerate inhomogeneous modes, having linearly varying or/and circularly polarized amplitude, can be excited on a traction-free boundary by means of reflection or within the Rayleigh wave for, respectively, two- and one-parameter manifolds in the space of orientations of the free surface and propagation direction. Various settings are identified which ensure reflected and surface-localized wave packets comprising a degenerate inhomogeneous mode.

Oscillator-strength enhancement of electric-dipole-forbidden transitions in evanescent light at total reflection

The absorption line strengths of electric-dipole-forbidden (magnetic dipole and electric quadrupole) transitions have been calculated in the evanescent light field that accompanies the total reflection of light. Owing to the complex wave and polarization vectors of the evanescent light, the apparent oscillator strength is enhanced from that in the propagating light and the enhancement for the electric quadrupole transition depends on the polarization vector of the incident light. Separation of the contribution from each component of the wave and polarization vectors is proposed with a magnetic-sublevel-resolved measurement for the $(s\text{\ensuremath{-}}d)$ electric quadrupole transition.