Transverse Wave Number Research Articles

Chromodynamic Weibel instabilities in relativistic nuclear collisions

Employing a previously derived formulation, and extending the treatment from purely transverse modes to wave vectors having a longitudinal component, we discuss the prospects for the occurrence of Weibel-type color-current filamentation in high-energy nuclear collisions. Numerical solutions of the dispersion equation for a number of scenarios relevant to RHIC and LHC suggest that modes with (predominantly transverse) wave numbers of several hundred MeV may become moderately agitated during the early collision stage. The emergence of filamentation helps to speed up the equilibration of the parton plasma and it may lead to nonstatistical azimuthal patterns in the hadron final state.

Transverse instability and its long-term development for solitary waves of the (2+1)-dimensional Boussinesq equation.

The stability properties of line solitary wave solutions of the (2+1)-dimensional Boussinesq equation with respect to transverse perturbations and their consequences are considered. A geometric condition arising from a multisymplectic formulation of this equation gives an explicit relation between the parameters for transverse instability when the transverse wave number is small. The Evans function is then computed explicitly, giving the eigenvalues for the transverse instability for all transverse wave numbers. To determine the nonlinear and long-time implications of the transverse instability, numerical simulations are performed using pseudospectral discretization. The numerics confirm the analytic results, and in all cases studied, the transverse instability leads to collapse.

Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability

The guidance conditions of modes with both real and imaginary transverse wave numbers inside a dielectric slab with negative permittivity and permeability are solved. We show that for real transverse wave numbers, cutoffs exist for all modes, unlike in conventional media where the first even mode is always propagating. In addition, we also show that guided modes exist for imaginary transverse wave numbers, with the power concentrated at the interfaces instead of having maxima inside the slab. A graphical method of determining the imaginary transverse wave numbers of the guided modes is introduced which clearly identifies the different conditions of propagation depending on the properties of the slab. In particular, propagation of guided waves inside less dense negative media is shown to be possible.

Front and back instability of a liquid film on a slightly inclined plate

We study the transverse instability of a liquid ridge on horizontal and inclined substrates using a film evolution equation based on a long wave approximation. The equation incorporates an additional pressure term—the disjoining pressure—accounting for the effective interaction of the film with the substrate. On a horizontal substrate the dominant instability mode is varicose, but may turn into a zigzag mode on a slightly inclined substrate depending on the inclination angle and the ridge volume. For larger angles or volumes the instabilities at the front and back decouple. The linear stability properties of a one-dimensional transverse ridgelike state are studied in detail, and an energy analysis is used to demonstrate that the disjoining pressure provides the dominant instability mechanism at both the front and the back, while the body force is responsible for the main differences between these two instabilities. An amplitude equation for the time evolution of perturbations with small transverse wave numbers is derived that predicts correctly the linear crossing of the most dangerous eigenvalues at zero wave number in the inclined case, in contrast to the situation on a horizontal substrate.

Absorption and dichroism spectra of cylindrical J aggregates and chlorosomes of green bacteria

We study the absorption and linear and circular dichroism spectra of molecular aggregates having the shape of a cylinder. Examples are the chlorosomes of green bacteria and recently synthesized cyanine J aggregates, called amphi-pipes. We use a Frenkel exciton model and exploit the cylinder symmetry to separate the exciton states into bands with different transverse wavenumbers. Only three of these bands are optically active. The delicate interference between the contributions of these three bands to the CD spectrum, make this spectrum very sensitive to system parameters, such as the cylinder length. This offers a natural explanation for the observed strong variation of the CD spectra of chlorosomes with sample preparation technique.

On the origin of filamentary structure in sunspot penumbrae: linear instabilities

The fine structure present in sunspot penumbrae first appears when filamentary convection sets in at the outer edge of large pores, coinciding with an increase in magnetic field inclination to the vertical. The formation of this filamentary structure is investigated in a highly idealized Boussinesq model. A two-dimensional equilibrium is constructed with the magnetic field at the bottom of the layer concentrated towards one side of the box, but fanning out towards the top of the layer, mimicking a sunspot. This two-dimensional steady state is then perturbed in the third direction, to seek filamentary instabilities leading to a filamentary structure. The two-dimensional model is found to be highly unstable for a range of transverse wavenumbers. The form of the instability is such that an alternating pattern of bright and dark filaments develops at the upper surface. This is the first numerical evidence of filamentary instabilities driven by external convection.

A Numerical Study of TM-Type Surface Waves on a Grounded Dielectric Slab Covered by a Doubly Periodic Array of Metallic Patches

In this paper we numerically study the propagation of surface waves guided by a metal-backed dielectric slab with biperiodic metallizations on its surface. Such structures are electromagnetic absorbing screens when the dielectric slab is lossy. In this paper, the surface waves are characterized by their longitudinal and transverse wave numbers, which are deduced from the complex pole locations of the reflection coefficient of the screens. The reflection coefficients can be obtained with a moment method. These reflection coefficients are generalized to complex incident wave numbers. The poles are isolated in the complex plane with the help of the argument principle and are calculated with a numerical method based on Muller's algorithm. Then the parametric study of the wave numbers of the surface waves shows that the absorption of an electromagnetic wave by the screens at normal incidence is due to a resonance of the real part of the transverse wave number of the excited surface wave. We also show that there exists a Brewster incidence angle for the absorbing screens with suitable metallization array dimensions. This Brewster angle appears when the pole crosses the branch cut of the two-sheeted Riemann space of the reflection coefficient.

A NUMERICAL STUDY OF TM-TYPE SURFACE WAVES ON A GROUNDED DIELECTRIC SLAB COVERED BY A DOUBLY PERIODIC ARRAY OF METALLIC PATCHES - Abstract

In this paper we numerically study the propagation of surface waves guided by a metal-backed dielectric slab with biperiodic metallizations on its surface. Such structures are electromagnetic absorbing screens when the dielectric slab is lossy. In this paper, the surface waves are characterized by their longitudinal and transverse wave numbers, which are deduced from the complex pole locations of the reflection coefficient of the screens. The reflection coefficients can be obtained with a moment method. These reflection coefficients are generalized to complex incident wave numbers. The poles are isolated in the complex plane with the help of the argument principle and are calculated with a numerical method based on Müller's algorithm. Then the parametric study of the wave numbers of the surface waves shows that the absorption of an electromagnetic wave by the screens at normal incidence is due to a resonance of the real part of the transverse wave number of the excited surface wave. We also show that there exists a Brewster incidence angle for the absorbing screens with suitable metallization array dimensions. This Brewster angle appears when the pole crosses the branch cut of the two-sheeted Riemann space of the reflection coefficient.

Restricted equivalence of paired epsilon–negative and mu–negative layers to a negative phase–velocity material ( aliasleft–handed material)

The time–harmonic electromagnetic responses of (a) a bilayer made of an epsilon–negative layer and a mu–negative layer, and (b) a single layer of a negative phase–velocity material are compared. Provided all layers are electrically thin, a restricted equivalence between (a) and (b) exists. The restricted equivalence depends on the linear polarization state and the transverse wavenumber. Implications for perfect lenses and parallel–plate waveguides are considered.

Optical Properties of Helical Cylindrical Molecular Aggregates: The Homogeneous Limit

Using a Frenkel exciton model, we study the optical absorption spectrum and linear and circular dichroism (CD) spectra of cylindrical molecular aggregates. We demonstrate that such aggregates can always be described as a stack of molecular rings with nearest-neighbor rings rotated relative to each other by a helical angle γ. For homogeneous aggregates, the cylindrical symmetry allows for a decomposition of the Hamiltonian into a set of effective one-dimensional Hamiltonians, which are characterized by a transverse wavenumber k2. The helical nature of the cylinder renders these Hamiltonians complex and noninversion symmetrical in general. Only the bands with k2 = 0 and k2 = ±1 are dipole-allowed and yield contributions to the various linear spectra studied. The k2 decomposition also allows for a convenient separation of the CD into ring and helical contributions, which in turn allows us to explain the strong sensitivity of this spectrum to various system parameters, such as the molecular orientations and the ratio of cylinder length and circumference. The latter is explicitly demonstrated by numerically studying the size dependence of the spectra for chlorosomes of green bacteria. The results suggest that the strong variation of the CD as reported experimentally may result from size variations. We also present analytical results valid for long cylinders. In this case, we find three superradiant states to be responsible for the complete linear optical response: one at total wave vector k = 0 and the other two (degenerate) at wave vectors determined by the circumference and the helical angle γ.

Quantum properties of transverse pattern formation in second-harmonic generation

We investigate the spatial quantum noise properties of the one-dimensional transverse pattern formation instability in intracavity second-harmonic generation. The Q representation of a quasi-probability distribution is implemented in terms of nonlinear stochastic Langevin equations. We study these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold for pattern formation, beams with opposite direction of the off-axis critical wave numbers are shown to be highly correlated. This is observed for the fundamental field, for the second-harmonic field, and also for the cross-correlation between the two fields. Nonlinear correlations involving the homogeneous transverse wave number, which are not identified in a linearized analysis, are also described. The intensity differences between opposite points of the far fields are shown to exhibit sub-Poissonian statistics, revealing the quantum nature of the correlations. We observe twin beam correlations in both the fundamental and second-harmonic fields, and also nonclassical correlations between them.

Localized interface optical-phonon modes in two coupled semi-infinite superlattices

The existence and features of the localized interface optical-phonon modes (IOPM's) in two coupled semi-infinite superlattices with a frequency-independent defect layer are investigated in the dielectric continuum approximation. A comparison of the localized IOPM's between structures with frequency-independent defect layer (type I structure) and frequency-dependent defect layer (type II structure) is made. We find that the antisymmetric localized modes in type I structure display interesting features significantly different from those in the type II structure. The existence and localization of the antisymmetric modes in type I structure strongly depend on the nature of the defect layer, transverse wave number, the thickness of the defect layer and the constituent layers. However, the symmetric localized modes are not sensitive to the nature and thickness of the defect layer.

Efficient analysis of periodic dielectric waveguides using Dirichlet-to-Neumann maps.

We present a numerical scheme for the analysis of periodic dielectric waveguides using Floquet-Bloch theory. The problem of finding the fundamental propagation modes is reduced to a nonlinear eigenvalue problem involving Dirichlet-to-Neumann maps. This approach leads to much smaller matrix problems than the ones that have appeared previously. By an increase of the discretization fineness, any desired precision of the method can be achieved. We discuss an eigensolver and extend the conventional rule to choose the branches of the transverse wave numbers. This ensures analytic dependence on the Floquet multiplier and convergence of the nonlinear solver. We demonstrate that even for a complicated multilayer waveguide structure the propagation factors can be calculated within seconds to several digits of accuracy.

Scalar approximation feasibility analysis near the cutoff frequency of HE1 n fibre mode with account of material losses

Eigenvalue equations for rigorous HE 1 n and scalar LP 0 n modes of a step-index fibre are solved numerically above and below the cutoff frequency with account of material losses in the fibre cladding. Polarisation corrections to transverse wavenumbers of the LP 02 mode are calculated. Behaviour of dispersion curves in a complex plane of transverse wavenumber in cladding is taken as a basis of the analysis. Transmittance of a lossy fibre junction consisting of the single-mode and bimodal segments is evaluated. Error in the scalar approximation is proved to increase significantly near the cutoff frequency.

Raman sidescatter in numerical models of short pulse laser plasma interactions

Certain reduced models of a plasma are subject to a phenomenon known as the ultraviolet catastrophe, whereby the Raman growth rate diverges with increasing transverse wave number. Numerical solutions that make use of such models cannot account for large angle scattering. Several of these models are evaluated in terms of their ability to reproduce the growth rates given by the two-dimensional Raman dispersion relation. The quasistatic approximation causes a much more severe ultraviolet catastrophe than does the paraxial approximation alone. Removal of the quasistatic approximation eliminates the ultraviolet catastrophe provided nonparaxial terms are retained. Fully explicit particle-in-cell simulations show that large angle scattering leads to a fine structure which perturbs the pump wave and heats the plasma.

Spatial forcing of spontaneous optical patterns.

A nonlinear optical system, which spontaneously forms hexagonal patterns, is exposed to a weak, spatially modulated forcing. As forcing, stationary hexagonal patterns are used under variation of their transverse wave number. In the experiment, we observe a locking when the forcing wave number is close to one of the critical wave numbers of the unforced system. Outside the locking regimes, forcing provokes spatiotemporal disorder. The system response is characterized quantitatively with respect to its dynamics and to its spatial order.

Stability of the Flow in a Streaky Structure and the Development of Perturbations Generated by a Point Source Inside It

The flow stability in a boundary layer with an inhomogeneous spanwise-periodic velocity profile modeling the streaky structure that develops at a high level of turbulence of the incident flow is analyzed in the three-dimensional formulation for perturbations with an arbitrary transverse period. It is shown that in the presence of inhomogeneity the dispersion relation for the Tollmien-Schlichting waves is split into two branches periodic in the transverse wave number, which correspond to symmetric and antisymmetric modes. The solution for the packet of inhomogeneous-flow modes generated by localized time-periodic fluid injection/ejection is found. The shape of this packet corresponds qualitatively to the shape of the Tollmien-Schlichting wave packet, but the fine perturbation structure inside it is sharply different.

Computation of Broadband Noise Radiated by a Ducted Fan

— Acoustic pressure amplitude Am! a — Speed of sound B — Number of rotor blades b — Rotor blade span C — Blade load constant — Spherical coordinates for free-field radiation D,,# — Cylindrical coordinates of a source on the rotor d,$, y1 y — Blade load, and its azimuthal Fourier transform F,F f — Frequency G — Green’s function I — Sound intensity — Integral on a point source ! — Bessel function of first kind and of order m Jm — Total, transverse, and axial wave-numbers K,kt,kz L — Duct length l — Radial turbulence length scale — Spinning mode (m azimuthal, radial) m,! ! — Axial Mach number in the annular duct in front Max of the rotor — Tip rotational Mach number Mtip — Mach number of the uniform flow in the duct Mz N — Rotor angular rotation speed (either in rpm or in Hz) n — Number of point sources along the blade span in non-compact calculations — Sound pressure in the duct and in the far field, p,P respectively q — Exponent of decrease of the blade pressure fluctuations at high frequency R — Duct radius — Cylindrical coordinates of a point in the duct r,%,x1 x S — Blade surface area — Reception time, emission time t,& — Rotation speed of a point source on a blade Urot W — Sound power — Dirac function ' — Mean fluid density (0 — Fan hub-to-tip ratio ) — -th root of *m! ! Jm ! 0 — Rotor angular rotation speed ( ) + + ! 2,N — Angular frequency ( ) ! 2,f ! aK

The group velocity of electromagnetic waves diffracted by a small aperture

Diffraction of electromagnetic waves by an aperture in an infinite opaque screen is approached using an integral expression characterized by the spatial Fourier transform at the aperture. The group velocity of the field propagated from the aperture assumes a continuous distribution of values corresponding to the distribution in transverse wavenumber. The gravitational Doppler shift is computed for an aperture that is small compared to a wavelength. It is found that the integral expression can be evaluated analytically, leading to a distribution of Doppler shifts; the minimum Doppler shift is on the order of one part in 10 15. Every additional order of magnitude increase in the Doppler shift results in a decrease in amplitude by two orders of magnitude.

Ionization instabilities of an electromagnetic wave propagating in a tenuous gas

A theory is developed to study the scattering instability that occurs when a laser pulse propagates through and ionizes a gas. The instability is due to the intensity dependence of the ionization rate, which leads to a transversely structured free electron density. The instability is convective in the frame of the laser pulse, but can have a relatively short growth length scaling as Lg∼k0/kp2, where k0 is the laser wave number, kp2=ωp2/c2 and ωp is the plasma frequency. The most unstable perturbations correspond to a scattering angle for which the transverse wave number is around the plasma wave number, kp. The scattered light is frequency upshifted. The comparison between simple analytic theory and numerical simulation shows good agreement.