Vacuum Plane-wave Research Articles

Causality in Scalar-Einstein Waves

A wavelike scalar-Einstein solution is found and indicating vectors constructed from the Bel-Robinson tensor are used to study which objects co-move with the wave and whether gravitational energy transfer is null. It is found that this Bel-Robinson energy criteria gives null energy transfer for both the vacuum plane wave and the scalar plane wave.

Broadband Polarization Degeneracy of Guided Waves in Subwavelength Structured ZnO Pattern

Polarization degeneracy of electromagnetic plane waves in vacuum and in any bulk isotropic media is the keynote operational principle of many optical devices such as polarizers and interferometers. However, surface and guided waves spectra are typically either not degenerated at all or meet degeneracy only at very specific dispersion points. In this paper, we offer a design of a periodic photonic structure based on zinc oxide (ZnO) nanocylinders providing the broadband polarization degeneracy of the guided waves in the near-IR frequency range. We analyze the impact of the spatial dispersion and substrate on the degeneracy breaking. We offer the design based on ZnO nanocylinders with aluminum-doped zinc oxide substrate, achieving the degeneracy in the vicinity of a telecommunication wavelength, for the practical implementation. Finally, we propose and verify numerically a potentially important device–waveguide polarizer, which is the analogue to the $\lambda /4$ plate for the guided waves.

Spacetime characterizations of Λ-vacuum metrics with a null Killing 2-form

An exhaustive list of four-dimensional Λ-vacuum spacetimes admitting a Killing vector ξ whose self-dual Killing two-form is null is obtained assuming that the self-dual Weyl tensor is proportional to the tensor product of by itself. Our analysis complements previous results (Mars 1999 Class Quantum Grav. 16 2507–23; Mars and Senovilla 2015 Ann. H. Poincaré 16 1509–50) concerning the case with non-null . We analyze both cases with Λ vanishing or not. In the latter case we prove that must hold necessarily, and we find a characterization of the Einstein spacetimes conformal to pp-waves. In the former case we obtain spacetime characterizations of vacuum plane waves and of the stationary vacuum Brinkmann spacetimes. At the light of the full set of results, old and new, we reformulate the case with non-null and . We finally present a table collecting the results for both null, and non-null, .

Controlling the wave propagation through the medium designed by linear coordinate transformation

Based on the principle of transformation optics, we propose to control the wave propagating direction through the homogenous anisotropic medium designed by linear coordinate transformation. The material parameters of the medium are derived from the linear coordinate transformation applied. Keeping the space area unchanged during the linear transformation, the polarization-dependent wave control through a non-magnetic homogeneous medium can be realized. Beam benders, polarization splitter, and object illusion devices are designed, which have application prospects in micro-optics and nano-optics. The simulation results demonstrate the feasibilities and the flexibilities of the method and the properties of these devices. Design details and full-wave simulation results are provided. The work in this paper comprehensively applies the fundamental theories of electromagnetism and mathematics. The method of obtaining a new solution of the Maxwell equations in a medium from a vacuum plane wave solution and a linear coordinate transformation is introduced. These have a pedagogical value and are methodologically and motivationally appropriate for physics students and teachers at the undergraduate and graduate levels.

Vacuum plane waves: Cartan invariants and physical interpretation

As an application of the Cartan invariants obtained using the Karlhede algorithm, we study a simple subclass of the PP-wave spacetimes, the gravitational plane waves. We provide an invariant classification of these spacetimes and then study a few notable subcases: the linearly polarized plane waves, the weak-field circularly polarized waves, and another class of plane waves found by imposing conditions on the set of invariants. As we study these spacetimes we relate the invariant structure (i.e., Cartan scalars) to the physical description of these spacetimes using the geodesic deviation equations relative to timelike geodesic observers.

Black holes and black strings in plane waves

We investigate the construction of black holes and black strings in vacuum plane wave spacetimes using the method of matched asymptotic expansions. We find solutions of the linearised equations of motion in the asymptotic region for a general source on a plane wave background. We observe that these solutions do not satisfy our previously defined conditions for being asymptotically plane wave. Hence, the space of asymptotically plane wave solutions is restricted. We consider the solution in the near region, treating the plane wave as a perturbation of a black object, and find that there is a regular black string solution but no regular black hole solution.

Late-time behaviour of the tilted Bianchi type VIh models

We study tilted perfect fluid cosmological models with a constant equation of state parameter in spatially homogeneous models of Bianchi type VIh using dynamical systems methods and numerical experimentation, with an emphasis on their future asymptotic evolution. We determine all of the equilibrium points of the type VIh state space (which correspond to exact self-similar solutions of the Einstein equations, some of which are new), and their stability is investigated. We find that there are vacuum plane-wave solutions that act as future attractors. In the parameter space, a ‘loophole’ is shown to exist in which there are no stable equilibrium points. We then show that a Hopf-bifurcation can occur resulting in a stable closed orbit (which we refer to as the Mussel attractor) corresponding to points both inside the loophole and points just outside the loophole; in the former case the closed curves act as late-time attractors while in the latter case these attracting curves will co-exist with attracting equilibrium points. In the special Bianchi type III case, centre manifold theory is required to determine the future attractors. Comprehensive numerical experiments are carried out to complement and confirm the analytical results presented. We note that the Bianchi type VIh case is of particular interest in that it contains many different subcases which exhibit many of the different possible future asymptotic behaviours of Bianchi cosmological models.

Evanescent Plane Waves in Multilayer Structures

We have considered evanescent plane waves in structures with a layer of a substance with e, μ < 0 and with a layer of a well-reflecting metal, e < 0, μ ≥ 1. Waves with increased amplitude as compared with the initial wave have been found to occur, due to which evanescent waves with wave number as in the initial wave but with increased amplitude arise behind these layers. A composite material with e, μ < 0 at optical frequencies are proposed. Surface waves on a metal layer are considered in detail. It is shown that surface waves with a sufficiently arbitrary wave number can be excited. It is also shown that, on very thin layers, surface waves with wave number exceeding ten times that of a homogeneous plane wave in vacuum can be excited. Propagation losses are calculated. For a silver layer, the wave path can be from 30 up to 100 wavelengths. Practical use in developing techniques for optical transformations of short-wave surface waves in 2D space, similar to those in 3D space, are pointed out.

Classical theory of Compton scattering: Assessing the validity of the Dirac-Lorentz equation

The Dirac-Lorentz equation describes the dynamics of a classical point charge in an electromagnetic field, accounting for radiative effects in a manifestly covariant and gauge-invariant manner. The validity of this equation is assessed by direct comparison between the Dirac-Lorentz dynamics of an electron subjected to a plane wave in vacuum and the well-known recoil associated with Compton scattering. In the small recoil limit, the classical Dirac-Lorentz is shown to yield the correct momentum transfer. For larger values of the recoil, the quantum scale appears explicitly, and the classical Dirac-Lorentz equation does not properly model this situation, as shown by deriving an exact analytical solution for a monochromatic plane wave of wave number k0 to any order in k0r0, where r0 is the classical electron radius.

Inhomogeneous perturbations of plane-wave spacetimes

Recently it was shown that the exact cosmological solutions known as the vacuum plane-wave solutions are late-time attractors for an open set of the spatially homogeneous Bianchi universes containing a non-inflationary γ-law perfect fluid. In this paper we study inhomogeneous perturbations of these plane-wave spacetimes. By using expansion-normalized scale-invariant variables, we show that these solutions are unstable to generic inhomogeneous perturbations. The crucial observation for establishing this result is a divergence of the expansion-normalized frame variables which ultimately leads to unstable modes.

A dynamical systems approach to the tilted Bianchi models of solvable type

We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VIh and VIIh) with a perfect fluid and a linear barotropic γ-law equation of state. In particular, we study the late-time behaviour of tilted Bianchi models, with an emphasis on the existence of equilibrium points and their stability properties. We briefly discuss the tilting Bianchi type V models and the late-time asymptotic behaviour of irrotational Bianchi type VII0 models. We prove the important result that for non-inflationary Bianchi type VIIh models vacuum plane-wave solutions are the only future attracting equilibrium points in the Bianchi type VIIh invariant set. We then investigate the dynamics close to the plane-wave solutions in more detail, and discover some new features that arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of tilt. We point out that in a tiny open set of parameter space in the type IV model (the loophole) there exist closed curves which act as attracting limit cycles. More interestingly, in the Bianchi type VIIh models there is a bifurcation in which a set of equilibrium points turns into closed orbits. There is a region in which both sets of closed curves coexist, and it appears that for the type VIIh models in this region the solution curves approach a compact surface which is topologically a torus.

Vacuum plane waves in 4+1 D and exact solutions to Einstein's equations in 3+1 D

In this paper, we derive homogeneous vacuum plane-wave solutions to Einstein's field equations in 4+1 dimensions. The solutions come in five different types of which three generalize the vacuum plane-wave solutions in 3+1 dimensions to the (4+1)-dimensional case. By doing a Kaluza–Klein reduction we obtain solutions to the Einstein–Maxwell equations in 3+1 dimensions. The solutions generalize the vacuum plane-wave spacetimes of Bianchi class B to the non-vacuum case and describe spatially homogeneous spacetimes containing an extremely tilted fluid. Also, using a similar reduction we obtain (3+1)-dimensional solutions to the Einstein equations with a scalar field.

Scattering states of hydrogenic atomic system in front of a metal surface

The Schrödinger equation for the continuum states of a hydrogenic system in frontof a metal surface described by a step potential is solved using prolate spheroidalcoordinates. The potential considered includes the classical core image on themetal side.The boundary conditions used describe an electron incident on thesurface from the metal side, and consist of incident and reflected plane waves inthis sub-space, and a transmitted plane wave in vacuum. The presence of thenuclear charge on the vacuum side and the polarization it induces onthe surface, described by an image charge, act as scattering centres thatproduce an outgoing spherical wave in the asymptotic region.We present theexact continuum wavefunction for different values of the energy and theremaining quantum numbers. Using the condition of continuity of thewavefunction and its normal derivative on the surface plane we obtain thesolution in analytical form. Efficient algorithms, easily implemented on anymicrocomputer, allow for the calculation of the separation constants of thewave equation, the amplitudes of the waves scattered from the charge andits image, its phase shifts and from them the continuum wavefunction.

String theory and the classical stability of plane waves

The presence of fields with negative mass-squared typically leads to some form of instability in standard field theories. The observation that, at least in the light-cone gauge, strings propagating in plane wave spacetimes can have world sheet scalars with such tachyonlike masses suggests that the supergravity background may itself be unstable. To address this issue, we perform a perturbative analysis around the type IIB vacuum plane wave, the solution which most obviously generates world sheet scalars with negative mass-squared. We argue that this background is perturbatively stable.

Generating asymptotically plane wave spacetimes

In an attempt to study asymptotically plane wave spacetimes which admit an event horizon, we find solutions to vacuum Einstein's equations in arbitrary dimension which have a globally null Killing field and rotational symmetry. We show that while such solutions can be deformed to include ones which are asymptotically plane wave, they do not posses a regular event horizon. If we allow for additional matter, such as in supergravity theories, we show that it is possible to have extremal solutions with globally null Killing field, a regular horizon, and which, in addition, are asymptotically plane wave. In particular, we deform the extremal M2-brane solution in 11-dimensional supergravity so that it behaves asymptotically as a 10-dimensional vacuum plane wave times a real line.

Superluminality in Gaussian beams

On the basis of Rayleigh–Sommerfeld vectorial diffraction formulas, we show that the radiation from a pulsed Gaussian planar source propagates at a slightly superluminal group velocity beyond the Rayleigh distance, in agreement with a recent prediction from the approximate paraxial theory of diffraction. Moreover, superluminality can be sizably enhanced up to velocities 1.5% faster than c (speed of a plane wave in vacuum) by diminishing the diameter of the source down to one wavelength.

Spin driven motion in intense spacetime wave geometries

The motion of a massive particle with intrinsic spin in a gravitational Einstein vacuum plane wave background is explored using the pole-dipole approximation to the Dixon multipole expansion for matter with compact support. Motivated by application to astrophysical processes the dynamical behavior of the spin and particle motion is described by numerically solving a system of non-linear first order ordinary differential equations. Some results are displayed in a reference frame adapted to the transverse nature of a monochromatic polarised gravitational wave of arbitrary intensity. .

Simple wave solutions for the Maxwell equations in bianisotropic, nonlinear media, with application to oblique incidence

We analyze the propagation of electromagnetic waves in nonlinear, bianisotropic, nondispersive, homogeneous media using simple waves and six-vector formalism. The Maxwell equations are formulated as an eigenvalue problem, whose solutions are equivalent to the characteristic propagation directions. We solve the oblique incidence of plane waves in vacuum on a half space of nonlinear material, and present a method to calculate the reflected and transmitted fields for all angles of incidence and all polarizations of the incident field. Numerical examples for reflection and transmission illustrate the field dependence of the Brewster angle, and the birefringence of an anisotropic material.

On some colliding plane wave solutions

A one-to-one correspondence is presented which enables one to pass from colliding plane waves with parallel polarizations and electromagnetic field to nonparallel polarized colliding plane waves in vacuum and conversely. This correspondence is used to derive new solutions to Einstein’s equations in the context of colliding plane waves. This generating technique has its antecedent in the Bonnor trans- formation for stationary axisymmetric solutions.

On limits of spacetimes-a coordinate-free approach

A coordinate-free approach to limits of spacetimes is developed. The limits of the Schwarzschild metric as the mass parameter tends to 0 or infinity are studied, extending previous results. Besides the known Petrov-type-D and type-O limits, three vacuum plane-wave solutions of Petrov type N are found to be limits of the Schwarzschild spacetime.