Superluminal Phase Velocity Research Articles

Laser-plasma acceleration beyond wave breaking

Laser wakefield accelerators rely on the extremely high electric fields of nonlinear plasma waves to trap and accelerate electrons to relativistic energies over short distances. When driven strongly enough, plasma waves break, trapping a large population of the background electrons that support their motion. Aside from limiting the maximum electric field, this trapping can lead to accelerated electron bunches with large energy spreads. Here, we introduce a novel regime of plasma wave excitation and wakefield acceleration that allows for arbitrarily high electric fields while avoiding the deleterious effects of unwanted trapping. The regime, enabled by spatiotemporal shaping of laser pulses, exploits the property that nonlinear plasma waves with superluminal phase velocities cannot trap charged particles and are therefore immune to wave breaking.

Superluminal phase velocity approach for suppression of Numerical Cherenkov Instability in Maxwell solver

A modification of a standard finite-difference time-domain (FDTD) Maxwell solver is proposed based on the inclusion of the terms of the higher order in the finite differences approximation. By selecting the coefficients of this hybrid scheme the numeric dispersion of the electromagnetic waves can be fine-tuned. It is shown that a particular choice of the coefficients leads to the phase velocity of all the waves being slightly larger than speed of light. Results of the 3D Particles-In-Cells (PIC) simulations demonstrate that the proposed scheme of the Maxwell solver is efficient to mitigate the Numerical Cherenkov Instability (NCI) when simulating ultrarelativistic charged beams.

Stochastic electron heating in the laser and quasi-static electric and magnetic fields

The dynamics of relativistic electrons in the intense laser radiation and quasi-static electromagnetic fields both along and across the laser propagating direction are studied in the 3/2 dimensional (3/2D) Hamiltonian framework. It is shown that the unperturbed oscillations of the relativistic electron in these electric fields could exhibit a long tail of the amplitude of harmonics which makes an onset of stochastic electron motion be a primary candidate for electron heating. Chirikov-like mappings which describe the recurrence relations of electron energy and time passing through zero canonical momentum plane are derived, and then, the criteria for instability are obtained. It follows that for both transverse and longitudinal electric fields, there exist upper limits of the stochastic electron energy depending on the laser intensity and electric field strength. These maximum energies could be increased by a weak electric field. However, the maximum energy is reduced for the superluminal phase velocity in both cases. The impacts of the magnetic fields on the electron dynamics are different for these two cases and discussed qualitatively. These analytic results are confirmed by the numerical simulations of solving the 3/2D Hamiltonian equations directly.

Electron dynamics in the laser and quasi-static electric and magnetic fields

3/2 dimensional Hamiltonian equations, accounting for arbitrary polarized plane wave laser radiation and arbitrary electric and magnetic fields in the directions both along and across to the direction of the laser beam propagation, are derived for superluminal phase velocity of the laser radiation. An impact of superluminal laser radiation phase velocity on the transition to stochastic electron motion is studied.

Angular and Spectral Distributions of the Broadband Radiation of a Photoemission Source

Angular dependence of the electric field of electromagnetic wave generated by a rectangular photoemission source with the given surface density of dipole moment is determined. The dipole emission is initiated by the wave that propagates along the surface at a superluminal phase velocity. The spectral distribution of the radiation is determined, and the angular distribution of the radiation energy is calculated.

Combining Newton’s second law and de Broglie’s particle-wave duality

Abstract All matter can exhibit wave-like behaviour, and Louis de Broglie first predicted light to display the dual characteristics as both a collection of particles, called photons, or in some respects as a wave. The particle velocity is the group velocity of the wave, and if the particle velocity u g is subluminal then the associated wave or phase velocity u p through the de Broglie relation u g u p = c 2 is necessarily superluminal. This is believed not to contradict the fact that information cannot be carried faster than the velocity of light c because the wave phase is supposed to carry no energy. However, the superluminal phase velocity may well be physically significant, and here we propose that the sub particle world and the super wave world might be equally important, and that each might exert an influence on the other, such that any mechanical equations must not only be Lorentz invariant but they must also be invariant under the transformation connecting the sub and super worlds. Following this approach, Einstein’s equation E = mc 2 becomes simply E = ( m + m ′ ) c 2 , where m and m ′ are masses given by Einstein expressions arising from the perceived sub and superluminal velocities u g and u p respectively. This modification, although superficially simple, results from non-conventional physics and gives rise to an extension of Newton’s second law, that might well account for the extra energy and mass that is known to exist in the universe, and referred to as dark energy and dark matter. An explicit solution for photons and light predicts a non-zero photon rest-mass m 0 = h ν / 2 c 2 , where h is Planck’s constant and ν is the light frequency. Interestingly, the associated energy of this mass is the zero-point energy, believed to be the lowest energy that a quantum mechanical system may possess.

Antireflection coating of barriers to enhance electron tunnelling: exploring the matter wave analogy of superluminal optical phase velocity

The tunnelling of electrons through barriers is important in field emission sources and in interconnects within electronic devices. Here we use the analogy between the electromagnetic wave equation and the Schrodinger equation to find potential barriers that, when added before an existing barrier, increase the transmission probability. A single pre-barrier of negative potential behaves as a dielectric “antireflection coating”, as previously reported. However, we obtain an unexpected and much greater enhancement of transmission when the pre-barrier has a positive potential of height smaller than the energy of the incident electron, an unfamiliar optical case, corresponding to media with superluminal phase velocities as in dilute free electron media and anomalous dispersion at X-ray frequencies. We use a finite difference time domain algorithm to evaluate the transmission through a triangular field emission barrier with a pre-barrier that meets the new condition. We show that the transmission is enhanced for an incident wavepacket, producing a larger field emission current than for an uncoated barrier. Examples are given of available materials to enhance transmission in practical applications. The results are significant for showing how to increase electron transmission in field emission and at interconnects between dissimilar materials in all types of electronic devices.

Net electron energy gain induced by superluminal phase velocity and subluminal group velocity of a laser in a plasma channel

We examine electron dynamics induced by laser-plasma interaction in a two-dimensional plasma channel, taking into action the laser phase velocity as well as the group velocity. The coupled effects of phase velocity, group velocity, and plasma channel on electron dynamics are discussed in detail. The superluminal phase velocity and the corresponding subluminal group velocity of the laser result in rich and complex electron dynamics, which are depicted in the plane of the phase velocity and plasma charge density. For weak superluminosity of the phase velocity, the effects of the phase velocity and the group velocity can be neglected. For moderate superluminosity of the phase velocity, a cross-over region can exist, where the highly energetic electron could be found and the net energy gain is several times greater than the energy gain in vacuum. For strong superluminosity of the phase velocity, the dephasing rate increases and thus limits the electron energy gain from the laser. However, the asymmetric laser pulse, attributed by the superluminal phase velocity and the subluminal group velocity, results in the electron getting adjustable net energy gain from the laser. The electron oscillations are no longer limited by the charge density threshold and the electron can always get net energy from the laser. These electron dynamics can also be modified by adjusting the polarization of the laser.

Controlling the superluminal

controlling the superluminal

Superluminal wave propagation in a non‐Foster negative capacitor loaded transmission line

Superluminal wave propagation phenomenon achieved from a periodic structure in which a transmission line (TL) is loaded with non-Foster negative capacitors is presented. The loading decreases the effective capacitance and the effective permittivity of the dielectric substrate of the TL. An experimental investigation of the superluminal phase and group velocity in the non-Foster loaded TL is reported. The phase and group velocities are extracted from measured S-parameters. To do so, three non-Foster negative capacitors operating over [50–350 MHz] frequency band are integrated in a TL. Superluminal broadband effects are obtained from 50 to 220 MHz. The negative capacitors loaded TL paves the way to innovative broadband leaky wave antennas, active metamaterial surfaces and cloaking devices.

Universal scalings for laser acceleration of electrons in ion channels

We analytically investigate the acceleration of electrons undergoing betatron oscillations in an ion channel, driven by a laser beam propagating with superluminal (or luminal) phase velocity. The universal scalings for the maximum attainable electron energy are found for arbitrary laser and plasma parameters by deriving a set of dimensionless equations for paraxial ultra-relativistic electron motion. One of our analytic predictions is the emergence of forbidden zones in the electrons' phase space. For an individual electron, these give rise to a threshold-type dependence of the final energy gain on the laser intensity. The universal scalings are also generalized to the resonant laser interaction with the third harmonic of betatron motion and to the case when the laser beam is circularly polarized.

Superluminal media formed by photonic crystals for transformation optics-based invisibility cloaks

We have developed an approach to building superluminal medium for transformation optics‐based devices, including invisibility cloaks, from photonic crystals. Analysis of dispersion diagrams of 2D arrays composed from dielectric rods has shown that at frequencies corresponding to the second bands formed due to bandgap opening at increase of rod permittivity, the medium formed by arrays exhibits refractive indices providing for superluminal phase velocities of propagating waves. It is further demonstrated that rod arrays with various lattice constants could be used for realizing a range of superluminal index values prescribed by transformation optics for cylindrical cloaks at arbitrary chosen operating frequency. The performed studies allowed for solving a row of problems with employment rod arrays in the cloak medium: in particular, formulating transformation optics‐based prescriptions for refractive index dispersion in the cloaking shell, defining the dimensions of array fragments capable of responding similar to infinite arrays, finding optimal distribution of linear arrays sets at their coiling to form concentric material layers in the cloaking shell, and employing interaction between neighboring array sets with various lattice constants to assist the realization of prescribed index dispersion. The performance of the superluminal medium formed by rod array sets was demonstrated on an example of a cloaking shell developed for microwave frequency range. In contrast to metamaterial-based cloak media, the developed media requires neither material homogenization, nor obtaining the effective parameters with peculiar values and Lorentz’s type resonances in rods. Combination of these advantages and low losses makes photonic crystals perspective materials for invisibility cloaks operating in THz and optical ranges.

The effect of superluminal phase velocity on electron acceleration in a powerful electromagnetic wave

In this paper, we examine the effect that electromagnetic dispersion has on the motion of an electron in a relativistically strong plane wave. We obtain an analytic solution for the electron momentum and check this solution against direct numerical integration of the equations of motion. The solution shows that even a relatively small difference between the phase velocity of the wave, vp, and the speed of light, c, can significantly alter the electron dynamics if the normalized wave amplitude a0 exceeds 2c/(vp−c). At this amplitude, the maximum longitudinal electron momentum scales only linearly with a0, as opposed to a02. We also show that at this amplitude the impact of an accelerating longitudinal electric field and electron pre-acceleration is negated by the superluminous phase velocity of the wave. This has implications for the potential of Direct Laser Acceleration of electrons. We point out that electromagnetic dispersion can arise from both propagation in a plasma and from propagating the laser in...

Against dogma: On superluminal propagation in classical electromagnetism

It is deeply entrenched dogma that relativity theory prohibits superluminal propagation. It is also experimentally well-established that under some circumstances, classical electromagnetic fields propagate through a dielectric medium with superluminal group velocities and superluminal phase velocities. But it is usually claimed that these superluminal velocities do not violate the relativistic prohibition. Here I analyze electromagnetic fields in a dielectric medium within a framework for understanding superluminal propagation recently developed by Geroch (1996, 2011) and elaborated by Earman (2014). I will argue that for some parameter values, electromagnetic fields do propagate superluminally in the Geroch–Earman sense.

Lorentz symmetry violating low energy dispersion relations from a dimension-five photon scalar mixing operator

Dimension-five photon $(\gamma )$ scalar $(\phi)$ interaction terms usually appear in the bosonic sector of unified theories of electromagnetism and gravity. In these theories the three propagation eigenstates are different from the three field eigenstates. The dispersion relation in an external magnetic field shows that, for a non- zero energy $(\omega)$, out of the three propagating eigenstates one has superluminal phase velocity $v_p$. During propagation, another eigenstate undergoes amplification or attenuation, showing signs of an unstable system. The remaining one maintains causality. In this paper, using techniques from optics as well as gravity, we identify the energy $(\omega)$ interval outside which $v_p \le c$ for the field eigenstates $|\gamma_{\parallel} > $ and $ |\phi > $, and stability of the system is restored. The behavior of group velocity $v_g$ is also explored in the same context. We conclude by pointing out its possible astrophysical implications.

PROPAGATION AND STABILITY OF SUPERLUMINAL WAVES IN PULSAR WINDS

Nonlinear electromagnetic waves with superluminal phase velocity can propagate in the winds around isolated pulsars, and around some pulsars in binary systems. Using a short-wavelength approximation, we find and analyze an integrable system of equations that govern their evolution in spherical geometry. A confined mode is identified that stagnates to finite pressure at large radius and can form a precursor to the termination shock. Using a simplified criterion, we find this mode is stable for most isolated pulsars, but may be unstable if the external pressure is high, such as in the pulsar wind nebulae in starburst galaxies and in W44. Pulsar winds in eccentric binary systems, such as PSR 1259-63, may go through phases with stable and unstable electromagnetic precursors, as well as phases in which the density is too high for these modes to propagate.

Transverse relativistic effects in paraxial wave interference

We consider relativistic deformations of interfering paraxial waves moving in the transverse direction. Owing to superluminal transverse phase velocities, noticeable deformations of the interference patterns arise when the waves move with respect to each other with non-relativistic velocities. Similar distortions also appear on a mutual tilt of the interfering waves, which causes a phase delay analogous to the relativistic time delay. We illustrate these observations by the interference between a vortex wave beam and a plane wave, which exhibits a pronounced deformation of the radial fringes into a fork-like pattern (relativistic Hall effect). Furthermore, we describe an additional relativistic motion of the interference fringes (a counter-rotation in the vortex case), which becomes noticeable at the same non-relativistic velocities.

Ultra-broadband simultaneous superluminal phase and group velocities in non-Foster epsilon-near-zero metamaterial

Experimental investigation of ultra-broadband simultaneous superluminal phase and group velocity in recently introduced epsilon-near-zero (ENZ) non-Foster metamaterial is reported. The phase and group velocities were extracted both from the measurements of scattering parameters in the frequency domain and the measurements of propagation time of broadband Gaussian pulse in time domain. Reported superluminal effects are extremely broadband (relative bandwidth of 180% (1:20)) and they are fundamentally different from widely reported narrowband experiments based on the anomalous dispersion. The phenomenon of simultaneous superluminal phase and group velocities may find applications in transformation electromagnetic devices and in communication systems.

FORMULATION OF MULTIWIRE MAGNETIC TRANSMISSION-LINE THEORY

Time- and frequency-domain theory of multiwire magnetic transmission lines is presented for the flrst time. The familiar theory of electric multiconductor transmission lines (MTL) is based on the manipulation of two matrices, the longitudinal impedance and the transverse admittance. However, for magnetic MTLs, the key matrices are the transverse impedance and the longitudinal admittance. It is shown how the latter matrices are deflned and how they should be used to determine the modal propagation constants and modal characteristic wave admittances that characterize the various travelling wave modes of magnetic MTLs. The theory is illustrated considering a three-wire system with three-fold symmetry. Simulation results, in the range 0.1GHz to 10GHz, are presented, showing that the magnetic MTL can exhibit superluminal phase velocity and zero attenuation dispersion.

Low-loss directional cloaks without superluminal velocity or magnetic response

The possibility of making an optically large (many wavelengths in diameter) object appear invisible has been a subject of many recent studies. Exact invisibility scenarios for large (relative to the wavelength) objects involve (meta)materials with superluminal phase velocity [refractive index (RI) less than unity] and/or magnetic response. We introduce a new approximation applicable to certain device geometries in the eikonal limit: piecewise-uniform scaling of the RI. This transformation preserves the ray trajectories but leads to a uniform phase delay. We show how to take advantage of phase delays to achieve a limited (directional and wavelength-dependent) form of invisibility that does not require loss-ridden (meta)materials with superluminal phase velocities.