Superluminal Localized Solutions to Maxwell Equations propagating along a waveguide: The finite-energy case

In a previous paper of ours [Phys. Rev. E64 (2001) 066603, e-print physics/0001039] we have shown localized (non-evanescent) solutions to Maxwell equations to exist, which propagate without distortion with Superluminal speed along normal-sized waveguides, and consist in trains of "X-shaped" beams. Those solutions possessed therefore infinite energy. In this note we show how to obtain, by contrast, finite-energy solutions, with the same localization and Superluminality properties. [PACS nos.: 41.20.Jb; 03.50.De; 03.30.+p; 84.40.Az; 42.82.Et. Keywords: Wave-guides; Localized solutions to Maxwell equations; Superluminal waves; Bessel beams; Limited-dispersion beams; Finite-energy waves; Electromagnetic wavelets; X-shaped waves; Evanescent waves; Electromagnetism; Microwaves; Optics; Special relativity; Localized acoustic waves; Seismic waves; Mechanical waves; Elastic waves; Guided gravitational waves.]Comment: plain LaTeX file (12 pages), plus 10 figure

Amplification of evanescent waves in a lossy left-handed material slab

We carry out finite-difference time-domain (FDTD) simulations, with a specially-designed boundary condition, on pure evanescent waves interacting with a lossy left-handed material (LHM) slab. Our results provide the first full-wave numerical evidence for the amplification of evanescent waves inside a LHM slab of finite absorption. The amplification is due to the interactions between the evanescent waves and the coupled surface polaritons at the two surfaces of the LHM slab and the physical process can be described by a simple model.Comment: 4 pages, 2 figure

Plane waves with negative phase velocity in Faraday chiral mediums

The propagation of plane waves in a Faraday chiral medium is investigated. Conditions for the phase velocity to be directed opposite to the direction of power flow are derived for propagation in an arbitrary direction; simplified conditions which apply to propagation parallel to the distinguished axis are also established. These negative phase-velocity conditions are explored numerically using a representative Faraday chiral medium, arising from the homogenization of an isotropic chiral medium and a magnetically biased ferrite. It is demonstrated that the phase velocity may be directed opposite to power flow, provided that the gyrotropic parameter of the ferrite component medium is sufficiently large compared with the corresponding nongyrotropic permeability parameters.Comment: accepted for publication in Phys. Rev.

Solitary wave solution to the generalized nonlinear Schrodinger equation for dispersive permittivity and permeability

We present a solitary wave solution of the generalized nonlinear Schrodinger equation for dispersive permittivity and permeability using a scaling transformation and coupled amplitude-phase formulation. We have considered the third-order dispersion effect (TOD) into our model and show that soliton shift may be suppressed in a negative index material by a judicious choice of the TOD and self-steepening parameter.Comment: 6 page

Resonant and anti-resonant frequency dependence of the effective parameters of metamaterials

We present a numerical study of the electromagnetic response of the metamaterial elements that are usedto construct materials with negative refractive index. For an array of split ring resonators (SRR) we find that the resonant behavior of the effective magnetic permeability is accompanied by an anti-resonant behavior of the effective permittivity. In addition, the imaginary parts of the effective permittivity and permeability are opposite in sign. We also observe an identical resonant versus anti-resonant frequency dependence of the effective materials parameters for a periodic array of thin metallic wires with cuts placed periodically along the length of the wire, with roles of the permittivity and permeability reversed from the SRR case. We show in a simple manner that the finite unit cell size is responsible for the anti-resonant behavior

Plasma Wave Properties of the Schwarzschild Magnetosphere in a Veselago Medium

We re-formulate the 3+1 GRMHD equations for the Schwarzschild black hole in a Veselago medium. Linear perturbation in rotating (non-magnetized and magnetized) plasma is introduced and their Fourier analysis is considered. We discuss wave properties with the help of wave vector, refractive index and change in refractive index in the form of graphs. It is concluded that some waves move away from the event horizon in this unusual medium. We conclude that for the rotating non-magnetized plasma, our results confirm the presence of Veselago medium while the rotating magnetized plasma does not provide any evidence for this medium.Comment: 20 pages, 15 figures, accepted for publication in Astrophys. Space Sc

X-wave mediated instability of plane waves in Kerr media

Plane waves in Kerr media spontaneously generate paraxial X-waves (i.e. non-dispersive and non-diffractive pulsed beams) that get amplified along propagation. This effect can be considered a form of conical emission (i.e. spatio-temporal modulational instability), and can be used as a key for the interpretation of the out of axis energy emission in the splitting process of focused pulses in normally dispersive materials. A new class of spatio-temporal localized wave patterns is identified. X-waves instability, and nonlinear X-waves, are also expected in periodical Bose condensed gases.Comment: 4 pages, 6 figure

Crustal constraint through complete model space screening for diverse geophysical datasets facilitated by emulation

Deep crustal constraint is often carried out using deterministic inverse methods, sometimes using seismic refraction, gravity and electromagnetic datasets in a complementary or “joint” scheme. With increasingly powerful parallel computer systems it is now possible to apply joint inversion schemes to derive an optimum model from diverse input data. These methods are highly effective where the uncertainty in the system is small. However, given the complex nature of these schemes it is often difficult to discern the uniqueness of the output model given the noise in the data, and the application of necessary regularization and weighting in the inversion process means that the extent of user prejudice pertaining to the final result may be unclear. We can rigorously address the subject of uncertainty using standard statistical tools but these methods also become less feasible if the prior model space is large or the forward simulations are computationally expensive. We present a simple Monte Carlo scheme to screen model space in a fully joint fashion, in which we replace the forward simulation with a fast and uncertainty-calibrated mathematical function, or emulator. This emulator is used as a proxy to run the very large number of models necessary to fully explore the plausible model space. We develop the method using a simple synthetic dataset then demonstrate its use on a joint data set comprising first-arrival seismic refraction, MT and scalar gravity data over a diapiric salt body. This study demonstrates both the value of a forward Monte Carlo approach (as distinct from a search-based or conventional inverse approach) in incorporating all kinds of uncertainty in the modelling process, exploring the entire model space, and shows the potential value of applying emulator technology throughout geophysics. Though the target here is relatively shallow, the methodology can be readily extended to address the whole crust

Isothermal Plasma Wave Properties of the Schwarzschild de-Sitter Black Hole in a Veselago Medium

In this paper, we study wave properties of isothermal plasma for the Schwarzschild de-Sitter black hole in a Veselago medium. We use ADM 3+1 formalism to formulate general relativistic magnetohydrodynamical (GRMHD) equations for the Schwarzschild de-Sitter spacetime in Rindler coordinates. Further, Fourier analysis of the linearly perturbed GRMHD equations for the rotating (non-magnetized and magnetized) background is taken whose determinant leads to a dispersion relation. We investigate wave properties by using graphical representation of the wave vector, the refractive index, change in refractive index, phase and group velocities. Also, the modes of wave dispersion are explored. The results indicate the existence of the Veselago medium.Comment: 24 pages, 12 figures, accepted for publication in Astrophys. Space Sci. arXiv admin note: text overlap with arXiv:1101.0884 and arxiv:1007.285