Superluminal Regime Research Articles

Periodic traveling waves in the ϕ^{4} model: Instability, stability, and localized structures.

We consider the instability and stability of periodic stationary solutions to the classical ϕ^{4} equationnumerically. In the superluminal regime, the model possesses dnoidal and cnoidal waves. The former are modulationally unstable and the spectrum forms a figureeight intersecting at the origin of the spectral plane. The latter can be modulationally stable, and the spectrum near the origin in that case is represented by vertical bands along the purely imaginary axis. The instability of the cnoidal states in that case stems from elliptical bands of complex eigenvalues far from the spectral plane origin. In the subluminal regime, there exist only snoidal waves which are modulationally unstable. Considering the subharmonic perturbations, we show that the snoidal waves in the subluminal regime are spectrally unstable with respect to all subharmonic perturbations, while for the dnoidal and cnoidal waves in the superluminal regime, the transition between the spectrally stable state and the spectrally unstable state occurs through a Hamiltonian Hopf bifurcation. The dynamical evolution of the unstable states is also considered, leading to some interesting localization events on the spatio-temporal backgrounds.

Anomalous Optical Propagation and Potential Sensitivity Enhancement in a Micro-Coil Resonator Based on Microfiber

The resonance characteristics of the micro-coil resonator(MCR) with different turns and coupling conditions are presented, which show that the effective length of the MCR with small coupling coefficient at primary resonant is independent of the turns, and the resonance dips always appear in pairs corresponding to multiple critical-coupling because of the periodicity of coupling strength. However, complicated resonance is observed in an MCR with larger coupling coefficient and turns. The superluminal or subluminal propagation regime can be obtained respectively by adjusting the coupling condition, and the effect of loss on them in different coupling conditions is investigated. There is such a loss threshold in the critical-coupling and over-coupling conditions, near which the group refractive index abrupt changes between positive and negative extremum, and the threshold is increased by 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> orders of magnitude under over-coupling condition compared with critical-coupling. In view of the transmission near a resonant evolve not only with the detuning of transmission phase, but also drastically with the adjustment of coupling condition which will be modulated by the cladding refractive index and coupling length. Hence a potential sensitivity enhancement for biochemical and inertial sensing based on MCR is also investigated briefly.

Front-induced transitions control THz waves

Relativistically moving dielectric perturbations can be used to manipulate light in new and exciting ways beyond the capabilities of traditional nonlinear optics. Adiabatic interaction with the moving front modulates the wave simultaneously in both space and time, and manifests a front-induced transition in both wave vector and frequency yielding exotic effects including non-reciprocity and time-reversal. Here we introduce a technique called SLIPSTREAM, Spacetime Light-Induced Photonic STRucturEs for Advanced Manipulation, based on the creation of relativistic fronts in a semiconductor-filled planar waveguide by photoexcitation of mobile charge carriers. In this work, we demonstrate the capabilities of SLIPSTREAM for the manipulation of terahertz (THz) light pulses through relativistic front-induced transitions. In the sub-luminal front velocity regime, we generate temporally stretched THz waveforms, with a quasi-static field lasting for several picoseconds tunable with the front interaction distance. In the super-luminal regime, the carrier front outpaces the THz pulse and a time-reversal operation is performed via a front-induced intra-band transition. We anticipate our platform will be a versatile tool for future applications in the THz spectral band requiring direct and advanced control of light at the sub-cycle level.

Longitudinal electrostatic waves in isotropic thermal plasmas: Ultrarelativistic pair plasmas

The dispersion relation of longitudinal electrostatic waves in unmagnetized isotropic thermal plasmas is investigated in the collisionless limit using fully relativistic kinetic plasma theory. Specifically, an electron-positron plasma is studied in the limits of nonrelativistic and ultrarelativistic plasma temperatures. In the limit of nonrelativistic plasma temperatures, the earlier dispersion relation, based on nonrelativistic dispersion theory, is reproduced. In the limit of ultrarelativistic plasma temperatures, we analyze analytically and numerically the dispersion relation of the longitudinal electrostatic mode which occurs in the subluminal and superluminal frequency regime. We correct some earlier results in the literature on the subluminal dispersion relation.

Microwave-induced orbital angular momentum transfer

The microwave-induced orbital angular momentum (OAM) transfer from a Laguerre-Gaussian (LG) beam to a weak plane-wave is studied in a closed-loop four-level ladder-type atomic system. The analytical investigation shows that the generated fourth field is an LG beam with the same OAM of the applied LG field. Moreover, the microwave-induced subluminal generated pulse can be switched to the superluminal one only by changing the relative phase of applied fields. It is shown that the OAM transfer in subluminal regime is accompanied by a slightly absorption, however, it switches to the slightly gain in superluminal regime. The transfer of light’s OAM and control of the group velocity of the generated pulse can prepare a high-dimensional Hilbert space which has a major role in quantum communication and information processing.

Analysis of light propagation in an anomalously dispersive medium

We analyse the propagation of a probe laser pulse though a medium of atoms in the double Λ configuration with two closely spaced upper levels. The medium is irradiated with a strong coherent field and is additionally incoherently pumped. Depending on the parameters of the system the dispersion of the medium may change alternatively from normal to anomalous with absorption varying from positive to negative (gain). The incoherent optical pump was found to be the switch between the sub- and the superluminal regime. A laser field propagating through such an optical system can experience alternatively the negative or positive group velocity. The dynamics of propagation in the case of positive but larger than c group velocities is investigated in particular. In this paper we show how the description in terms of the group velocity breaks down in the superluminal regime.

Superluminal electromagnetic solitary waves in electron-positron plasmas

The propagation of an electromagnetic wave packet in an electron-positron plasma, in the form of coupled localized electromagnetic excitations, is investigated, from first principles. By means of the Poincaré section method, a special class of superluminal localized nonlinear stationary solutions, existing along a separatrix curve, are proposed as intrinsic electromagnetic modes in a relativistic electron-positron plasma. The ratio of the envelope time scale to the carrier wave time scale of these envelope solitary waves critically depends on the carrier's phase velocity. In the strongly superluminal regime, vph/c ≫ 1, the large difference between the envelope and carrier time scales enables us to carry out a multiscale perturbative analysis resulting in an analytical form of the solution envelope. The analytical prediction thus obtained is shown to be in agreement with the solution obtained via a direct numerical integration.

Demonstration of images with negative group velocities

We report the experimental demonstration of the superluminal propagation of multi-spatial-mode images via four-wave mixing in hot atomic vapor, in which all spatial sub-regions propagate with negative group velocities. We investigate the spatial mode properties and temporal reshaping of the fast light images, and show large relative pulse peak advancements of up to 64 % of the input pulse width. The degree of temporal reshaping is quantified and increases as the relative pulse peak advancement increases. When optimized for image quality or pulse advancement, negative group velocities of up to v(g)=-c/880 and v(g)=-c/2180, respectively, are demonstrated when integrating temporally over the entire image. The present results are applicable to temporal cloaking devices that require strong manipulation of the dispersion relation, where one can envision temporally cloaking various spatial regions of an image for different durations. Additionally, the modes involved in a four-wave mixing process similar to the present experiment have been shown to exhibit quantum correlations and entanglement. The results presented here provide insight into how to tailor experimental tests of the behavior of these quantum correlations and entanglement in the superluminal regime.

Light propagation in a solid doped with erbium ions: From ultraslow light to the superluminal regime

Abstract In this article we report on ultraslow or fast light propagation, exciting behavior that become achievable thanks to the Coherent Population Oscillations effect (CPO). We show that the group velocity, the speed at which light propagates, can be drastically modified and engineered using the CPO effect in a crystal doped with triply ionized erbium ions, namely: Er3+:Y2SiO5. The steep dispersion of the index of refraction caused by the CPO effect is at the origin of group velocities as low as v g = 3 m / s . By inverting the slope of the index dispersion, we can make, in the same crystal, light go faster than if it was propagating in vacuum. This particular regime is characterized by larger than c or negative group velocities. In the 3-mm-long Er3+:Y2SiO5 crystal, we have achieved a delay of − 0.2 ms corresponding to a group velocity of v g = − 15 m / s . To cite this article: E. Baldit et al., C. R. Physique 10 (2009).

Fundamental role of the retarded potential in the electrodynamics of superluminal sources: reply to comment

Neither Eq. (6.52) of Jackson [Classical Electrodynamics, 3rd ed. (Wiley, 1999)] nor Hannay's derivation of that equation in the preceding Comment [J. Opt. Soc. Am. A26, 2107 (2009)] is applicable to a source whose distribution pattern moves faster than light in vacuo with nonzero acceleration. It is assumed in Hannay's derivation that the retarded distribution of the density of any moving source will be smooth and differentiable if its rest-frame distribution is. By working out an explicit example of a rotating superluminal source with a bounded and smooth density profile, we show that this assumption is erroneous. The retarded distribution of a rotating source with a moderate superluminal speed is, in general, spread over three disjoint volumes (differing in shape from one another and from the volume occupied by the source in its rest frame) whose boundaries depend on the space-time position of the observer. Hannay overlooks the fact that the limits of integration in his expression for the retarded potential are not differentiable, as functions of the coordinates of the observer, when the distribution pattern of the source moves faster than light. These limits, which delineate the boundaries of the retarded distribution of the source, have divergent gradients at those points on the source boundary that approach the observer, along the radiation direction, with the speed of light at the retarded time. In the superluminal regime, derivatives of the integral representing the retarded potential are well defined only as generalized functions.

ABOUT FERMI ACCELERATION AT RELATIVISTIC SHOCKS AND THE SCATTERING ISSUE

Difficulties arise in the process of Fermi acceleration at relativistic shocks because they are generically in the superluminal regime and they strongly compress turbulence downstream. Under reasonable conditions usually considered for the turbulent spectrum upstream, cosmic rays do not undergo the scattering that would allow them to make several Fermi cycles. An intense short scale turbulence must be excited in order that the Fermi process can be operative. In this paper, we show the requirement for the turbulence spectrum and give a solution to this issue in the form of the generation of intense compressive waves at short scale upstream. We indicate how the magnetic turbulence compression downstream should not be an obstacle for getting a significant return probability. Thus we conclude that, despite the necessity of some further analysis, the Fermi process at relativistic shock is still promising.

Modulation-frequency-controlled change from sub- to superluminal regime in highly doped erbium fibers

We report a change from sub- to superluminal propagation upon increasing the modulation frequency of an amplitude-modulated 1,550 nm signal when propagating through highly doped erbium fibers pumped at 980 nm. We show that the interplay between the pump absorption and the pump-power broadening of the spectral hole induced by coherent population oscillations may drastically affect the fractional advancement or delay of the signal for the considered fibers.

THz generation via optical rectification with ultrashort laser pulse focused to a line

We report on efficient THz pulse generation via optical rectification with femtosecond laser pulses focused to a line by a cylindrical lens. This configuration provides phase-matched conditions in the superluminal regime. 35 pJ THz pulses have been generated with this technique in a stoichiometric LiNbO3 crystal pumped by 2 μJ femtosecond laser pulses at room temperature. An unusual superquadratic rise of the THz pulse energy with the laser pulse energy has been observed at high laser energies. This extraordinary energy dependence of the THz generation efficiency is explained by self-focusing of the laser beam in the crystal. Z-scan measurements and comparison of the THz pulse spectra created with laser pulses having different energies confirm this interpretation.

Reply to comments on "Generation of focused, nonspherically decaying pulses of electromagnetic radiation"

The criticism made by Hannay [preceding Comment, Phys. Rev. E 62, 3008 (2000)] is unfounded since the steps, familiar from the subluminal regime, that are taken in his argument are not mathematically permissible when the distribution pattern of the source is moving and has volume elements that approach the observer with the speed of light and zero acceleration along the radiation direction. In the superluminal regime, the retarded time is a multivalued function of the observation time and so the retarded potential for the radiation from a localized source cannot be represented, as Hannay assumes, by an integral over all space whose integrand entails a differentiable retarded distribution of the source density. Contrary to what is claimed by Hewish [Comment in this issue, Phys. Rev. E 62, 3007 (2000)], moreover, there is no discrepancy between conventional antenna theory and the analysis that appears in Phys. Rev. E 58, 6659 (1998). The characteristics of the new type of emission predicted by this analysis, and received from pulsars, differ from those of the radiation that is produced by known leaky waveguides because there are at present no antennas in which the emitting electric current is both volume-distributed and has the time dependence of a traveling wave with an accelerated superluminal motion.