Velocity Of Light In Vacuum Research Articles

Propagation of optical pulses in a resonantly absorbing medium: Observation of negative velocity in Rb vapor

Propagation of optical pulses in a resonantly absorbing medium is studied. Propagation time of nanosecond pulses was measured for the Rb ${D}_{1}$ transition. At the center of two absorption lines, delay of the pulse peak which is about ten times as large as the pulse width was observed, where zero delay is defined for the propagation with the light velocity in vacuum. On the other hand, at the peak of an absorption line, negative delay was observed for large absorption, where the advance time is as large as 25% of the pulse width. Simulation including the effect of absorption and phase shift reproduced well the experimental results.

On the velocity of propagation of a signal in nonlinear optical media

The maximum velocity of propagation of a signal, which is defined as the velocity of propagation of the wave front, is considered for electromagnetic waves in nonlinear media. It is shown that the magnitude of velocity is determined to a considerable extent on the form of the constitutive equation defining the relation between the polarization of the medium with the radiation field strength. In the noninertial nonlinearity model, this velocity may be smaller (in media with self-focusing nonlinearity) or larger (defocusing nonlinearity) than the velocity of light in vacuum. For real nonlinear media, for which the inertia of their response is taken into account, the wave front velocity coincides with the velocity of light in vacuum.

Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams

It is well known that very high axial – or longitudinal – electric fields can be obtained in vacuo using very intense focused laser beams. If these fields are in the transverse magnetic TM01 mode, very high gains in energy (exceeding 1 GeV) can be obtained if sufficiently energetic ultra-relativistic electrons (say 1 GeV) are injected on-axis and near the optimum phase. This energy gain is obtained even though the phase velocity of the axial component of the TM01 laser beam is greater than the vacuum velocity of light. The result is apparently related to the Gouy phase shift at focus.

Observation of small group velocity in two-dimensional AlGaAs-based photonic crystal slabs

The characteristics of the small group velocity ${\ensuremath{\nu}}_{g}$ were experimentally studied with special concern to a flat band in AlGaAs-based two-dimensional photonic crystal slabs by using a time-of-flight method of a 200 fs light pulse. Two kinds of triangular air-rod samples, i.e., a deeply perforated waveguide and a perforated membrane suspended in air were used. For the former with the numbers of rod's row N of 10, ${\ensuremath{\nu}}_{g}$ was found to vary from $0.17\ifmmode\times\else\texttimes\fi{}c$ at a wavelength far from the band edge to $0.03\ifmmode\times\else\texttimes\fi{}c$ at the edge; c is the light velocity in vacuum. For the latter with N of 26, ${\ensuremath{\nu}}_{g}$ was observed to be in a range of $(0.05--0.07)\ifmmode\times\else\texttimes\fi{}c.$ The significance of the result is discussed.

Stimulated Brillouin scattering of a short pulse laser in a self-induced plasma channel

An intense short pulse laser with Gaussian radial profile of intensity propagating through homogeneous plasma depletes electrons from the axial region due to the radial ponderomotive force, leaving ions immobile. The resulting electron density profile and relativistic mass nonlinearity aid the laser to propagate self-guided, overcoming diffraction divergence with minimum spot size, few times of c/ωp, where c is the velocity of light in vacuum and ωp is the plasma frequency at equilibrium. The laser undergoes stimulated Brillouin backscattering in the self-induced plasma channel. As the ratio of the oscillatory electron velocity to the velocity of light, |v0|/c exceeds 0.1, the ion acoustic wave goes over to a reactive quasimode with large growth rate, comparable to ion plasma frequency. The nonlocal effects due to high intensity laser play a major role in the growth rate of the ion acoustic reactive quasimode. In a plasma of 5 KeV electron temperature, the largest value of the growth rate occurs at a plasma density n00≅0.6ncr, where ncr is the critical density.

On the propagation velocity of a wave packet in an amplifying medium

It is shown that the delay time of a weak signal propagating in an amplifying medium on the wings of the spectral amplification line may be shorter than the time of propagation of the signal with the velocity of light in vacuum. It is found that in this case, the time dependence of the signal is exactly 'reconstructed' at the point of detection, and the detection of the signal continues even if it is abruptly terminated at the point of transmission. It is also shown that using the complex time of group delay of the signal, it is possible to improve the accuracy of the results in the first order of dispersion theory within this approximation.

On the photon vector potential

A method of calculating the expression for the single-photon classic vector potential is proposed. The calculation is performed within the model framework of a non-relativistic one-dimensional harmonic oscillator interacting with a quantized electromagnetic field and with the field of a single external photon. The calculated vector potential of the single photon, i.e. the single-photon wave packet, complies with d'Alembert's equation to the accuracy of the calculations performed in the paper. In a system of coordinates that moves together with the photon with the velocity of light in vacuum, the expression for that wave packet is independent of time. The integral of the energy density calculated with the help of the single-photon vector potential as taken over the volume throughout the space is equal to the photon energy quantum, i.e. the integral is finite and does not depend on time.

Superluminal interactions in near-field optics.

The fact that photons emitted from an electric-dipole active atom cannot be spatially localized better than to the near-field zone of the atom is seen as the origin of genuine superluminality. By means of a simple model dipole current density the general theory is used to demonstrate numerically how superluminality enters the near-field dynamics, and how from a measurement one could be tempted to believe that superluminal propagation effects occur. Furthermore, it is shown how for source-detector distances larger than a pulse length one should be able to divide the pulse into two separate parts: one purely superluminal part arising solely in the non-local generation process of the field, and another part seemingly propagating with superluminal speed. We comment on different velocity analyses, and we argue that the only fundamental velocity entering the problem is the vacuum velocity of light, which in a measurement would appear as the velocity of the trailing edge of the pulse.

Extremely short and quasi-monochromatic electromagnetic solitons in a two-component medium

The propagation of extremely short (without high-frequency filling) pulses and nonresonant envelope solitons in a two-component medium comprising two-level atoms with substantially different quantum transition frequencies was studied. The dynamics of a pulse whose reciprocal time scale lay between these frequencies was shown to be described by the Kosevich-Kovalev equation, the one-way variant of which was the Konno-Kameyama-Sanuki equation. If the transition dipole moments of medium components were equal, the one-way equation became integrable. Soliton and soliton-like solutions to these equations were used to analyze pulse propagation regimes at various two-component medium initial states. The stability of these localized wave formations was analyzed. The possible existence of stable soliton-like pulses propagating in a nonequilibrium medium at group velocities exceeding the velocity of light in vacuum was discussed.

PERFECT FLUID COSMOLOGIES WITH VARYING LIGHT SPEED

We have found exact constant solutions for the cosmological density parameter using a generalization of general relativity that incorporates a cosmic time-variation of the velocity of light in vacuum and the Newtonian gravitation constant. We have determined the conditions when these solutions are attractors for an expanding universe and solved the problems of the Standard Big Bang model for perfect fluids.

What if there are superluminal signals?

Recent experiments with microwaves indicate the existence of signals travelling faster than the vacuum velocity of light. At first glance these signals lead to paradoxical situations which seem to be in conflict with special relativity. We show that the arguments which lead to this contradiction presuppose that superluminal signals are not generally available and that the space-time geometry must be established by means of light rays. Hence we argue that superluminal signals will not necessarily invalidate special relativity.

Evanescent modes are not necessarily Einstein causal

Previously, experiments with microwave signals have shown that evanescent modes can travel faster than light. Several theoretical investigations have proven that in the case of signals with unlimitedly high frequency components, such superluminal velocities do not violate Einstein causality, thus group, signal, and energy velocities are \(\)c where c is the vacuum velocity of light. In this letter I shall show that frequency band limitation is a fundamental property of signals and that such signals containing only evanescent modes can violate Einstein causality.

Cosmologies with varying light speed

We analyze a generalization of general relativity that incorporates a cosmic time variation of the velocity of light in vacuum, $c,$ and the Newtonian gravitation ``constant'' $G$ proposed by Albrecht and Magueijo. We find exact solutions for Friedmann universes and determine the rate of variation of $c$ required to solve the flatness and classical cosmological constant problems. Potential problems with this approach to the resolution of the flatness and classical cosmological constant problems are highlighted. Reformulations are suggested which give the theory a more desirable limit as a theory of varying $G$ in the limit of constant $c$ and its relationship to theories with varying electron charge and constant $c$ are discussed.

On the possible influence of global cosmic rotations on the setting up of a space-time grid in vicinity of the earth

As Landau and Lifshitz have shown, for a rotating observer anisotropy of light velocity in vacuum, with peak-to-peak equal to doubled linear velocity of rotation, should take place. In experiments performed so far, this anisotropy due to our secular and annual rotations has not manifested itself clearly. Here the reasons of that are discussed, and some experimental refinements are proposed. The corresponding measurable effects are comparable with the accuracy achieved in techniques setting up a space-time global grid in vicinity of the Earth.

Theory of randomly inhomogeneous waveguides with slight material dispersion: II. Parabolic graded-index fibres

This paper, following directly from Part I, continues to demonstrate the use of the paraxial approximation in solving the time-dependent wave equation for the propagation of signals in slightly dispersive optical materials with some Gaussian randomness of the permittivity. With the same emphasis as in Part I, a path-integral formulation is employed. Attention is focused on a parabolic graded-index fibre with ⟨1/nk 0( r )⟩=(1+αr 2 ⊥/2)/n¯k 0, α>0. Arising from the possibility of replacing the autocorrelation function of the permittivity by a quadratic function, some final concise expressions are derived. It is shown that if a signal begins propagating with a Gaussian power density ⟨|u( r , 0)|2⟩, the Gaussianity of the function ⟨|u( r , t)|2⟩ is maintained at all later times t. The longitudinal shape of the function ⟨|u( r , t)|2⟩ exhibits attenuation and broadening dependent on the dispersiveness of the optical medium under consideration. The perpendicular shape of the function ⟨|u( r , t)|2⟩ oscillates with the angular frequency Ω⊥=[cvx (k 0α/n¯ k 0 ]1/2 where c and vx (k 0) are, respectively, the velocity of light in vacuum and the axial group velocity of light corresponding to kx =k 0. Special attention is devoted to the limiting case when α→0, i.e. to propagation in a bulk dispersive optical medium.

Plasma-aided radiation guiding in a free-electron laser

The introduction of a plasma in a free-electron laser (FEL) helps radiation guiding via nonlinear refraction. At high-radiation power density, when oscillatory electron velocity is comparable to the electron thermal velocity, the radiation pushes plasma radially out, forming a depleted plasma duct and guiding the radiation. The radius of the self-trapped laser is /spl sim/c//spl omega//sub po/, where /spl omega//sub po/ is the unperturbed plasma frequency and c is the velocity of light in vacuum.

Integrated optical chemical and direct biochemical sensors

Abstract An overview is given on work by the author's group on integrated optical (IO) sensors. The sensors make use of guided waves or modes in optical waveguides, in particular of the orthogonally polarized TE 0 and TM 0 modes in very thin planar waveguides of high refractive index. The principle of all direct (bio)chemical waveguide or IO sensors is as follows. A chemically selective coating on the waveguide surface binds the analyte molecules contained in the gaseous or liquid sample. Thus, the refractive index of the medium near the waveguide surface (more precisely, within the penetration depth Δz of the evanescent field of the guided wave) is changed. This effect in turn induces changes ΔN TE 0 and ΔN TM 0 of the effective refractive indices N TE 0 and N TM 0 of the guided modes. for example, in biochemical affinity sensors the chemically selective coating contains receptor molecules that specifically or selectively bind certain ligands as analyte molecules; in particular, in immunosensors or immunoassays the receptors are antibodies (or antigens, respectively) and the analyte molecules are the corresponding antigens (or antibodies). These ‘direct’ affinity of immunosensors eliminate the use of (e.g., fluorescently) labelled reagents. Effective refractive-index changes ΔN can also be induced by two other effects; namely by unspecific adsorption of molecules on the (uncoated) waveguide surface (or in pores of a waveguiding film F itself if it is microporous) and by refractive-index changes Δn C of the liquid sample. In the latter case the IO sensors work as refractometers. The effective refractive indices N give the phase velocity ν ph = c / N of the guided modes, where c is the velocity of light in vacuum. This means that the effective refractive-index changes ΔN can be measured by various optical means. Consequently, a number of different types of IO sensors can be used, in particular, grating couplers and interferometers. In the paper, I report on our own work on IO sensors including: the discovery of the basic sensor effect with grating couplers as sensors for relative-humidity changes, the theory of the sensor sensitivities, and experimental results obtained with three different types of IO sensors developed in our laboratory, namely input grating couplers, output grating couplers and the difference or polarimetric interferometer. The experiments have been performed with dip-coated SiO 2 TiO 2 waveguiding films of refractive index n F ≈ 1.75–1.88, on glass, silica and silicon wafers with oxidized buffer layers as substrates. The sensors working as refractometers are tested, for example, with glucose solutions of different concentrations. The adsorption of proteins (h-IgG, BSA, protein A, avidin) is monitored in real time. Not only the surface concentration Γ, with a resolution of a few pg mm −2 , but also the thickness d F′ and the refractive index n F′ of the adsorbing (mono)layers are determined as functions of time. Also immunoreactions (e.g., between h-IgG and anti-h-IgG, and between IgGs and protein A) and affinity reactions (between avidin and biotinylated proteins, such as biotin BSA) are observed in real time. The feasibility of IO immunosensors or affinity sensors or immunoassays with sub-nanomolar detection limits is demonstrated.

Time-dependent X-ray Bragg diffraction

The theory of time-dependent X-ray Bragg diffraction by crystals is developed on the basis of the Green-function (point-source) formalism. A general case of incident radiation partially coherent in time and space is considered. The time-delay effect of the diffracted radiation is described when the ultrashort time duration incident pulse strikes the crystal surface. The problem in question is closely connected with the effect of time delay in the resonance scattering of synchrotron radiation by nuclei in a crystal. It is found that, for the case where the incident wave is plane (or is an incoherent superposition of plane waves) and the time-dependent pulse is a pseudo δ function in time, the instantaneous crystal reflectivity is a smooth temporal function and tends to the value corresponding to the integrated reflectivity calculated by means of the conventional dynamical–kinematical X-ray diffraction theory. If the incident X-ray pulse profile is a pseudo 6 function in both time and space, the temporal crystal response has the same functional dependence as the spatial distribution of the diffracted intensity under the condition of conventional Bragg diffraction of the X-ray beam with lateral width < toc, where the time delay to is equal to Λ/2πc and (μoC)−1 in the cases of dynamical and kinematical X-ray scattering within a crystal, respectively (Λ is the X-ray extinction length, μo is the linear absorption coefficient and c is the velocity of light in vacuum).

Electron acceleration by laser wake field

The acceleration of electrons in the longitudinal electron plasma wave (EPW) created in the wake of an ultra-intense layer pulse is examined analytically. Our analysis is one-dimensional and assumes a square-shaped pulse which propagates in a well underdense plasma with the velocity of light in vacuum. Acceleration length and accelerated electron energies are predicted as a function of the EPW phase velocity and the laser irradiance. Comparison with electron acceleration in the usual sinusoidal EPW created by a low-intensity laser pulse is done.

Electrostatic and kinetic energies in the wake wave of a short laser pulse

The electrostatic and kinetic energies available in the longitudinal electron plasma wave created in the wake of an ultraintense laser pulse are obtained analytically. The analysis is one dimensional and assumes a square-shaped pulse that propagates in a highly underdense plasma with the velocity of light in vacuum. The length scale for laser depletion is given as a function of the laser irradiance and the electron density.