Anomalous pulse delay in microwave propagation: A plausible connection to the tunneling time

Group delay of evanescent signals in a waveguide with barrier

The time history of subsequent tunneled wave packets can represent a more meaningful way to describe signal evolutions and to determine the group delay than the detection of a demodulated monopulse envelope. In the present experimental research, the delay of transmitted tunneled packets was found to be shorter than that measurable in vacuum, in good agreement with the phase time and Esposito's equation and independent of the barrier length. The wave packets did not show narrowing and "reshaping," so these phenomena did not appear to be the reason of the short delay experienced. The latter was not found to be proportional to the amplitude of the incident signal.

Polarization-dependent tunneling of light in gradient optics

Reflection-refraction properties of photonic barriers, formed by dielectric gradient nanofilms, for inclined incidence of both S - and P -polarized electromagnetic waves are examined by means of exactly solvable models. We present generalized Fresnel formulas, describing the influence of the nonlocal dispersion on the reflectance and transmittance of single- and double-layer gradient photonic barriers for S and P waves and arbitrary angles of incidence. The nonlocal dispersion of such layers, arising due to a concave spatial profile of dielectric susceptibility across the plane film, is shown to result in a peculiar heterogeneity-induced optical anisotropy, providing the propagation of S (P) waves in tunneling (traveling) regimes. The results obtained indicate the possibility of narrow-band nonattenuated tunneling (complete transmittance) of oblique S waves through such heterogeneous barriers, and the existence of spectral areas characterized by the strong reflection of P waves and profound contrast between transmitted S and P waves. The scalability of obtained exact analytical solutions of Maxwell equations into the different spectral ranges is discussed and the application potential of these phenomena for miniaturized polarizers and filters is demonstrated.

Reflectionless tunneling of light in gradient optics

We analyze the optical (or microwave) tunneling properties of electromagnetic waves passing through thin films presenting a specific index profile that provides a cutoff frequency when the films are used below this frequency. We show that, contrary to the usual case of a square index profile, where tunneling is accompanied by a strong attenuation of the wave due to reflection, such films present the possibility of reflectionless tunneling, where the incoming intensity is totally transmitted.

Negative group velocity and group delay in left-handed media

The dynamics of wave propagation in media with negative index of refraction is analyzed through analytical calculations, simulations, and experiments. Using a free space setup, the transmission characteristics of two split ring resonator and strip wire left-handed media (LHM), designed for operation at K -band frequencies (18-26 GHz), are measured. The first LHM, which is 3 unit cells long in the propagation direction, exhibits a maximum negative group delay of -0.9 ns . The second LHM (4 unit cells long) exhibits a maximum negative group delay of -1.2 ns . For both LHM the bandwidth of the negative group delay (and hence the negative group velocity) region was approximately 250 MHz.

Unexpected behavior of crossing microwave beams

An anomalous effect in the near field of crossed microwave beams, consisting in an unexpected transfer of modulation from one beam to the other, cannot be fully interpreted, at least not in a simple way, in terms of the usual electromagnetic or related framework. It is hypothesized that a local breaking of the Lorentz invariance, already invoked for an alternative interpretation of superluminal behaviors in these kinds of systems, could provide a partial explanation of the present results, although other interpretations cannot be completely ruled out.

Anomalous delay in wave propagation and tunneling: a transition-elements analysis of the traversal time

An alternative model for near-field propagation and optical tunneling is proposed following the lines of the path-integral method developed by Feynman, and in particular by using a transition-elements analysis. Such a model was able to account for the frequency dependency of delay-time results of an experiment involving microwave propagation in the near field using two horn antennas [A. Ranfagni et al., Phys. Rev. E 66, 036111 (2002)]. Furthermore, this approach is also capable of interpreting delay-time results as a function of the barrier width in a frustrated total internal reflection experiment performed at the microwave scale and in the optical region.

Anomalous pulse delay in microwave propagation: A stochastic process interpretation

An experiment involving microwave propagation in the near-field region with two horn antennas demonstrated a superluminal behavior which is strongly dependent on the frequency. The models previously proposed are found to be inadequate for interpreting the results. An attempt is made within the framework of a stochastic model, which can be improved by a path-integral analysis.

Measurement of superluminal optical tunneling times in double-barrier photonic band gaps

Tunneling of optical pulses at 1.5 microm wavelength through double-barrier periodic fiber Bragg gratings is experimentally investigated in this paper. Tunneling time measurements as a function of the barrier distance show that, far from resonances of the structure, the transit time is paradoxically short--implying superluminal propagation--and almost independent of the barrier distance. This result is in agreement with theoretical predictions based on phase-time analysis and provides, in the optical context, an experimental evidence of the analogous phenomenon in quantum mechanics of nonresonant superluminal tunneling of particles across two successive potential barriers.

On the apparent superluminality of evanescent waves

There have been many recent theoretical and experimental reports on the propagation of light pulses at speeds exceeding the speed of light in vacuum $c$ within media with anomalous dispersion, either opaque or with gain. Superluminal propagation has also been reported within vacuum, in the case of inhomogeneous pulses. In this paper we show that the observations of superluminal and non-causal propagation of evanescent pulses under the conditions of frustrated internal reflection are only apparent, and that they can be simply explained employing an explicitly (sub)luminal causal theory. However, the usual one-dimensional approach to the analysis of pulse propagation has to be abandoned and the spatial extent of the incoming pulse along the directions normal to the propagation direction has to be accounted for to correctly interpret the propagation speed of these evanescent waves. We illustrate our theory with animations of the time development of a pulse built upon the Huygen's construction.

Propagation speed of evanescent modes

The group velocity of evanescent waves (in undersized waveguides, for instance) was theoretically predicted, and has been experimentally verified, to be superluminal (v(g)>c). By contrast, it is known that the precursor speed in vacuum cannot be larger than c. In this paper, by computer simulations based on Maxwell equations only, we show the existence of both phenomena. In other words, we verify the actual possibility of superluminal group velocities, without violating the so-called (naive) Einstein causality.

Time-domain detection of superluminal group velocity for single microwave pulses

Single microwave pulses centered at 9.68 GHz with 100-MHz (full width at half maximum) bandwidth are used to evanescently tunnel through a one-dimensional photonic crystal. In a direct time-domain measurement, it is observed that the peak of the tunneling wave packets arrives (440+/-20) ps earlier than the companion free space (air) wave packets. Despite this superluminal behavior, Einstein causality is not violated since the earliest parts of the signal, also known as the Sommerfeld forerunner, remain exactly luminal. The frequency of oscillations and the functional form of the Sommerfeld forerunner for any causal medium are derived.

Observation of superluminal behaviors in wave propagation

The possibility of observing superluminal behavior in the propagation of localized microwaves over distances of tens of wavelengths is experimentally demonstrated. These types of waves, better than the evanescent modes of tunneling, can contribute to answering the question on the luminal limit of the signal velocity.

Reshaping of femtosecond pulses by the Gouy phase shift

It is shown that because of the phase anomaly a femtosecond pulse propagates on the optical axis with a velocity greater than c in the vicinity of the focus not only for large but also small values of the Fresnel number. The group velocity is calculated and its physical meaning discussed. Analytical expressions are derived for the electric field. The causality of the system is proved. The mechanism of the superluminality is a reshaping process caused by the interference. Contrary to other superluminal phenomena, the superluminal propagation occurs in a classically not forbidden region.