We report on the experimental observation of superluminal reflection of picosecond optical pulses at 1.5 microm using a specially designed 30-cm-long fiber Bragg grating (FBG) that realizes a spectral reflectivity profile given by the superposition of two closely spaced Lorentzian lines. Probing pulses of 380 ps duration tuned midway between the two Lorentzian lines are reflected without appreciable distortion with a measured peak pulse advancement of approximately 60 ps. The achievement of the negative group delay is due to the interference of the two resonance modes of the FBG structure and has a close connection to the phenomenon of negative group velocity for pulse propagation in an inverted medium possessing a doublet line.
We report on the experimental observation of superluminal reflection of picosecond optical pulses at 1.5 microm using a specially designed 30-cm-long fiber Bragg grating (FBG) that realizes a spectral reflectivity profile given by the superposition of two closely spaced Lorentzian lines. Probing pulses of 380 ps duration tuned midway between the two Lorentzian lines are reflected without appreciable distortion with a measured peak pulse advancement of approximately 60 ps. The achievement of the negative group delay is due to the interference of the two resonance modes of the FBG structure and has a close connection to the phenomenon of negative group velocity for pulse propagation in an inverted medium possessing a doublet line.
Optical pulse propagation in photonic grating structures can show anomalous (i.e., superluminal or negative) group velocities under certain circumstances owing to the anomalous dispersive properties induced by the periodic grating structure. Such phenomena can be observed for either linear pulse propagation in passive dielectric grating structures, such as in fiber Bragg gratings (FBGs), as well as in frequency-conversion processes exploiting second-order cascading effects in quasi-phase-matched (QPM) nonlinear crystals. Engineering of the grating structure can be exploited to observe a wide variety of anomalous pulse transmission and reflection behaviors. In this article, we review the main recent experimental and theoretical achievements obtained by our group in this field. In particular, we report on superluminal propagation of picosecond optical pulses at the 1.5-μm wavelength of optical communications in FBGs, both in transmission and reflection configurations, with the observation of group velocities as large as ∼5c/sub 0/. We also show that the phenomenon of transparent pulse propagation at a negative group velocity in a gain doublet atomic amplifier, recently observed in cesium vapor by Wang and co-workers (L. J. Wang, A. Kuzmich, and A. Dogariu, Nature vol.406, p.277-9, 2000), can be achieved as well in a photonic parametric amplifier by exploiting the anomalous dispersive properties of the amplifier induced by a suitably designed QPM grating profile.
The existence of anomalous, i.e. superluminal or negative, group velocities [1] provides one of the most amazing phenomenon of wave propagation which is compatible with, and even a consequence of, causality [2]. Anomalous wave propagation generally relies on the resonant interaction of light with an atomic medium, i.e. it exploits the dispersive properties of absorptive [3] or inverted [4,5] atomic media near resonances. Evanescent wave propagation across photonic barriers [1] provides the other wide framework where anomalous group velocities have been observed, however in such cases the achievement of a negative group velocity seems unlikely. By exploiting the dispersive properties of a gain doublet, a narrow spectral region of transparent anomalous dispersion around the dip center of two Lorentzian gain lines, leading to negative transit times and no pulse attenuation, can be created [4]. A recent demonstration thereof has been indeed reported in an experiment by Wang and coworkers using Cs vapor [5].
The propagation of a pulse through one-dimensional photonic crystals that contain a dispersive and absorptive defect layer doped with two-level atoms is discussed. The dynamical evolution of the pulse inside the photonic crystal is presented. Superluminal negative group velocity (the peak appears at the exit end before it reaches the input end) is discovered. Although the group velocity is larger than c and even negative, the velocity of energy propagation never exceeds the vacuum light speed. The appearance of the superluminal advance or subluminal delay of the pulse peak inside the photonic crystal or at the exit end is due to the wave interference from Bragg reflections.
In the region between two lines of a doublet of an inverted medium, there exists a point of zero group-velocity dispersion, where highly superluminal effects may be observable without significant gain, loss, distortion, or broadening. The results of this group-velocity analysis hold for sufficiently narrow-band, analytic pulses, and do not constitute a violation of causality, although the group, ``signal,'' and energy velocities as defined by Sommerfeld and Brillouin may all exceed c or even become negative. No sharp disturbance in the pulse (a real signal) could propagate faster than light, but the scheme offers an unusual noiseless amplification scheme for the leading edge of a pulse, both at the classical and at the single-photon level.
For a pulse with carrier frequency detuned less than an atomic plasma frequency but outside a narrow Lorentzian gain line, the group velocity will be negative. Unlike propagation at the center of an absorption line, the energy velocity is approximately equal to the group velocity, and is also negative. We show that a classical Gaussian pulse with such a carrier frequency will propagate at the negative group velocity for many atomic plasma wavelengths, before dispersion deforms the pulse shape. The peak of the transmitted pulse leaves the gain medium before the peak of the incident pulse enters, i.e., the pulse is transmitted superluminally. For a sufficiently long medium the exit pulse is well resolved from a comparison pulse traveling through an equal distance of vacuum. There is no conflict with causality, as numerical simulations with a switched-on Gaussian demonstrate. We propose an experiment to observe this kind of propagation by sending a pulsed probe beam through a Xe gas cell pumped to achieve inversion.
Anomalous dispersion cannot occur in a transparent passive medium where electromagnetic radiation is being absorbed at all frequencies, as pointed out by Landau and Lifshitz. Here we show, both theoretically and experimentally, that transparent linear anomalous dispersion can occur when a gain doublet is present. Therefore, a superluminal light-pulse propagation can be observed even at a negative 7group velocity through a transparent medium with almost no pulse distortion. Consequently, a negative transit time is experimentally observed resulting in the peak of the incident light pulse to exit the medium even before entering it. This counterintuitive effect is a direct result of the rephasing process owing to the wave nature of light and is not at odds with either causality or Einstein's theory of special relativity.