Scientific community has well recognized that a Lorentzian medium exhibits anomalous dispersion behavior in its resonance absorption region. To satisfy the Krammers-Kronig relation, such an anomalous region has to be accompanied with significant loss, and thus, experimental observations of negative group velocity in this region generally require a gain-assisted approach. In this letter, we demonstrate that the negative group velocity can also be observed in the absence of absorption resonance. We show that the k-surface of a passive uniaxial Lorentzian medium undergoes a distortion near the plasma frequency. This process yields an anomalous dispersion bandwidth that is far away from the absorption resonance region, and enables the observation of negative group velocity at the plasma frequency band. Introducing anomalous dispersion in a well-controlled manner would greatly benefit the research of ultrafast photonics and find potential applications in optical delay lines, optical data storage and devices for quantum information processing.
Scientific community has well recognized that a Lorentzian medium exhibits anomalous dispersion behavior in its resonance absorption region. To satisfy the Krammers-Kronig relation, such an anomalous region has to be accompanied with significant loss, and thus, experimental observations of negative group velocity in this region generally require a gain-assisted approach. In this letter, we demonstrate that the negative group velocity can also be observed in the absence of absorption resonance. We show that the k-surface of a passive uniaxial Lorentzian medium undergoes a distortion near the plasma frequency. This process yields an anomalous dispersion bandwidth that is far away from the absorption resonance region, and enables the observation of negative group velocity at the plasma frequency band. Introducing anomalous dispersion in a well-controlled manner would greatly benefit the research of ultrafast photonics and find potential applications in optical delay lines, optical data storage and devices for quantum information processing.
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].
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.
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.
Two theorems on the group velocity are presented in this paper. First a simple proof is given that for any dispersive dielectric, there must be a frequency at which the group velocity of an electromagnetic pulse becomes abnormal, i.e., greater than the vacuum speed of light, infinite, or negative. Second, at the frequency at which the attenuation (or gain) is a maximum, the group velocity must be abnormal (or normal). This second theorem is more widely applicable, e.g., to propagation in waveguides or through multilayer dielectrics. To illustrate these theorems we discuss dispersion in a medium with two resonance lines, one absorption and the other gain. We find that the group velocity is abnormal within the absorption line and in a transparent region outside the gain line.
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.
Summary form only given. We use gain-assisted linear anomalous dispersion to demonstrate superluminal light pulse propagation with a negative group velocity through a transparent atomic medium. We place two Raman gain peaks closely to obtain an essentially lossless anomalous dispersion region that results in a superluminal group velocity. The group velocity of a pulse in this region exceeds c and can even become negative,while the shape of the pulse is preserved. We measured a negative group velocity index of n/sub g/=-315(/spl plusmn/5). Experimentally, a light pulse propagating through the spin-polarized atomic vapor cell exits from it earlier than propagating through the same distance in vacuum by a time difference that is 315 times of the vacuum light propagation time L/c=0.2 ns.