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European Quantum Electronics Conference (EQEC)

Experimental demonstration of "fast light" in an absorptionless, non-reflective system using the birefringence of a photonic crystal

D.R. SoIIi, Colin F. McCormick, Claus Ropers, James J. Morehead, R. Y. Chiao, J. Miguel Hickmann

Published Nov 15, 2004• 0 citations
Publisher

Abstract

This study investigates the first experimental observation of faster-than-c group velocities in a passive system with neither absorption nor reflection. The investigation shows that superluminal and even negative group velocities can exist because of interference, instead of absorption or reflection. Results suggest that causal superluminal propagation can potentially be observed in any system in which input energy can escape into other modes. These results also demonstrate a particularly unusual application of the amplitude-phase Kramers-Kronig (K-K) relations; for the system being described, an infinitesimal adjustment of parameters radically affects the validity of the K-K transformation between amplitude and phase.

DOI
10.1109/eqec.2003.1314013

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This study investigates the first experimental observation of faster-than-c group velocities in a passive system with neither absorption nor reflection. The investigation shows that superluminal and even negative group velocities can exist because of interference, instead of absorption or reflection. Results suggest that causal superluminal propagation can potentially be observed in any system in which input energy can escape into other modes. These results also demonstrate a particularly unusual application of the amplitude-phase Kramers-Kronig (K-K) relations; for the system being described, an infinitesimal adjustment of parameters radically affects the validity of the K-K transformation between amplitude and phase.
We examine the effect of superluminal signal propagation through a birefringent crystal, where the effect is not due to absorption or reflection, but to the filtration of a special polarization component. We first examine the effect by a stationary phase analysis, with results consistent with those of an earlier analysis of the system. We supplement this analysis by considering the transit of a Gaussian wave and find bounds for the validity of the stationary phase result. The propagation of the Gaussian wave is illustrated by figures.
We investigate nonanalyticities (e.g., zeros and poles) of refractive index $n(\ensuremath{\omega})$ and group index ${n}_{g}(\ensuremath{\omega})$ in different optical media. We first demonstrate that while a Lorentzian dielectric has no nonanalyticity in the upper half of the complex frequency plane (CFP), its group index---which governs the pulse-center propagation---possesses zeros in the same region. Thus we classify the nonanalyticities as in the (a) first order (refractive index or reflection) and (b) second order (group index or group delay). The latter contains the derivative of the former. Then, we study a possible connection between the negative superluminal velocities and the presence of nonanalyticities in the upper half of the CFP. We show that the presence of nonanalyticities in the upper half of the CFP for (a) the first-order and (b) the second-order responses are accompanied by the appearance of negative (a) phase and (b) group velocities, respectively. We also distinguish between two kinds of superluminosity, v>cv>cv>c and v<0v<0v<0, where we show that the second one (v<0v<0v<0) appears with the violation of KKRs.
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.
We demonstrated superluminal light propagation with a negative group velocity of -5.7 m/s in a photorefractive Bi 12SiO20 crystal by using the dispersive phase coupling effect in a nondegenerate two-wave mixing process. To the best of our knowledge, this is the first experimental demonstration of superluminal light propagation at room temperature in solids by using a classical wave mixing technique. In addition, we showed the tunability of the group velocity of light between the negative (superluminal light) and the positive (subluminal light) by simply tuning the experimental conditions such as the frequency of the coupling beam, the incident intensity, and the externally applied electric fields.
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.