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Journal of Henan University

Optical Pulses Propagation Through One-Dimensional Photonic Crystals with Dispersive Defect

Xu Gang

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

With transfer matrix,the paper gets the dynamic evolution of the pulse inside the 1DPCs.In case of no dispersive defect,superluminality becomes subliminality.If there exist two-level atoms with dispersive defect,the subliminality becomes superluminality.At last,the paper points out that although the group velocity is larger than c and even negative,the velocity of energy propagation never exceeds the vacuum light speed.This phenomenon is the result of the wave interference from Bragg reflection.

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With transfer matrix,the paper gets the dynamic evolution of the pulse inside the 1DPCs.In case of no dispersive defect,superluminality becomes subliminality.If there exist two-level atoms with dispersive defect,the subliminality becomes superluminality.At last,the paper points out that although the group velocity is larger than c and even negative,the velocity of energy propagation never exceeds the vacuum light speed.This phenomenon is the result of the wave interference from Bragg reflection.
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.
The propagation of a pulse through onedimensional photonic crystals with a dispersive and gain defect layer is discussed. The dispersion and gain of the defect layer is described by Lorentz oscillator model. It is found that the pulse pea k exhibits subluminal and superluminal behaviors with varying strength of the os cillator. The Poynting vector and energy velocity can be negative, but the latte r is never faster than the vacuum light speed c. The advance or delay of the pulse peak is a result of the coherent superposition of all Fourier components which experienced different phase shift and different amplification in the medium.
The propagation of pulses through dispersive media was investigated by solving Maxwell's equations without any approximation. We show that the superluminal propagation of pulses through anomalous dispersive media is a result of the interference of different frequency components composed of the pulse. The coherence of the pulse plays an important role for the superluminal propagation. With the decrease of the coherence of the pulse, the propagation changes from superluminal to subluminal. We have shown that the anomalous dispersion (the real part of the susceptibility) not the amplification (the imaginary part of the susceptibility) plays the essential role in the superluminal propagation. Although the superluminality always exists as long as the spectrum of the coherent pulse is within the anomalously dispersive region, both the energy propagation velocity and the frontal velocity never exceed the light speed in the vacuum. The output pulse through the medium is not the original pulse; instead it carries the information of the original pulse and the information of the prepared medium.
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.
We report the experimental manipulation of the group velocities of reflected and transmitted light pulses in a degenerate two-level atomic system driven by a standing wave, which is created by two counter-propagating light beams of equal frequencies but variable amplitudes. It is shown that the light pulse is reflected with superluminal group velocity while the transmitted pulse propagates from subluminal to superluminal velocities via changing the power of the backward coupling field. We find that the simultaneous superluminal light reflection and transmission can be reached when the power of the backward field becomes closer or equal to the forward power, in this case the periodical absorption modulation for photonic structure is established in atoms. The theoretical discussion shows that the anomalous dispersion associated with a resonant absorption dip within the gain peak due to four-wave mixing leads to the superluminal reflection, while the varying dispersion from normal to anomalous at transparency, transparency within absorption, and electromagnetically induced absorption windows leads to the subluminal to superluminal transmission.