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Chinese Journal of Physics

Time-domain analysis of superluminal effect for one-dimensional Fabry-Pérot cavity

Hsin-Yu Yao, Tsun‐Hsu Chang

Published Sep 1, 2020• 1 citation
Publisher

Abstract

This work develops a time-domain approach to explain the origin of superluminality, i.e. , an apparent faster-than-light phenomenon in one-dimensional Fabry-Pérot cavities. The interferences between multiple-reflection echoes are tracked and analyzed. Under the quasi-static condition, the destructive interference is found to result in the advancement of the superposed pulse as compared to its parent signals. It is the key to the superluminal effect. On the contrary, constructive interference can lead to the retardation of the superposed pulse. For a cavity operated at the off-resonance state, the competition between roundtrip destructive interference (group advancement) and multiple-roundtrip constructive interference (group retardation) determines how short the group delay can be observed. Manipulating the competition between roundtrip interferences opens numerous opportunities in controlling the signal delays or shaping the pulse waveforms.

DOI
10.1016/j.cjph.2020.08.020

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This work develops a time-domain approach to explain the origin of superluminality, i.e. , an apparent faster-than-light phenomenon in one-dimensional Fabry-Pérot cavities. The interferences between multiple-reflection echoes are tracked and analyzed. Under the quasi-static condition, the destructive interference is found to result in the advancement of the superposed pulse as compared to its parent signals. It is the key to the superluminal effect. On the contrary, constructive interference can lead to the retardation of the superposed pulse. For a cavity operated at the off-resonance state, the competition between roundtrip destructive interference (group advancement) and multiple-roundtrip constructive interference (group retardation) determines how short the group delay can be observed. Manipulating the competition between roundtrip interferences opens numerous opportunities in controlling the signal delays or shaping the pulse waveforms.
Extraordinary group delays shorter than the transit time of light propagating at ccc through an equal distance have been experimentally demonstrated in single-Fabry-P\'erot (FP) waveguide systems and cascaded-FP structures under off-resonant conditions. These ``superluminal'' phenomena are well explained by the multiple-reflection destructive interference that reduces the intracavity stored energy when operating off resonances. Excellent agreement between theory and experiment is obtained when the dispersive effects of reflective boundaries are considered. These results provide further insight into the nature of apparent superluminality in regions of allowed propagation.
Pulse propagation through 1-dimensional stratified media is studied. The general features of pulse propagation in relation to the delay or advancement of the pulse are discussed. It is shown that in a lossless system with spatial symmetry the reflected and the transmitted pulses have the same delay or advancement. The phase times and the explicit output pulse profiles for an input Gaussian pulse are calculated. While recalling recent results for a variety of systems (resonant absorbers or heterogeneous medium in a Fabry-Perot cavity, a slab of negative index medium, a left-handed/right-handed periodic structure, etc.), new results involving coupled waveguides and a high finesse cavity containing an electromagnetically induced transparency (EIT) medium are presented. Calculations clearly show that for pulses with a carrier tuned at the resonance of the stratified media, one generally has subluminal propagation. Alternatively, in stop gaps or away from the resonances one ends up with superluminal transit. In the case of the EIT cavity it is shown that the large dispersion offered by the intracavity medium can lead to substantial superluminality (ng≃−106) with peak transmission as high as 20%. This is in sharp contrast to large signal attenuation for usual superluminal transit. Note also that EIT, to the best of the authors knowledge, has so far been used to achieve only slow light.
We identify the universal mechanism that is responsible for superluminal (faster-than-light) traversal times as well as the narrowing of wave packets transmitted through various nondissipative media. This mechanism is shown to be predominantly destructive interference between successive wave-packet components traversing all accessible causally retarded paths. It strongly depends on wave-packet coherence and width, and can cause superluminal traversal not only in evanescent-wave ``tunneling'' but also in allowed propagation. \textcopyright{} 1996 The American Physical Society.
There have been many recent theoretical and experimental reports on the propagation of light pulses at speeds exceeding the speed of light in vacuum ccc 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.
In this paper, we study theoretically the behavior of a pulse as it propagates through an intracavity fast-light medium. The method of using a transfer function to determine a pulse after it passes through a cavity is well known. However, this approach cannot be used to determine the behavior of the pulse inside the cavity. To circumvent this constraint, we use an approach that starts by finding a self-consistent solution for a monochromatic field of infinite spatial and temporal extents, and determine its amplitudes before, inside, and after the cavity. We then construct a Gaussian input pulse by adding a set of these waves, properly phased and weighted, to represent a moving pulse before the cavity. Adding these waves at various time intervals then yields the complete spatial profile everywhere, including before, inside and after the cavity. We first confirm the prediction of this model by analyzing the behavior of a pulse passing through an empty cavity, and comparing the prediction of the output with the one produced by the transfer function method. We then apply the technique to a cavity containing a fast-light medium. The resulting model allows us to visualize the behavior of the pulse as it propagates superluminally inside the cavity, and interferes with itself through multiple bounces. For a vanishing group index, an interference pattern is formed immediately after the pulse enters the cavity, with an output pulse emerging with no time delay or distortion. The results obtained here illustrates the physical mechanism behind pulse propagation through a white light cavity, a process we have proposed earlier for realizing a high bandwidth, long delay data buffering system
Causality and special relativity pose an upper limit to the amount of advance that an optical pulse can acquire during a superluminal propagation. Such a limit can be circumvented if the pulse, before entering the superluminal medium, is retarded by letting it propagate under normal dispersion. We present an experimental evidence of this fact by showing that a laser pulse propagating in an atomic vapor, quasi resonant with an inverted transition and in conditions of anomalous dispersion, moves faster if it is previously retarded in a cell containing the same medium with no population inversion. Optical transmission lines often need an amplification stage to overcome the signal attenuation and the unavoidable delay respect to propagation at c; in this paper we tailor such stage to provide also an optical controlled recover of such delay. We believe that our results can open exciting prospects for real-life optical data processing and communication.