Abstract
We experimentally examined the development of superluminal pulse propagation through a serial array of high-Q ring resonators that provides a dynamic recurrent loop. As the propagation distance, i.e., the number of ring resonators that the pulses passed through increased, the pulse advancement increased linearly, largely maintaining its Gaussian shape. The sharp edge encoded at the front of the pulse was, however, neither advanced nor delayed, in good accordance with the idea that information propagates at the speed of light. We also carried out a numerical simulation on the superluminal to subluminal transition of the pulse velocity, which appeared after the pulse had propagated a long distance. The time delays, which we calculated using the saddle point method and based on the net delay, were in good agreement with our results, even when predictions based on the traditional group delay failed completely. This demonstrates the superluminal to subluminal transition of the propagation velocity.
Highlights
We experimentally examined the development of superluminal pulse propagation through a serial array of high-Q ring resonators that provides a dynamic recurrent loop
We developed the concept of traditional group velocity vg discussed in Lorentz media to describe the pulse propagation in a serial array of ring resonators
The time delays calculated based on the saddle point method well describe the results, even where the traditional group velocity method τg fails completely, and shows the superluminal to subluminal transition in the propagation velocity
Summary
In continuous media, modified definitions of group velocity have been developed to model the pulse propagation in a Lorentz medium[28] One such approach is the saddle-point method[31], in which spectral shift during propagation is considered in terms of the drift of the saddle point during path integration in the complex plane. The solid green line (line 3) shows the expected time delay for the case in which the pulse propagates with traditional group velocity, defined by Eq (6). The time delays calculated based on the saddle point method well describe the results, even where the traditional group velocity method τg fails completely, and shows the superluminal to subluminal transition in the propagation velocity. This is reasonable because the net delay employs the transmitted profile SN(ω) directly in the calculation of the spatial average, while the saddle point method uses ωN to represent the transmitted frequency
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