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Physical Review A

Development of the pulse peak from peak-truncated Gaussian optical pulses in a serial array of high- Q ring resonators

Makoto Tomita, Taichi Sudo, Kota Yoshimura, Daiki Sugio

Published Oct 9, 2020• 6 citations
Publisher

Abstract

We experimentally examined the propagation of a Gaussian-shaped temporal pulse through a serial array of ring resonators, truncating the pulse before its peak. We observed the process whereby a smooth pulse peak related to the Gaussian pulse emerged even when the incident pulse was truncated before its peak, as the pulse passed through an increasing number of ring resonators. The peak emerged when the negative group delay accumulated beyond the pulse truncation time point. This result demonstrated that the earlier portion of the input pulse envelope developed into a smooth Gaussian-shaped pulse peak in the superluminal pulse in good agreement with the analyses based on the instantaneous spectrum. We also discussed the propagation of truncated pulses in a slow light system, where the peak disappeared in the output pulse despite the peak in the input pulse.

DOI
10.1103/physreva.102.043507

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We experimentally examined the propagation of a Gaussian-shaped temporal pulse through a serial array of ring resonators, truncating the pulse before its peak. We observed the process whereby a smooth pulse peak related to the Gaussian pulse emerged even when the incident pulse was truncated before its peak, as the pulse passed through an increasing number of ring resonators. The peak emerged when the negative group delay accumulated beyond the pulse truncation time point. This result demonstrated that the earlier portion of the input pulse envelope developed into a smooth Gaussian-shaped pulse peak in the superluminal pulse in good agreement with the analyses based on the instantaneous spectrum. We also discussed the propagation of truncated pulses in a slow light system, where the peak disappeared in the output pulse despite the peak in the input pulse.
A series of experiments is performed to examine the arrival of a pulse peak, using a Gaussian-shaped temporal wave packet as the input pulse and truncating it at various positions on or before the peak of the packet. When the truncating point is within the negative group delay limit of the fast light medium, a smooth Gaussian peak is observed at the exit port, despite the absence of an input pulse peak. The experimental results explicitly demonstrate that the superluminal propagation of a smooth Gaussian-shaped pulse peak is an analytic continuation over time of the earlier portion of the input pulse envelope. To investigate the physical meaning of the pulse peak further, we also examine the propagation of triangular-shaped pulses, for which the pulse peak can be recognized as a nonanalytical point.
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.
We examined the propagation of nonanalytical points encoded on temporally Gaussian-shaped optical pulses in fast and slow light in an optical ring resonator at $\ensuremath{\lambda}$ = 1.5 \ensuremath{\mu}m. The temporal peak of the Gaussian pulse was either advanced or delayed, reflecting anomalous or normal dispersions in the ring resonator, relevant to under- or overcoupling conditions, respectively. The nonanalytical points were neither advanced nor delayed but appeared as they entered the ring resonator. The nonanalytical points could be interpreted as information; therefore, the experimental results suggested that information velocity is equal to the light velocity in vacuum or the background medium, independent of the group velocity. The transient behaviors at the leading and trailing edges of the nonanalytical points are discussed in terms of optical precursors.
We experimentally investigated optical pulse propagation through an amplifying ring resonator, in which a semiconductor optical amplifier was used as a loss or gain medium. Initially, the transmission intensity showed resonance dips as a function of laser frequency. These dips were gradually filled and transformed into resonance peaks as the amplification gain increased. A Gaussian-shaped temporal pulse was either advanced by −7.3 ns at low amplification gain or delayed up to 45 ns at high gain. System operation was classified into a complete set of the four regions depending on the gain parameter, and experimental delay times were analyzed based on relevant system dispersion.
To investigate the physical meaning of pulse peak in fast and slow light media, we investigated propagation of differently shaped pulses experimentally, controlling the sharpness of the pulse peak. Symmetric behavior with respect to fast and slow light was observed in traditional Gaussian pulses; that is, propagated pulses were advanced or delayed, respectively, whereas the pulse shape remained unchanged. This symmetry broke down when the pulse peak was sharpened; in the fast light medium, the sharp pulse peak propagated with luminal velocity, and the transmitted pulse deformed into a characteristic asymmetric profile. In contrast, in the slow light medium, a time-delayed smooth peak appeared with a bending point at t=0t=0t=0. This symmetry breaking with respect to fast and slow light is a universal characteristic of pulse propagation in causal dispersive systems. The sharp pulse peak can be recognized as a bending nonanalytical point and may be capable of transferring information.
We examined the propagation of bending nonanalytical points encoded on temporally smooth Gaussian-shaped optical pulses in fast- and slow-light media, using an optical ring resonator. For bending nonanalytical points, the pulse function is continuous, but the first-order derivative is discontinuous, in contrast to traditional nonanalytical points in which the pulse function itself is discontinuous. The nonanalytical points were neither advanced nor delayed, but appeared at the same instance as they entered the ring resonator, in good accordance with the fact that the information velocity was equal to the light velocity in vacuum or the background medium. The differences between the traditional discontinuous and the present bending nonanalytical points were investigated.