Direct Experimental Observation of Pulse Temporal Behavior in Integrated-Optical Ring-Resonator with Negative Group Velocity

We report a direct experimental observation of pulse temporal behavior in an integrated optical two-port ring-resonator circuit as a function of coupling strength, including the transition across the critical coupling point. We demonstrate the observation of pulse ‘advancement’ in the negative vg regime and pulse delay in the positive vg regime. We also observed a smooth transition of the pulse shape from highly negative to highly positive vg (or vice versa) through a pulse splitting phenomenon. The observed phenomena agree well to theoretical simulations. Introduction The possibility to control the light group velocity (vg) is currently an interesting research topic [1-6]. The capability to make light to travel with low vg (e.g. much lower than light velocity in vacuum c in a so called slow-light phenomenon [1]), has raised many prospects in application areas of optical signal processing, light sources, optical sensing, etc. Besides, light can also be forced to travel with large vg (e.g. larger than c), or even with negative vg [1-6] either by engineering the material dispersion of the medium [2, 3] or the waveguide dispersion of the structure [4]. Although the phenomenon of negative vg seems to be counter-intuitive as the peak of the output pulse appears earlier than the peak of the input pulse, its consistency with the causality principle has been experimentally verified [5]. It is well known that in lossy two-port ring-resonator (TPRR) circuits as shown in Fig. 1, in the undercoupling condition, light can have a negative group velocity [7] as shown in Fig. 2. Experimental [8] and theoretical [4, 6] studies on such a phenomenon has also been carried out. However, since it is understood that there will be no true negative delay (or ’advancement’) in such a phenomenon (hence not so useful for signal processing applications), there is not much attention paid on experimental aspects for this phenomenon, compared to works on the same phenomenon using e.g. atomic gases [2] or fibers [3]. In fact, experiments using an integrated optical chip can be more handy and within the reach of many research groups. Also, we have theoretically showed [6] that such phenomenon has similar enhancing light-matter-interaction feature, like its slow-light counterpart, and therefore will be useful for applications like integrated-optical sensing. Consequently, further study and better understanding on such phenomenon from experimental aspect, are indispensable. In this paper, we report the first direct experimental observation of pulse temporal behavior at the output of such a resonator for the regimes of negative and positive vg, and transition between them across critical coupling point. Experimental Set-up For this experiment, we chose a TPRR which was originally designed for a delay line for optical beamforming applications [9]. The TPRR, which was designed and fabricated by Lionix BV [10], The Netherlands, has a controllable coupling constant and resonant wavelength through a thermo-optical mechanism. This Si3N4 based TPRR has a geometric ring round-trip length of 11916.4μm and supports a single q-TE mode with neff and dneff/dλ (as calculated by a vectorial mode solver) of 1.6499 and -0.1029μm, respectively. For a detailed description Ring resonator